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Parental influences on mathematics achievement of children of immigrant backgrounds Kerr, Zuzana 2007

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PARENTAL INFLUENCES ON MATHEMATICS ACHIEVEMENT CHILDREN OF IMMIGRANT BACKGROUNDS by ZUZANA KERR B.A.H., The U n i v e r s i t y of Winnipeg, 2002 4.A., The U n i v e r s i t y of B r i t i s h Columbia, 2004 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Spec i a l Education) THE UNIVERSITY OF BRITISH COLUMBIA October, 2007 © Zuzana Kerr, 2007 A b s t r a c t The g o a l o f t h e p r e s e n t s t u d y was t o c o m p a r e t h e m a t h e m a t i c a l p e r f o r m a n c e o f c h i l d r e n who h a v e f o r e i g n b o r n p a r e n t s a n d E n g l i s h a s a s e c o n d l a n g u a g e ( E S L ) t o t h e p e r f o r m a n c e o f n a t i v e E n g l i s h s p e a k i n g c h i l d r e n w i t h C a n a d i a n b o r n p a r e n t s f r o m k i n d e r g a r t e n t o g r a d e 6 . The f u n c t i o n o f t h e c o u n t r y o f o r i g i n a s a p o s s i b l e v a r i a b l e h a v i n g a n i m p a c t o n m a t h e m a t i c a l a c h i e v e m e n t was a l s o c o n s i d e r e d . I n - g r a d e s 5 a n d 6, c h i l d r e n a n d p a r e n t s w e r e g i v e n a q u e s t i o n n a i r e a d d r e s s i n g a t t i t u d e s t o w a r d s e d u c a t i o n a n d m a t h e m a t i c s , p a r e n t a l i n v o l v e m e n t a n d t h e home l e a r n i n g e n v i r o n m e n t . The r e l a t i o n s h i p b e t w e e n t h e s e f a c t o r s a n d t h e c h i l d r e n ' s p e r f o r m a n c e was i n v e s t i g a t e d . I t was f o u n d t h a t , o n a l l n u m e r a c y m e a s u r e s , i m m i g r a n t / E S L c h i l d r e n p e r f o r m e d a s w e l l o r b e t t e r t h a n n a t i v e E n g l i s h s p e a k i n g c h i l d r e n w i t h C a n a d i a n b o r n p a r e n t s . T h i s d i f f e r e n c e was m o r e p r o f o u n d i n g r a d e s 3 t o 6, i n w h i c h i m m i g r a n t / E S L c h i l d r e n p e r f o r m e d h i g h e r o n a number o f n u m e r a c y m e a s u r e s c o m p a r e d t o n a t i v e E n g l i s h s p e a k i n g c h i l d r e n w i t h C a n a d i a n b o r n p a r e n t s . I n g r a d e s 2 t o 6, E a s t A s i a n s t u d e n t s h a d t h e h i g h e s t s c o r e s o n n u m e r a c y m e a s u r e s c o m p a r e d t o E u r o p e a n s , M i d d l e E a s t e r n a n d F i l i p i n o s t u d e n t s . I m m i g r a n t p a r e n t s s h o w e d h i g h e r i n v o l v e m e n t i n t h e i r c h i l d r e n ' s m a t h e m a t i c a l l e a r n i n g ( e . g . , t u t o r i n g , a s p i r a t i o n f o r higher education and b e t t e r grades f o r the c h i l d r e n ) when compared to Canadian born parents. These a t t i t u d e s were r e f l e c t e d i n the c h i l d r e n ' s b e l i e f s about mathematics and t h e i r performance. There were only a few s i g n i f i c a n t d i f f e r e n c e s between the questionnaire respons of the three immigrant groups (East Asian, F i l i p i n o and Middle Eastern). Both parents' and c h i l d r e n ' s a t t i t u d e s towards mathematics and the l e a r n i n g environment at home were r e l a t e d to the c h i l d r e n ' s numeracy performance. Findings of the present study help to understand the f a c t o r s a s s o c i a t e d with the school achievement of student with recent immigrant backgrounds and the importance of f a m i l y i n f l u e n c e s on m o t i v a t i o n and school success of the students. iv TABLE OF CONTENTS A b s t r a c t i i T a b l e o f ' C o n t e n t s i v L i s t o f T a b l e s v i i L i s t o f F i g u r e s x I n t r o d u c t i o n 1 E n g l i s h a s a S e c o n d L a n g u a g e S t a t u s 3 A g e U p o n A r r i v a l 7 F a m i l y I n f l u e n c e s o n S t u d e n t s ' S c h o l a s t i c P e r f o r m a n c e 1 1 M a t h e m a t i c s a n d S o c i o - C u l t u r a l F a c t o r s 2 3 M a t h e m a t i c a l A c h i e v e m e n t o f A s i a n S t u d e n t s 3 0 S c h o o l i n g 3 6 H o m e w o r k 3 9 P a r e n t a l I n f l u e n c e s 4 1 S t u d e n t s ' P e r c e p t i o n 4 3 P r e s e n t S t u d y a n d H y p o t h e s i s 4 5 M e t h o d 4 9 P a r t i c i p a n t s 4 9 S c h o o l s a n d S o c i o - E c o n o m i c S t a t u s 5 3 S t u d e n t s ' P e r f o r m a n c e 54 M e a s u r e s U s e d i n K i n d e r g a r t e n 5 5 N u m e r a c y 5 5 V i s u a l - S p a t i a l I n t e g r a t i o n 5 6 M e m o r y 5 6 L i t e r a c y 57 M e a s u r e s U s e d i n G r a d e 1 t o 6 58 N u m e r a c y 58 V i s u a l - S p a t i a l I n t e g r a t i o n 5 9 M e m o r y 5 9 L i t e r a c y 60 S t u d e n t ' s P e r f o r m a n c e a m o n g D i f f e r e n t I m m i g r a n t g r o u p s 6 1 C h i l d r e n ' s Q u e s t i o n n a i r e 63 P a r e n t s ' Q u e s t i o n n a i r e 65 R e s u l t s 7 0 P e r f o r m a n c e o f t h e C h i l d r e n 7 0 K i n d e r g a r t e n 7 1 G r a d e 1 7 1 G r a d e 2 7 3 G r a d e 3 7 3 V TABLE OF CONTENTS (continued) Grade 4 76 Grade 5 7 6 Grade 6 7 9 Country of O r i g i n and Numeracy Performance 82 WRAT I I I Computational A r i t h m e t i c 82 WJ I I I C a l c u l a t i o n 86 WJ I I I Math Fluency 8 9 C o r r e l a t i o n among Measures i n E a r l y and Later Grades 92 K and Grade 6 Numeracy and Memory C o r r e l a t i o n s 92 Grade 1 and 5 Numeracy and Memory C o r r e l a t i o n s 94 K and Grade 6 Memory C o r r e l a t i o n s 97 Grade 1 and 5 Memory C o r r e l a t i o n s 98 K and Grade 6 L i t e r a c y C o r r e l a t i o n s 98 Grade 1 and 5 L i t e r a c y C o r r e l a t i o n s 100 Summary of Child r e n ' s Performance 101 Independent T-test A n a l y s i s 101 ANOVA A n a l y s i s of Four Language Groups 103 C o r r e l a t i o n among E a r l y and Later Measures 103 Numeracy Questionnaire 104 Childr e n ' s Questionnaire 104 Chil d r e n ' s Questionnaire and D i f f e r e n t Immigrant Groups 107 Parents' Questionnaire I l l Parents' Questionnaire and D i f f e r e n t Immigrant Groups 116 C o r r e l a t i o n among Par e n t a l and Child r e n ' s Responses 121 C u l t u r a l and S o c i a l Background of Fa m i l i e s Based on the Questionnaire 123 Re l a t i o n s h i p between C h i l d r e n ' s Questionnaire Responses and Their Performance on Selected Numeracy Measures 126 Grade 5 127 Grade 6 130 Re l a t i o n s h i p between P a r e n t a l Questionnaire Responses and Their Performance on Selected Numeracy Measures 132 Grade 5 133 Grade 6 133 Summary of Numeracy Questionnaire Results 139 Childr e n ' s Questionnaire 139 Parents' Questionnaire 140 C o r r e l a t i o n among Parents' and Child r e n ' s 141 Questionnaire Responses Numeracy Outcomes and Questionnaire Responses 141 Discussion/Conclusion , 143 VI TABLE OF CONTENTS (continued) Numeracy Performance 14 5 L i t e r a c y Performance 151 A t t i t u d e s towards Education and Mathematics, Home Support and Numeracy Performance 154 P r a c t i c a l I m p l i c a t i o n s 165 Concluding Remarks 167 References 171 V l l LIST OF TABLES Table 1: Sample D i s t r i b u t i o n across Grades: Numeracy Performance 50 Table 2: Sample D i s t r i b u t i o n i n the F i n a l Year of Study: Questionnaire 51 Table 3: Language D i s t r i b u t i o n of the Sample with Immigrant Background 52 Table 4: Kindergarten Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 72 Table 5: Grade 1 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 74 Table 6: Grade 2 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 75 Table 7: Grade 3 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 77 Table 8: Grade 4 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 78 Table 9: Grade 5 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 80 Table 10: Grade 6 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents 81 Table 11: ANOVA of Four Language Groups' Performance on the WRAT-III Computational A r i t h m e t i c ( P e r c e n t i l e ) across Seven Grades 84 Table 12: Mean D i f f e r e n c e : F i s h e r ' s LSD WRAT-III Computational A r i t h m e t i c 85 Table 13: ANOVA of Four Language Groups' Performance on the WJ-III C a l c u l a t i o n ( P e r c e n t i l e ) across Seven Grades... 87 Table 14: Mean D i f f e r e n c e : F i s h e r ' s LSD WJ-III C a l c u l a t i o n 88 Table 15: ANOVA of Four Language Groups' Performance on the WJ-III Math Fluency ( P e r c e n t i l e ) across Seven Grades 90 Table 16: Mean D i f f e r e n c e : F i s h e r ' s LSD WJ-III Math Fluency 91 viii LIST OF TABLES (continued) Table 17: The I n t e r c o r r e l a t i o n among Numeracy and Memory Measures Administered i n Kindergarten and Grade 6 93 Table 18: The I n t e r c o r r e l a t i o n among Numeracy and Memory Measures Administered i n Grades 1 and 5 95 Table 19: The I n t e r c o r r e l a t i o n among Memory Measures Administered i n K and Grade 6 98 Table 20: The I n t e r c o r r e l a t i o n among Memory Measures Administered i n Grades 1 and 5 99 Table 21: The I n t e r c o r r e l a t i o n among among L i t e r a c y Measures Administered i n Kindergarten and Grade 6 99 Table 22: The I n t e r c o r r e l a t i o n among among L i t e r a c y Measures Administered i n Grades 1 and 5 100 Table 23: Chil d r e n ' s Questionnaire (Part 1) 105 Table 24: Chil d r e n ' s Questionnaire (Part 2) 106 Table 25: Chil d r e n ' s Questionnaire: Immigrant Groups (Part 1) 108 Table 26: Chil d r e n ' s Questionnaire: Immigrant Groups (Part 2) 110 Table 27: Cross-Tabulation A n a l y s i s of Parent Questionnaire Responses: Mathematics and School Success (part 1) , 112 Table 28: Cross-Tabulation A n a l y s i s of Parent Questionnaire Responses: Mathematics and School Success (part 2) 114 Table 29: Cross-Tabulation A n a l y s i s of Parent Questionnaire Responses: Mathematics 115 Table 30: Parent Questionnaire Responses: Immigrant Groups Mathematics and School Success (part 1) 117 Table 31: Parent Questionnaire Responses: Immigrant Groups Mathematics and School Success (part 2) 119 Table 32: Parent Questionnaire Responses: Immigrant Groups, Mathematics.. 120 Table 33: The I n t e r c o r r e l a t i o n among Ch i l d r e n ' s and Pare n t a l Questionnaire Responses 122 IX LIST OF TABLES (continued) Table 34: R e l a t i o n s h i p between Grade 5 Numeracy Performance of C h i l d r e n and Their Questionnaire Responses 128 Table 35: R e l a t i o n s h i p between Grade 6 Numeracy Performance of C h i l d r e n and Their Questionnaire Responses 131 Table 36: R e l a t i o n s h i p between Grade 5 Numeracy Performance of C h i l d r e n and Their Parent's Questionnaire Responses 134 Table 37: R e l a t i o n s h i p between Grade 6 Numeracy Performance of C h i l d r e n and Their Parent's Questionnaire Responses 137 X LIST OF FIGURES Figure 1: Questionnaire f o r C h i l d r e n 64 Figure 2: Questionnaire f o r Parents 67 1 Parental Influences on Mathematical Achievement of Children of Immigrant Backgrounds School achievement i s a popular subject of research. Researchers t r y to understand f a c t o r s promoting school success, as w e l l as f a c t o r s which have a negative impact on i t . As s c i e n t i s t s , we are curious to know how to provide the best education f o r c h i l d r e n , and how to help them to become su c c e s s f u l a d u l t s . Canadian s o c i e t y i s c h a r a c t e r i z e d by c u l t u r a l and l i n g u i s t i c d i v e r s i t y , where c e r t a i n populations of students face unique challenges during t h e i r education. Schools are one of the many places where the c u l t u r a l and l i n g u i s t i c d i v e r s i t y of Canadian s o c i e t y i s evident. Many Canadian schools, p a r t i c u l a r l y those l o c a t e d i n major urban centers, are c h a r a c t e r i z e d by a larg e p r o p o r t i o n of c h i l d r e n who are f o r e i g n born and have E n g l i s h as a second language (ESL). In a d d i t i o n , there are c h i l d r e n who are born i n Canada, but s t i l l have E n g l i s h as a second language, because a language other than E n g l i s h i s spoken i n t h e i r homes. C h i l d r e n from immigrant f a m i l i e s are u s u a l l y non-native E n g l i s h speakers and face s p e c i f i c challenges i n school. Being educated i n a f o r e i g n language i s a s p e c i a l challenge, and even students from immigrant f a m i l i e s who are Canadian born experience a unique c u l t u r a l environment at home. Their parents are of t e n v u l n e r a b l e , l a c k i n g the s o c i a l and language support of 2 the c u l t u r e to which they were born; but t h i s does not have to mean that c h i l d r e n from immigrant f a m i l i e s are at a disadvantage compared to t h e i r peers. C h i l d r e n from immigrant f a m i l i e s have two languages and two c u l t u r e s that they might b e n e f i t from. There i s strong research evidence suggesting that students from immigrant f a m i l i e s do very w e l l a t school, and are high-achievers (Caplan, Choi, & Whitmore, 1991; 1992; Gibson, 1991; F u l i g n i , 1997; Rodriquez, 2002; Rumbaut, 1996; Waters, 1994; Zhang, 2001). At the same time, students w i t h a recent immigrant background a l s o face s p e c i f i c challenges n e g a t i v e l y a f f e c t i n g t h e i r school progress, and some studie s suggest that they s t r u g g l e at school (Derwing, DeCorby, Ichikawa, & Jamieson, 1999; Haung, 2000; Watt & Roessingh, 2001). The f i n d i n g s of current research l i t e r a t u r e regarding school achievement of immigrant students seems i n c o n s i s t e n t . As the immigrant population i n Canadian schools i s i n c r e a s i n g , i t i s important to understand the s p e c i f i c needs of these students, along with the p o s s i b l e b e n e f i t s of t h e i r unique c u l t u r a l and l i n g u i s t i c environments on t h e i r school achievement. When l o o k i n g at the achievement of students with immigrant backgrounds, various f a c t o r s need to be taken i n t o c o n s i d e r a t i o n , such as t h e i r language s k i l l s , p a r e n t a l and f a m i l y i n f l u e n c e s , and students' a t t i t u d e s towards schoo l i n g d e r i v i n g from t h e i r c u l t u r e . The goal of the present study i s to i n v e s t i g a t e the s p e c i f i c s of 3 mathematical achievement of immigrant students and the impact of the immigrant f a m i l i e s on the achievement i n mathematics of these students. English as a Second Language Status Coming from homes where a language other than E n g l i s h i s spoken may seem to be a c l e a r disadvantage. Knowledge of the language of i n s t r u c t i o n i s important f o r a c h i l d ' s success i n school. Besides general language s k i l l s , c h i l d r e n must acquire vocabulary and o r a l s k i l l s to meet the language demands unique to each subject area. In some s t u d i e s , i t was found that l i m i t e d E n g l i s h p r o f i c i e n c y n e g a t i v e l y impacts school achievement (e.g., Bradby, 1992; Duran & Weffer, 1992; S t i e f e l , Schwartz, & Conger, 2003; Wang, 1999). For example, a s t a t i s t i c a l p r o f i l e of New York C i t y elementary and middle schools showed that students who have l i m i t e d E n g l i s h p r o f i c i e n c y s t r u g g l e i n school, and many of them .are placed i n s p e c i a l education f u l l time. These students came from n e a r l y 170 language groups, but the predominant language w i t h i n t h i s ESL cohort was Spanish ( S t i e f e l , et a l . , 2003). S i m i l a r l y , i n a study of over 2000 middle school students i n C a l i f o r n i a , i t was found that students with l i m i t e d E n g l i s h p r o f i c i e n c y had s i g n i f i c a n t l y lower mathematical achievement than n a t i v e English-speaking students (Wang, 1999). In t h i s study, approximately 30% of the students i n t h i s school d i s t r i c t had a recent immigrant background. The l a r g e s t c u l t u r a l group 4 was Chinese, followed by Hispanic and A f r i c a n Americans (Wang, 1999) . At the same time, having a f i r s t language other than E n g l i s h may a l s o be b e n e f i c i a l . C h i l d r e n who acquire knowledge of more than one language are l i k e l y to b e n e f i t from i t i n terms of t h e i r l e a r n i n g and general c o g n i t i o n . The above-described s t a t i s t i c a l p r o f i l e of New York C i t y students a l s o revealed that students from homes where a language other than E n g l i s h was spoken, but who had acquired good E n g l i s h s k i l l s , obtained higher scores on standardized reading and math t e s t s than c h i l d r e n who were exposed only to E n g l i s h at home ( S t i e f e l et a l , 2003). S i m i l a r l y , the above-described middle school students i n C a l i f o r n i a of immigrant backgrounds obtained s i m i l a r achievement to t h e i r native-born peers as a group, although the students with l i m i t e d E n g l i s h p r o f i c i e n c y (approximately 33% of students i n the d i s t r i c t had l i m i t e d E n g l i s h p r o f i c i e n c y s k i l l s , 31% were b i l i n g u a l , and 30% spoke only English) performed s i g n i f i c a n t l y lower than other students (Wang, 1999). This again suggests that a language b a r r i e r , . r a t h e r than immigrant s t a t u s per se, has a negative impact on achievement. This conclusion was a l s o supported by the f i n d i n g s of a comprehensive survey of the educational progress of 2,420 e i g h t - and n i n t h grade students from recent immigrant f a m i l i e s l i v i n g i n three d i f f e r e n t areas of C a l i f o r n i a (Rumbaut, 1996). In order to be 5 included i n the study, the students themselves or e i t h e r of t h e i r parents had to be foreign-born. E l i g i b l e students were from Mexico, the P h i l i p p i n e s , Vietnam, Cambodia, Laos, and other Asian and L a t i n American c o u n t r i e s . The data i n d i c a t e d that immigrant students showed r a p i d school adjustment and i n some cases even b e t t e r school progress than t h e i r peers from n a t i v e -born f a m i l i e s ; however, flu e n c y i n E n g l i s h was a c r i t i c a l f a c t o r a f f e c t i n g achievement among immigrant students. Data showed that students who had l i m i t e d E n g l i s h p r o f i c i e n c y were most l i k e l y to attend i n n e r - c i t y schools and to be from f a m i l i e s experiencing the greatest socio-economic disadvantage. In c o n t r a s t , f a m i l i e s of students speaking only E n g l i s h had the highest socio-economic sta t u s by every i n d i c a t o r ; however, f u l l y b i l i n g u a l students whose f a m i l i e s ' socio-economic status was somewhere between these two groups had the highest school achievement (GPAs), despite the f a c t that E n g l i s h - o n l y speaking students as a group were from f a m i l i e s with the highest socio-economic status (Rumbaut, 1996). A l o n g i t u d i n a l study conducted i n Vancouver, Canada revealed that knowledge of a second language may be p o s i t i v e l y r e l a t e d to c e r t a i n aspects of school achievement, such as e a r l y reading s k i l l s (Lesaux & S i e g e l , 2003). There were 188 students with ESL, and 790 n a t i v e English-speaking c h i l d r e n w i t h i n t h i s sample. The predominant language backgrounds of ESL speakers 6 were Cantonese, Mandarin, Korean, Spanish, Persian, P o l i s h , and F a r s i . In t h i s study, c h i l d r e n of recent immigrant backgrounds who had very l i t t l e or no E n g l i s h when they s t a r t e d kindergarten performed as w e l l as n a t i v e English-speaking c h i l d r e n on most achievement measures i n grade 2. Moreover, on some achievement task s , such as word reading, word s p e l l i n g and a r i t h m e t i c , c h i l d r e n with ESL performed s i g n i f i c a n t l y b e t t e r than n a t i v e English-speaking c h i l d r e n . Not s u r p r i s i n g l y , i n kindergarten, c h i l d r e n with ESL performed more poorly on achievement tasks r e q u i r i n g language p r o f i c i e n c y (e.g., memory f o r sentences, pseudoword r e p e t i t i o n , and rhyme detection) than t h e i r non-ESL peers, although t h i s d i f f e r e n c e disappeared by grade 2 (Lesaux & S i e g e l , 2003). The authors of t h i s study suggested that the improved performance of the c h i l d r e n with ESL may be explained by an increase of m e t a l i n g u i s t i c awareness due to b i l i n g u a l i s m . These f i n d i n g s suggest t h a t , at the point when immigrant students become f u l l y p r o f i c i e n t i n E n g l i s h , they are l i k e l y to do w e l l i n school. L i m i t e d E n g l i s h p r o f i c i e n c y has a negative impact on the school achievement of students of recent immigrant backgrounds; however, i t does not appear to be immigrant status per se that has a n e g a t i v e l y impact on ed u c a t i o n a l outcome, but rat h e r l i m i t e d language p r o f i c i e n c y . Understandably, students s t r u g g l i n g with the language of i n s t r u c t i o n are l i k e l y to have lower grades. Nonetheless, one can be o p t i m i s t i c about t h e i r 7 f u t u r e , since they are l i k e l y e v e n t u a l l y to acquire f u l l E n g l i s h p r o f i c i e n c y , and to b e n e f i t from the p o s i t i v e impact of b i l i n g u a l i s m . Age upon A r r i v a l There i s l i k e l y to be a connection between the age upon a r r i v a l , E n g l i s h p r o f i c i e n c y , and school achievement of immigrant c h i l d r e n . C h i l d r e n who come to a new country at a young age are l i k e l y to be l e s s impacted by t h e i r l i m i t e d E n g l i s h s k i l l s , s i nce the language demands of school c u r r i c u l u m are l e s s e r i n e a r l y grades. Young c h i l d r e n t h e r e f o r e have more time than o l d e r c h i l d r e n to acquire good language s k i l l s before they are exposed to more demanding l e a r n i n g m a t e r i a l i n more advanced grades. A l s o , the long-term impact of "being behind" i s more severe i n advanced grades. One can imagine j o i n i n g a grade eight c l a s s , speaking l i t t l e E n g l i s h , being accustomed to d i f f e r e n t l e a r n i n g m a t e r i a l , g e t t i n g used to new school r u l e s , and t r y i n g to be accepted i n t o a new peer group. These students have a great deal of catching up to do on a v a r i e t y of l e v e l s , and are l i k e l y to be i n a need of remedial c l a s s e s and s p e c i a l language i n s t r u c t i o n f o r some time. In c o n t r a s t , immigrant c h i l d r e n s t a r t i n g kindergarten or grade one are not yet s t r o n g l y accustomed to any school system. Their peer group i s not l i k e l y to be d r a s t i c a l l y d i f f e r e n t from that i n t h e i r home-country, and the language demands of the cur r i c u l u m are r e l a t i v e l y low. I t i s 8 not s u r p r i s i n g that delayed school entry has an inverse r e l a t i o n s h i p with school achievement as i s shown i n the studies described i n the f o l l o w i n g paragraphs. An ethnographical study of Punjabi Sikh students from a C a l i f o r n i a High School included 42 Punjabi f a m i l i e s and 231 students, grades nine through twelve, who e x h i b i t e d as a group unusually high school achievement compared to t h e i r counterparts of European o r i g i n (Gibson & Bhachu, 1991). The age upon a r r i v a l among Punjabi Sikh students was a stronger determinant of t h e i r e ducational outcome than p a r e n t a l f a c t o r s such as income, education, and E n g l i s h p r o f i c i e n c y . The authors of t h i s study commented on t h i s phenomenon as f o l l o w s : "Although Sikh c h i l d r e n who r e c e i v e a l l t h e i r s c h o o l i n g i n V a l l e y s i d e manage, i n s p i t e -of the b a r r i e r s , to persevere and even do reasonably w e l l academically, l a t e r a r r i v a l s o f t e n f i n d the b a r r i e r s insurmountable. Many of those t r a n s f e r r i n g from Indian to American schools a f t e r f o u r t h grade, f o r example, never break out of a remedial or ESL i n s t r u c t i o n a l t r a c k during high school. These students manage, by and l a r g e , to complete requirements f o r a high school diploma, but they graduate without the academic, v o c a t i o n a l , or E n g l i s h language s k i l l s needed to be competitive i n the job market. These l a t e r a r r i v a l s , moreover, are g e n e r a l l y those subjected to the worst h o s t i l i t i e s by ignorant and r a c i s t classmates." 9 In a West German study using data from an annual r e p r e s e n t a t i v e sample of approximately 5,000 households, the r e l a t i o n s h i p between kindergarten attendance and seventh-grade school placement was analyzed (Spiess, Buchel, & Wagner, 2003). I t was found that c h i l d r e n of recent immigrant backgrounds who attended German kindergarten were l a t e r more l i k e l y to be placed i n t o a higher educational l e v e l of school. This r e l a t i o n s h i p was s i g n i f i c a n t only f o r c h i l d r e n i n immigrant households, not f o r c h i l d r e n of German born c i t i z e n s (Spiess et a l . , 2003). S i m i l a r l y , according to an US study using data from 1990 and 1980 US Census f i l e s , delayed school entry n e g a t i v e l y impacts l a t e r school achievement, but only i n the case of c e r t a i n immigrant groups (Gonzales, 2003). Findings of t h i s study showed that Mexican immigrants are a f f e c t e d most by delayed school entry. For example, Mexican c h i l d r e n a r r i v i n g i n the country between ages 9 and 11 obt a i n s i g n i f i c a n t l y fewer years of education than c h i l d r e n a r r i v i n g as young i n f a n t s up to f i v e years of age. Other immigrants from L a t i n America and from Europe are a l s o n e g a t i v e l y a f f e c t e d by l a t e r age of a r r i v a l and school entry; however, i n the case of immigrants of Asian, P a c i f i c I s l a n d e r , A f r i c a n and Middle Eastern o r i g i n s , no p a r t i c u l a r r e l a t i o n s h i p between t h e i r age of a r r i v a l and obtained years of schoo l i n g was found (Gonzales, 2003). A study of Turkish immigrant youth i n A u s t r a l i a a l s o suggested that 10 there was an inverse r e l a t i o n s h i p between the number of years of A u s t r a l i a n education and the p r o b a b i l i t y of e a r l y school drop-out among these students (Young, 1983). The d i f f e r e n t i a l impact of delayed school entry on l a t e r school achievement among various e t h n i c groups i s l i k e l y to be i n f l u e n c e d by s p e c i f i c f a c t o r s (e.g., socio-economic s t a t u s , p a r e n t a l support, acceptance of each immigrant group i n the new so c i e t y ) a s s o c i a t e d with each immigrant population. The r e s u l t s of a number of A l b e r t a s t u d i e s i n d i c a t e that the drop-out r a t e of ESL students i s much higher (74%) than the drop-out r a t e of the general population of high school students (30-35%) (Watt & Roessingh, 1994a, 1994b, 1996, 2001). A study i n v e s t i g a t i n g the academic achievement of 556 high school students with ESL from one urban school board i n A l b e r t a showed that school completion r a t e among students with ESL i s lower (approximately 54%) than the ra t e f o r a l l students i n A l b e r t a (approximately 70%) (Derwing, DeCorby, Ichikawa, & Jamieson, 1999). According to t h i s study, about 36% students with ESL dropped out f o r a v a r i e t y of reasons, and 10% of students with ESL l e f t school due to the age cap, which i s a r e g u l a t i o n implemented i n some provinces r e q u i r i n g that only students aged 19 or younger before September 1 rec e i v e high school funding. For example, i n A l b e r t a , students unable to f u l f i l l graduation requirements before the age of 19 cannot continue i n any K - 1 2 11 system, unless they are w i l l i n g to pay the f u l l cost of t h e i r high school education (Derwing e t . a l . , 1999). Regulations l i k e the age cap add to the challenges that immigrant students face at school. The age upon a r r i v a l i n a new country may a l s o be a f f e c t i n g the educational outcome of many immigrant students with ESL because of the operation of such age-based funding r e g u l a t i o n s . C h i l d r e n who s t a r t school i n a new country at an e a r l y age are l e s s l i k e l y to be a f f e c t e d by such r e g u l a t i o n s as the age cap than c h i l d r e n a r r i v i n g at a l a t e r age. O v e r a l l , the r e s u l t s of these stud i e s suggest t h a t , at l e a s t i n the case of some immigrant populations, an e a r l y age upon a r r i v a l to the new country has a p o s i t i v e impact on c h i l d r e n ' s l a t e r e d ucational outcomes. I t may be that younger c h i l d r e n adjust more e a s i l y to new c u r r i c u l a , and a new c u l t u r e than older c h i l d r e n . A c q u i s i t i o n of a new language may a l s o be e a s i e r f o r younger c h i l d r e n . Family Influences on Students' Scholastic Performance The r e s u l t s of a number of stud i e s suggest that there are s p e c i f i c c h a r a c t e r i s t i c s i n the f a m i l y backgrounds and home-c u l t u r e s of students of recent immigrant backgrounds that p o s i t i v e l y a f f e c t t h e i r school adjustment and academic achievement (e.g., Bankston, & Zhou, 1995; Caplan, Choi, & Whitmore, 1991; 1992; Gibson, 1991; F u l i g n i , 1997; Kao & Tienda, 1995). I t appears that the school success of students with 12 recent immigrant backgrounds may be at l e a s t p a r t l y explained by a strong emphasis on school achievement o r i g i n a t i n g i n students' f a m i l i e s . I t i s n a t u r a l to assume that parents' behavior has a s i g n i f i c a n t i n f l u e n c e on t h e i r c h i l d r e n ' s school achievement, though other f a c t o r s such as peers or the wider e c o l o g i c a l context always need to be considered as w e l l . The r e l a t i o n s h i p between parenting and c h i l d r e n ' s c o g n i t i v e and school achievement was shown by a number of s t u d i e s . For example, i t was found that the q u a l i t y of home s t i m u l a t i o n p r e d i c t e d the futur e school achievement of c h i l d r e n as young as 12 months (Van Doornick, C a l d w e l l , Wright, & Frankenberg, 1981), and that the l e v e l of p a r e n t a l engagement i n s t i m u l a t i n g a c t i v i t i e s with t h e i r 5 year o l d twins had a p o s i t i v e impact on t h e i r c h i l d r e n ' s performance on i n t e l l i g e n c e t e s t s (Kim-Cohen, M o f f i t , Caspi, & Taylor, 2004). Parents may i n f l u e n c e t h e i r c h i l d r e n ' s school achievement i n m u l t i p l e ways: by exposing them to s t i m u l a t i n g a c t i v i t i e s , m o t i v a t i n g them to do w e l l i n school, a s s i s t i n g them with t h e i r homework, and showing i n t e r e s t i n t h e i r c h i l d r e n ' s school performance. Parents of recent immigrant backgrounds are new to Canada, and t h e r e f o r e are l i k e l y to be more i n f l u e n c e d by the c u l t u r e of t h e i r home country than by Canadian c u l t u r e . Every c u l t u r e values education i n a s p e c i f i c way, and educ a t i o n a l methods d i f f e r g r e a t l y from c u l t u r e to c u l t u r e . Parents of recent immigrant backgrounds may have unusually high a s p i r a t i o n s f o r t h e i r c h i l d r e n i n terms of education and career. This may stem p a r t i a l l y from t h e i r c u l t u r a l background, and p a r t i a l l y from t h e i r status i n t h e i r new country. I t i s n a t u r a l f o r parents to wish success f o r t h e i r c h i l d r e n . For parents who are new to Canada, t h i s may be even more important. I f t h e i r c h i l d r e n do w e l l , i t means that t h e i r choice to come here was the r i g h t one and that t h e i r c h i l d r e n have adapted w e l l i n the new country. For many immigrant parents, hopes f o r a b e t t e r f u t u r e f o r t h e i r c h i l d r e n are among the most important f a c t o r s i n choosing to move to a new country. Many immigrant f a m i l i e s from various c u l t u r a l backgrounds (e.g., East Asian, European, C e n t r a l American, F i l i p i n o , Caribbean, and Indian) g r e a t l y value school success, and encourage t h e i r c h i l d r e n to do w e l l i n school (Caplan, et a l . , 1991/ 1992; Gibson, 1991; F u l i g n i , 1997; Waters, 1994;. In a study conducted to determine the r e l a t i v e impact of pa r e n t a l a t t i t u d e s and peer-support on the performance of students of immigrant backgrounds, students' own a t t i t u d e s and behaviors were a l s o considered ( F u l i g n i , 1997). Approximately 1,100 tenth-, e i g h t h - and s i x t h grade students reported on t h e i f a m i l y background, p a r e n t a l and peer support, and on t h e i r own academic a t t i t u d e s and behaviors. F i n a l grades i n mathematics and E n g l i s h were obtained from the students' o f f i c i a l school 14 records. I t was found that f i r s t generation ( i . e . , both students and parents were born outside of the United States) and second generation ( i . e . , at l e a s t one parent was born outside of the United States) students from immigrant f a m i l i e s who had a working knowledge of E n g l i s h r e c e i v e d higher grades i n both mathematics and E n g l i s h than the students from non-immigrant f a m i l i e s ( i . e . , both parents were born i n the United S t a t e s ) . Adolescent students from f i r s t and second generation immigrant f a m i l i e s adjusted to school remarkably w e l l , experienced great support i n t h e i r education e f f o r t s from t h e i r f a m i l i e s and peers, and had strong m o t i v a t i o n to succeed i n school, whether they were immigrants from East A s i a , Europe, the P h i l i p p i n e s or L a t i n America. As much as 70% of the ge n e r a t i o n a l d i f f e r e n c e s i n academic achievement was accounted f o r by educational attitude's and behaviors, even a f t e r c o n t r o l l i n g f o r students' SES background. F u l i n g n i (1997) concluded t h a t , "whereas important v a r i a t i o n s do e x i s t among these students, the adolescents from immigrant f a m i l i e s seem to share t h e i r parents' b e l i e f that education i s the most important route to t h e i r success i n t h i s country." S i m i l a r l y , i n a study i n v e s t i g a t i n g the l o n g i t u d i n a l achievement of e i g h t h - to twelfth-grade students with recent immigrant backgrounds, i t was found that d i f f e r e n c e s i n the school achievement of immigrant and n a t i v e youth appear to be 15 s i g n i f i c a n t l y i n f l u e n c e d by the behavior of the students' parents (Kao & Tienda, 1995). In t h i s study, students with immigrant parents d i d as w e l l i n school ( i n terms of t h e i r grades, achievement t e s t scores, and c o l l e g e a s p i r a t i o n s ) as students of native-born parents. This was true f o r Hispanic, black, and white students with recent immigrant backgrounds. Moreover, Asian youth with parents born outside of the United States showed higher educational achievement than students with native-born parents. Some p a r e n t a l behaviors were found to be a s s o c i a t e d with students' school achievement (grades) (Kao & Tienda, 1995). For example, immigrant parents were l e s s l i k e l y than native-born parents to have r u l e s about household chores, and the i m p o s i t i o n of household d u t i e s was found to have an inverse r e l a t i o n s h i p with school achievement. A l s o , immigrant parents participated'more i n parent-teacher conferences s p e c i f i c a l l y regarding the achievement of t h e i r c h i l d , but were l e s s l i k e l y to be i n v o l v e d i n other school a c t i v i t i e s (Kao & Tienda, 1995). Kao and Tienda (1995) concluded that native-born students with f o r e i g n born parents are the ones who are most l i k e l y to s t r i v e academically, because they are p r o f i c i e n t i n E n g l i s h , and t h e i r parents promote t h e i r academic success. In a l o n g i t u d i n a l study (K to grade three) conducted i n Vancouver, Canada of 97 c h i l d r e n , 32 had a primary language background other than E n g l i s h (Kerr, 2004). The main c u l t u r a l 16 group was composed of Persian speakers from Iran. A l t o g e t h e r there were 11 language groups w i t h i n the sample besides E n g l i s h . In t h i s study, i t was found that parents of recent immigrant backgrounds were s i g n i f i c a n t l y more l i k e l y to t u t o r t h e i r c h i l d r e n i n academic subjects at home than native-born parents. A l s o , c h i l d r e n with a recent-immigrant background (e.g., e i t h e r the c h i l d or at l e a s t one of the parents born outside of Canada) were, according to t h e i r parents, e n r o l l e d i n fewer e x t r a c u r r i c u l a r a c t i v i t i e s such as sports than t h e i r peers. When c h i l d r e n were t e s t e d on a number of achievement measures -predominantly i n mathematics, but a l s o i n c l u d i n g some reading measures - the performance of the two language groups (ESL versus n a t i v e E n g l i s h speakers) was very s i m i l a r at each grade l e v e l . Given t h i s s i m i l a r i t y of the two language groups, i t i s p l a u s i b l e that the t u t o r i n g i n t e r v e n t i o n by parents of immigrant backgrounds, and the f a c t that c h i l d r e n with ESL spend l e s s time i n e x t r a c u r r i c u l a r a c t i v i t i e s , c o n t r i b u t e to t h e i r achievement. I t i s p o s s i b l e that c e r t a i n p a r e n t a l i n f l u e n c e s of t h i s kind help c h i l d r e n with ESL to overcome some of the challenges that they face while t h e i r f a m i l i e s are a d j u s t i n g to a new country and l e a r n i n g a new language (Kerr, 2004). Findings i n the p r e v i o u s l y - d e s c r i b e d ethnographical study of Punjabi Sikh students from V a l l e y s i d e High School a l s o suggest that f a m i l y f a c t o r s are a f f e c t i n g the school success of 17 these students. Punjabi parents g r e a t l y s t r e s s school success to t h e i r c h i l d r e n , viewing education as a route to upward s o c i a l m o b i l i t y i n t h e i r new country. Punjabi parents were concerned with problems such as d i s c r i m i n a t i o n and racism i n school, but d i d not accept these d i f f i c u l t i e s as an excuse f o r poor academic performance by t h e i r c h i l d r e n . Punjabi students had very good school attendance, showed very few b e h a v i o r a l problems, appeared to be h i g h l y motivated to perform w e l l i n school, were l e s s i n v o l v e d i n a c t i v i t i e s u n r e l a t e d to school, such as jobs, s o c i a l i z e d l e s s a f t e r school, and spent more time doing homework than non-immigrant students. Students from B r i t i s h Sikh f a m i l i e s showed a s i m i l a r p a t t e r n of school involvement, and re c e i v e d s i m i l a r support from t h e i r f a m i l i e s (Gibson & Bhachu, 1991). In a study i n v e s t i g a t i n g the school achievement of students (K-12) from 200 Indochinese refugee f a m i l i e s l i v i n g i n low-income urban areas of the United States, i t was found that these students do very w e l l i n school, having unusually high grades and achievement t e s t scores compared to other students (Caplan et a l . , 1992). These students came from f a m i l i e s which were l i k e l y to s t r e s s the importance of grades and homework, were r e c e i v i n g a s s i s t a n c e with t h e i r homework from o l d e r s i b l i n g s and other f a m i l y members, and d a i l y spent more time doing homework than native-born students. A l s o , there was a p o s i t i v e r e l a t i o n s h i p between students' school achievement and t h e i r 18 immersion i n the c u l t u r a l values of t h e i r home country (Caplan et a l . ) . The importance of students' i d e n t i f i c a t i o n with the c u l t u r e of t h e i r country of o r i g i n was a l s o evident i n a study of 387 high-school students of recent Vietnamese o r i g i n l i v i n g i n L o u i s i a n a , where i t was found that the students' l i t e r a c y i n t h e i r n a t i v e language Vietnamese was p o s i t i v e l y r e l a t e d to t h e i r e t h n i c i d e n t i f i c a t i o n and school achievement (Bankston & Zhou, 1995) . In the above described study of e i g h t h - and ninth-grade students from Mexico, the P h i l i p p i n e s , Vietnam, Cambodia, Laos, and other Asian and L a t i n American c o u n t r i e s , a s i g n i f i c a n t e f f e c t of g e n e r a t i o n a l status on the achievement of students with recent immigrant backgrounds was a l s o found (Rumbaut, 1996) . Rumbaut (1996) describes the achievement of immigrant students across generations as f o l l o w s : " S i g n i f i c a n t l y , over time and generations i n the U.S., t h e i r E n g l i s h p r o f i c i e n c y and reading achievement t e s t scores went up, but the number of hours spent on homework went down, as d i d GPAs. This r e s u l t confirms s i m i l a r f i n d i n g s among immigrant students i n C a l i f o r n i a and elsewhere longer residence i n the U.S. and second-generation st a t u s was connected to d e c l i n i n g academic achievement and a s p i r a t i o n s , a l l other things being equal." In a study of the e t h n i c i t y and graduation r a t e of students from a r u r a l C a l i f o r n i a high school, school d i s t r i c t data of 19 l o n g i t u d i n a l academic progress of one c l a s s between the years 1981 and 1985 were used (Matute-Bianchi, 1986). In September, 1981, the ninth-grade student population was 643. The enrollment of Mexican-descent students i n t h i s high school was high (e.g., i n 1971, 34 percent students had a Spanish surname, and i n 1984 t h i s number increased to 57 percent). Forty nine percent of Mexican-descent students graduated i n 1985, compared to a graduation r a t e 60 percent of white students and, 87 percent of Japanese-descent students. I n t e r e s t i n g l y , the graduation r a t e of Spanish-descent students with l i m i t e d E n g l i s h p r o f i c i e n c y was higher (65 percent) than that of Spanish-descent students who were b i l i n g u a l or spoke E n g l i s h only (40 per c e n t ) . This f i n d i n g i s s u r p r i s i n g i n l i g h t of the p r e v i o u s l y - d e s c r i b e d s t u d i e s showing that l i m i t e d E n g l i s h p r o f i c i e n c y i s a f a c t o r d e t r i m e n t a l to school achievement. In order to understand t h i s f i n d i n g , the s p e c i f i c f a m i l y , language, and e t h n i c i d e n t i t y c h a r a c t e r i s t i c s a s s o c i a t e d with various subgroups of Mexican immigrants needs to be considered. Students of Mexican descent tend to s t r u g g l e i n school when the achievement of t h i s p o p ulation as a whole i s considered ( A r i a s , 1986); however, the heterogeneity among students of Mexican descent i s enormous. S p e c i f i c s o c i o - c u l t u r a l f a c t o r s are as s o c i a t e d with each of the subgroups w i t h i n the Mexican population i n terms of whom they i d e n t i f y with, what t h e i r goals 20 are, what t h e i r e t h n i c awareness i s , and t h e i r fluency i n Spanish and E n g l i s h . The f a c t o r s a s s o c i a t e d with each subgroup of the Mexican-descent p o p u l a t i o n a f f e c t the students' school achievement. Matute-Bianchi conducted f i e l d work i n v e s t i g a t i n g the school achievement of various subgroups of Mexican-descent students l i v i n g i n the United States (1991). Two groups of Mexican-descent students - r e f e r r e d to by the author as Chicano and Cholo - predominantly come from Mexican f a m i l i e s that have l i v e d i n the United States f o r generations. Students i d e n t i f y i n g with these two groups oppose the mainstream norms of North American s o c i e t y , perceive themselves as a s t i g m a t i z e d group with l i m i t e d o p p o r t u n i t i e s , and are l i k e l y to e x h i b i t b e h a v i o r a l problems and poor academic performance. In c o n t r a s t , Mexican-o r i e n t e d students, who were born i n Mexico but have l i v e d i n the United States f o r more than f i v e years, do w e l l i n school. They have t i e s to the new country, c l a i m Mexican i d e n t i t y , are t y p i c a l l y f u l l y b i l i n g u a l and are very s u c c e s s f u l i n school as a group. S i m i l a r l y , Mexican-American students who are born i n the United States to parents born i n Mexico do not as a group t y p i c a l l y experience academic d i f f i c u l t i e s . These students p r e f e r to speak E n g l i s h , and of t e n have not learned Spanish. They were described by teachers as a s s i m i l a t e d with l i t t l e p a r t i c i p a t i o n i n Mexican a c t i v i t i e s and school c l u b s . Recent 21 Mexican immigrant students are very popular among teachers f o r t h e i r r e s p e c t f u l , p o l i t e and courteous behavior, and t h e i r eagerness to l e a r n ; however, t h e i r school success i s of t e n impaired by t h e i r l i m i t e d p r o f i c i e n c y i n E n g l i s h (Matute-B i a n c h i , 1991). In another a n t h r o p o l o g i c a l study of recent immigrant high-school students from C e n t r a l America, teachers a l s o described these students as eager to please, s t r o n g l y motivated to l e a r n , and w e l l behaved. Parents of these students were predominantly u n s k i l l e d or s e m i - s k i l l e d workers, mostly i l l i t e r a t e w ith l i m i t e d E n g l i s h s k i l l s . They u n i v e r s a l l y reported that they consider education "the s i n g l e most s i g n i f i c a n t avenue to status m o b i l i t y i n a new l a n d " (Suarez-Orozco, 1991). I t seems that f i r s t generation Mexican students are l i k e l y to do w e l l i n school i f they acquire good E n g l i s h s k i l l s . S i m i l a r l y , students of parents born i n Mexico, who themselves were e i t h e r born i n the United States or l i v e d here most of t h e i r l i v e s , are u s u a l l y s u c c e s s f u l i n school. Conversely, the school m o t i v a t i o n of l a t e r generations of Mexican-descent students seems to be n e g a t i v e l y a f f e c t e d by s p e c i f i c s o c i o -c u l t u r a l f a c t o r s , e s p e c i a l l y by t h e i r perception of t h e i r m a r g i n a l i z e d status i n the mainstream s o c i e t y . Factors such as f a m i l y i n t e r e s t i n t h e i r c h i l d r e n ' s school achievement, t u t o r i n g , a s s i s t a n c e with homework and i m p o s i t i o n 22 on the students of household and outside-school r e s p o n s i b i l i t i e s seem to a f f e c t the school achievement and motiv a t i o n of immigrant students. Furthermore, there are d i f f e r e n c e s i n these f a c t o r s among immigrant and non-immigrant f a m i l i e s , as w e l l as w i t h i n various immigrant populations, depending on the country of o r i g i n , b e l i e f s about t h e i r new country, and ge n e r a t i o n a l s t a t u s of immigrant f a m i l i e s . Students' e t h n i c i d e n t i t y and p r o f i c i e n c y i n E n g l i s h and t h e i r mother tongue seem to pl a y a r o l e as w e l l , e s p e c i a l l y i n the case of c e r t a i n immigrant populations. I t appears that immigrant students who a r r i v e i n t o a new country at a young age, or were born there to f o r e i g n born parents, are most l i k e l y to experience school success. Their parents see education as the best way f o r t h e i r c h i l d r e n to achieve upward s o c i a l m o b i l i t y i n t h e i r new country. In a d d i t i o n , these students are f l u e n t i n E n g l i s h while maintaining t h e i r n a t i v e language, and have a tendency to develop an et h n i c immigrant i d e n t i t y , making them aware of t h e i r c u l t u r a l h e r i t a g e while accepting a new c u l t u r e . The immigrant students who are l i k e l y to s t r u g g l e at school seem e i t h e r to l a c k the necessary fluency i n E n g l i s h , or to be n e g a t i v e l y a f f e c t e d by the values of t h e i r peer group a s s o c i a t e d with t h e i r m i n o r i t y s t a t u s . When con s i d e r i n g these conclusions, the heterogeneity of immigrant populations should be kept i n mind. These c h a r a c t e r i s t i c s are l i k e l y to be true f o r many immigrant populations, while not to 23 be a p p l i c a b l e at a l l to some immigrant groups, depending both on country of o r i g i n and on the current country. Mathematics and Socio-Cultural Factors There are numerous environmental f a c t o r s i n f l u e n c i n g mathematical l e a r n i n g and achievement. They e x i s t w i t h i n both c r o s s - c u l t u r a l and s i n g l e c u l t u r e contexts. Various f a c t o r s such as c r o s s - n a t i o n a l d i f f e r e n c e s i n mathematical achievement are considered here, because of t h e i r relevance to the performance of immigrant students. Besides being exposed to formal mathematical i n s t r u c t i o n i n the classroom, c h i l d r e n a l s o acquire mathematical knowledge from o p p o r t u n i t i e s i n t h e i r d a i l y l i f e . For example, c h i l d r e n who a s s i s t t h e i r parents i n a store are l i k e l y to be more exposed to r e a l - l i f e mathematics than c h i l d r e n working on a farm or a s s i s t i n g with b a b y s i t t i n g . In a c r o s s - c u l t u r a l study, number knowledge, c a l c u l a t i o n a b i l i t i e s , and b a s i c a r i t h m e t i c s k i l l s among US f i f t h and second graders were compared to the performance of t h i r d and s i x t h graders from two A f r i c a n s o c i e t i e s . The advanced A f r i c a n grades were chosen to eq u a l i z e the length of schooling i n the two c o u n t r i e s . The sample c o n s i s t e d of approximately 16 c h i l d r e n at each grade l e v e l from each c u l t u r a l group (e.g., 16 second-grade US students; 16 Dioulas and Baoules third-grade students). On the m a j o r i t y of the t e s t s , t h i r d grade A f r i c a n c h i l d r e n obtained s i g n i f i c a n t l y 24 lower scores than US c h i l d r e n . The authors hypothesized that t h i s may be due to t h e i r u n f a m i l i a r i t y with s c h o o l i n g and language d i f f i c u l t y ; however, t h i s d i f f e r e n c e disappeared i n l a t e r grades, when A f r i c a n s i x t h - g r a d e r s performed as w e l l as t h e i r US counterparts. In a d d i t i o n , Dioula c h i l d r e n - whose s o c i e t y i s merchant, and t h e r e f o r e s t r e s s e s computational a c t i v i t i e s - o c c a s i o n a l l y performed at a higher l e v e l than Baoule c h i l d r e n , whose s o c i e t y i s predominantly a g r i c u l t u r a l (Ginsburg, Rosner, & R u s s e l l , 1981). In another three s t u d i e s i n v e s t i g a t i n g the mathematical performance of Baoule and Dioula c h i l d r e n , i t was found that r a p i d judgment of numerosity ( i . e . , the b a s i c concept of i n e q u a l i t y ) was as good among schooled as among unschooled nine to ten year o l d c h i l d r e n from these two s o c i e t i e s . In c o n t r a s t , Baoule c h i l d r e n , whose s o c i e t y i s ag r a r i a n , acquired good counting and a d d i t i o n s k i l l s only i f they r e c e i v e d schooling. Dioula c h i l d r e n from a merchant s o c i e t y acquired these s k i l l s r e gardless of t h e i r s c h o o l i n g experience (Posner, 1982). These r e s u l t s suggest that c e r t a i n mathematical s k i l l s , such as e s t i m a t i o n of q u a n t i t y , are u n i v e r s a l l y developed, while others such as a d d i t i o n are acquired only by means of formal education or c u l t u r a l opportunity. They are good examples of how both schooling and l i f e experience i n f l u e n c e the mathematical l e a r n i n g of c h i l d r e n . 25 During the 1970's, considerable research was done on the mathematical achievement of black students i n the United States. The N a t i o n a l L o n g i t u d i n a l Study of the High School Class of 1972 and a s p e c i a l N a t i o n a l Assessment of Mathematics i n 1975-76 revealed that black students have s i g n i f i c a n t l y lower mathematical achievement, and fewer e n r o l l i n mathematics c l a s s e s , than white students (Johnson, 1984; Jones, Burton, & Davenport, 1984). The N a t i o n a l Assessment of Educational Progress i n the 1980's and 1990's showed that the mathematical achievement of black students improved i n the f o l l o w i n g years, and moreover, black and Hispanic students made even greater gains than white students; however, the gap between the mathematical performance of white and black students remains s i g n i f i c a n t i n favor of white students at each age l e v e l (Matthews, Carpenter, L i n d q u i s t , & S i l v e r , 1984; Tate, 1997). Some studie s suggest that there i s no d i f f e r e n c e i n mathematical knowledge between black and white c h i l d r e n when they begin s c h o o l i n g (e.g., Ginsburg & R u s s e l l , 1981). Other st u d i e s suggest that there i s a d i f f e r e n c e , but only i n some areas, and that parents' background plays a r o l e from the beginning. For example, i n a study of the mathematical achievement of 825 Baltimore C i t y f i r s t graders, no d i f f e r e n c e between black and white c h i l d r e n was found using the C a l i f o r n i a Achievement Tests of computational s k i l l s ; however, white 26 c h i l d r e n obtained higher scores on math concept (reasoning) s k i l l s . In a d d i t i o n , i t was found t h a t , across race and socioeconomic s t a t u s , parents' expectations i n terms of t h e i r c h i l d r e n ' s achievement have a s i g n i f i c a n t i n f l u e n c e on c h i l d r e n ' s math s k i l l s at the beginning of grade one (Entwisle & Alexander, 1990). S i m i l a r l y , some researchers suggest that the gap i n mathematical performance between white and back students i s narrowing, but only i n c e r t a i n areas - such as b a s i c mathematical knowledge - and that language p r o f i c i e n c y e x p l a i n s some, but not a l l , of the variance (Secada, 1992) . Again, there i s a p a t t e r n of p a r e n t a l i n f l u e n c e on c h i l d r e n ' s achievement, and of s p e c i f i c c u l t u r a l f a c t o r s a f f e c t i n g some e a r l y mathematical s k i l l s while not having i n f l u e n c e on other mathematical s k i l l s . Furthermore, i n the case of black students w i t h a recent immigrant background, there seems to be a r e l a t i o n s h i p between the school achievement of these c h i l d r e n and t h e i r e t h n i c i d e n t i t y . For example, as i n the case of Hispanic students, second-generation West Indian and Haitian-American immigrant students form various e t h n i c i d e n t i t i e s a f f e c t i n g t h e i r school adjustment and l a t e r outcome. Waters (1994) describes t h i s s o c i a l behavior i n the f o l l o w i n g way: "Those youngsters who i d e n t i f y as black Americans tend to see more r a c i a l d i s c r i m i n a t i o n and l i m i t s to o p p o r t u n i t i e s f o r blacks i n the 27 United States. Those who i d e n t i f y as e t h n i c West Indians tend to see more o p p o r t u n i t i e s and rewards f o r i n d i v i d u a l e f f o r t and i n i t i a t i v e . I suggest that a s s i m i l a t i o n to America f o r the second-generation black immigrants i s complicated by race and c l a s s and t h e i r i n t e r a c t i o n , with upwardly mobile second-generation youngsters maintaining e t h n i c t i e s to t h e i r parents' n a t i o n a l o r i g i n and with poor inner c i t y youngsters a s s i m i l a t i n g to the black American peer c u l t u r e that surrounds them." In a l o n g i t u d i n a l study of academically s u c c e s s f u l Mexican immigrant students l i v i n g i n the United States, data on 157 students from the n i n t h grade through high school graduation were c o l l e c t e d (Duran & Weffer, 1992). I t was found that f a m i l y educational values had a s i g n i f i c a n t impact on the students' w i l l i n g n e s s to be e n r o l l e d i n a math and science enrichment program and to do e x t r a school work. A l s o , there was a p o s i t i v e r e l a t i o n s h i p between time devoted to homework and more advanced math/science coursework and higher Test of Achievement and P r o f i c i e n c y scores. The American College Testing Program achievement t e s t scores were g e n e r a l l y i n h i b i t e d by students' employment, i n d i c a t i n g that employment was n e g a t i v e l y a f f e c t i n g students' high-school achievement. Besides f a m i l y f a c t o r s impacting achievement and m o t i v a t i o n of these students, there was a l s o evidence found supporting the importance of mastery of E n g l i s h f o r academic success i n math and science c l a s s e s . "The 28 combined e f f e c t of length of residence and reading s k i l l s on math/science course t a k i n g was a l s o i n s t r u c t i v e : the poorer readers i n the group took fewer science courses. This suggests t h a t , i f we want to encourage language-minority students to be more i n v o l v e d i n l e a r n i n g science, we must a l s o give more a t t e n t i o n to the reading s k i l l s t hat enable them to master the subject area" (Duran & Weffer, 1992). In terms of E n g l i s h p r o f i c i e n c y , there seems to be a s p e c i f i c r e l a t i o n s h i p between l i m i t e d E n g l i s h p r o f i c i e n c y and mathematical achievement, but as i n the case of the general achievement of immigrant students who speak a language other than E n g l i s h at home, a c l e a r o n e - d i r e c t i o n a l r e l a t i o n s h i p between ESL and school performance does not e x i s t . For example, when the data of eight graders from the N a t i o n a l Educational L o n g i t u d i n a l Study 1988 were examined, i t was found that l i m i t e d E n g l i s h p r o f i c i e n c y n e g a t i v e l y i n f l u e n c e d Hispanic students' mathematical achievement, but the status of being a Hispanic student from a home where Spanish i s spoken does not n e g a t i v e l y a f f e c t mathematical performance (Bradby, 1992); however, not even the r e l a t i o n s h i p between l i m i t e d E n g l i s h p r o f i c i e n c y and school achievement a p p l i e s uniformly to a l l immigrant populations. For example, f o r Asian American students, no r e l a t i o n s h i p was found between t h e i r language sta t u s and mathematical achievement. Not even l i m i t e d E n g l i s h p r o f i c i e n c y 29 was a f f e c t i n g the mathematical performance of these students (Bradby, 1992). When mathematical achievement of 45,996 grade three and four students with recent immigrant backgrounds was analyzed i n the United States, Canada, England, A u s t r a l i a , and New Zealand using data from the T h i r d I n t e r n a t i o n a l Mathematics and Science Study (TIMSS), the performance of immigrant populations was not uniform across these c o u n t r i e s (Haung, 2000). While mathematical and science performance of students with recent immigrant backgrounds d i d not d i f f e r from the performance of t h e i r counterparts i n A u s t r a l i a and New Zealand, t h e i r mathematics and science achievement was s i g n i f i c a n t l y lower than that of the non-immigrant populations of England, Canada and the United States. In a d d i t i o n , there was a c r o s s - g e n e r a t i o n a l d i f f e r e n c e i n the achievement of the c h i l d r e n of immigrants. In Canada and the United States, both f i r s t and second generation immigrant c h i l d r e n scored lower than non-immigrant c h i l d r e n . In England, only students from f i r s t generation immigrant f a m i l i e s showed s i g n i f i c a n t l y lower performance on these t e s t s than t h e i r non-immigrant peers. O v e r a l l , the performance of c h i l d r e n coming from homes where a language other than E n g l i s h was spoken were n e g a t i v e l y a f f e c t e d by t h i s s t a t u s . I n t e r e s t i n g l y , i n a l l f i v e c o u n t r i e s , c h i l d r e n with ESL from second-generation immigrant f a m i l i e s scored s i g n i f i c a n t l y higher on the mathematics t e s t s 30 than non-immigrant c h i l d r e n with ESL such as F i r s t Nation students (Haung, 2000). The author speculated that t h i s may be due to the s o c i o - c u l t u r a l f a c t o r s a s s o c i a t e d with F i r s t Nation Populations, such as t h e i r s o c i a l d i f f i c u l t i e s and l i n g u i s t i c i s o l a t i o n . Mathematical Achievement of Asian Students Students of Asian o r i g i n are as a group are very s u c c e s s f u l i n t h e i r academic achievement, and i n o b t a i n i n g s c h o l a r s h i p s i n North America (e.g., Caplan et a l . , 1992; Chen, & Stevenson, 1995; Hirshman, & Wong, 1986; Sue & Okazaki, 1990). Mathematics achievement i s oft e n c i t e d as one of the strengths of Asian students, p a r t i c u l a r l y i n the case of Chinese, Japanese and Taiwanese students (e.g., Campbell & Xue, 2001; Chen & Stevenson, 1995; R o b i t a i l l e & Gardner, 1989; Stevenson et a l . , 1990; S t i g l e r , Lee, Lucker, & Stevenson, 1982; Wong, 1980; 1998). Studies i n v e s t i g a t i n g mathematical achievement of Asian students i n p a r t i c u l a r are described below. A l s o , some c h a r a c t e r i s t i c s a s s o c i a t e d with mathematics education i n A s i a , e s p e c i a l l y East A s i a , are considered. S p e c i a l a t t e n t i o n i s given to Asian students because of t h e i r e x c e l l e n t achievement i n mathematics when compared to other nations, and the success of immigrant students of Asian o r i g i n i n new co u n t r i e s such as the United States. 31 When the mathematical performance of US students i s compared to that of other i n d u s t r i a l n a tions, US students c o n s i s t e n t l y o b t a i n low achievement scores, e s p e c i a l l y when compared to students from East A s i a . This was shown when data from the I n t e r n a t i o n a l P r o j e c t f o r the E v a l u a t i o n of Educational Achievement (IEA) s t u d i e s were analyzed i n 1960's and 1980's. In the f i r s t IEA study, where the performance of 13 and 17 year o l d students from 12 i n d u s t r i a l c o u n t r i e s was compared, the performance of US students was s t r i k i n g l y poor (Husen, 1967). In h i s review, Geary gives t h i s example: the mean scores of US 13-year olds were "below the i n t e r n a t i o n a l mean i n every area assessed ( i . e . , a r i t h m e t i c , algebra, and geometry) (1996)." The performance of US 17-year olds was even more alarming. As a group they obtained the lowest o v e r a l l score when compared to the other 11 nations, and approximately 80 percent of them scored below the i n t e r n a t i o n a l average (Husen, 1967). The data from the second IEA study of 17 year o l d students from 22 d i f f e r e n t educational systems showed s i m i l a r l y discouraging r e s u l t s regarding the performance of US students (Crosswhite, Dossey, Swafford, McKnight, & Cooney, 1985) . Although the poor performance of US students received great a t t e n t i o n from the US media and government i n the 1980's, US students continue to e x h i b i t s i g n i f i c a n t l y lower mathematical achievement than East Asian students. For example, when the 32 performance of US, Chinese and Japanese students was examined again four and ten years l a t e r ( c h i l d r e n who were i n the f i r s t grade at the time of the o r i g i n a l study were i n the f i f t h grade the time of the second study, and the eleventh grade at the time of the t h i r d ) , the gaps between US and Asian students p e r s i s t e d (Stevenson, Chen, & Lee, 1993). In both grades, the performance of students from Sendai and T a i p e i was s u p e r i o r to that of students from Minneapolis. One of the most recent i n t e r n a t i o n a l s t u d i e s of mathematical achievement: (TIMSS), a l s o confirmed that students from four East Asian c o u n t r i e s - Hong Kong, Japan, Korea, and Singapore - maintained t h e i r s u p e r i o r performance, o b t a i n i n g the highest achievement scores among the nations s t u d i e d (Leung, 2002). The d i f f e r e n c e between the performance of US and East Asian students has already begun i n e a r l y grades. In a c r o s s - c u l t u r a l study of mathematical achievement of f i r s t and f i f t h graders i n B e i j i n g (264 students) and Chicago (480 students), i t was found that Chinese c h i l d r e n obtained s i g n i f i c a n t l y higher scores on mathematics t e s t s than US c h i l d r e n (Stevenson et a l . , 1990). When i n t e r p r e t i n g the r e s u l t s , the authors reported the f o l l o w i n g : "The d e f i c i e n c i e s of American c h i l d r e n were pervasive. In ne a r l y a l l comparisons, scores of the American c h i l d r e n were s i g n i f i c a n t l y below those of the Chinese c h i l d r e n . .... Chinese c h i l d r e n not only solved problems e f f e c t i v e l y , they 33 a l s o solved them r a p i d l y . ... Di f f e r e n c e s occurred not only on d i f f i c u l t items but were d i s t r i b u t e d throughout the range of problems." S i m i l a r l y , a l a r g e c r o s s - c u l t u r a l study of kindergarteners, f i r s t and f i f t h graders attending a number of schools i n Minneapolis (USA), Sendai (Japan), and T a i p e i (Taiwan), found that the performance of US c h i l d r e n was lower than that of Japanese c h i l d r e n i n a l l three grades, and lower i n grades 1 and f i v e than that of Chinese students (Stevenson, Lee, & S t i g l e r , 1986). Some d i f f e r e n c e s were again s t r i k i n g , e s p e c i a l l y when c o n s i d e r i n g that the mathematical achievement of Minnesota students i s ranked high among American s t a t e s . For example, the highest average score of a f i f t h - g r a d e Minnesota classroom was lower than the lowest average score of a Sendai classroom. Asian students continue to show su p e r i o r achievement a f t e r immigrating to North America; however, t h e i r performance i s lower than the performance of t h e i r peers educated i n A s i a . For example, when the impact of et h n i c s t a t u s on mathematics t e s t scores was analyzed, Asian-American students obtained the highest scores compared to three other e t h n i c groups (white, black and Hispanic) of American c h i l d r e n (Stevenson et a l . , 1990). A c r o s s - c u l t u r a l study conducted i n high schools i n the D i s t r i c t of Columbia, Minnesota, Taiwan, and Japan i n v e s t i g a t i n g the mathematical achievement and mo t i v a t i o n of 2,262 eleventh-34 grade students l i v i n g i n the United States, 1,475 i n China and 1,120 i n Japan found that students of Asian-American o r i g i n obtained higher scores on curriculum-based t e s t s of mathematics than t h e i r Caucasian-American peers (Chen, & Stevenson, 1995); however, the highest scores were obtained by Chinese and Japanese students. The authors concluded that s o c i o - c u l t u r a l f a c t o r s are p o s s i b l e reasons f o r the success of Asian-American students, o r i g i n a t i n g i n the students' f a m i l i e s , and a f f e c t i n g t h e i r m o t i v a t i o n and a t t i t u d e s towards school: " Asian-American students attended good schools, had parents and peers who held high academic standards, b e l i e v e d that the road to success was through e f f o r t , had very p o s i t i v e a t t i t u d e s about mathematics, were e n r o l l e d i n more c h a l l e n g i n g courses, s t u d i e d d i l i g e n t l y , and experienced l e s s i n t e r f e r e n c e with t h e i r schoolwork from jobs and i n f o r m a l peer i n t e r a c t i o n s (Chen, & Stevenson, 1995)." According to the authors, the . c u l t u r a l backgrounds of Chinese and Japanese students l i v i n g i n A s i a are c h a r a c t e r i z e d by s i m i l a r values and b e l i e f s regarding education. These values seem to change i n American students of Asian o r i g i n as they adjust to North American c u l t u r e through the process of a c c u l t u r a t i o n . Students of Asian o r i g i n a l s o e x c e l i n c o u n t r i e s such as Canada, where students perform very w e l l i n c r o s s - n a t i o n a l comparisons. Data from TIMSS-99 revealed t h a t , out of 38 35 c o u n t r i e s , only 6 had s i g n i f i c a n t l y higher o v e r a l l scores than Canada ( R o b i t a i l l e & Taylor, 2001). With the exception of Belgium, the c o u n t r i e s with s i g n i f i c a n t l y higher scores were a l l Asian (Japan, Hong Kong, Taiwan, Korea, Singapore). In a study of Canadian, Chinese, and Chinese-Canadian u n i v e r s i t y students, the same p a t t e r n occurred as described i n the case of American versus Asian and Asian-American students. This study of 72 students of Asian and non-Asian o r i g i n , and of students p r e v i o u s l y educated i n A s i a studying at the U n i v e r s i t y of Saskatchewan i n Canada, found t h a t , on tasks of complex a r i t h m e t i c , Chinese u n i v e r s i t y students educated i n A s i a performed b e t t e r than Canadian students of both Chinese and non-Asian o r i g i n . In a d d i t i o n , the performance on simple a r i t h m e t i c tasks was equal f o r Canadian students of Chinese o r i g i n and Chinese students from A s i a , and both groups obtained s i g n i f i c a n t l y higher scores on simple a r i t h m e t i c tasks than Canadian students of non-Asian o r i g i n . These r e s u l t s suggest that the d i f f e r e n c e i n some aspects of mathematics among these three c u l t u r a l groups - such as i n simple a r i t h m e t i c - i s not l i k e l y to be a t t r i b u t a b l e to the c r o s s - c u l t u r a l d i f f e r e n c e s i n formal s c h o o l i n g . Canadian students of both Asian and non-Asian o r i g i n were educated i n Canada, and t h e i r performance s i g n i f i c a n t l y d i f f e r e d . In c o n t r a s t , the performance of Asian s tudent s educated i n Canada was remarkably s i m i l a r to those educated i n A s i a (Campbell & Xue, 2001). S c h o o l i n g . A l t h o u g h i t may appear t h a t t h e r e i s l i t t l e commonali ty i n s t u d e n t s ' e d u c a t i o n a l backgrounds a c r o s s c o u n t r i e s such as Hong Kong, Japan , K o r e a , and S i n g a p o r e , except h i g h p o p u l a t i o n d e n s i t y and l a r g e c l a s s e s (which are known to have an i n v e r s e r e l a t i o n s h i p w i t h achievement) t h e r e are l i k e l y to be some common f a c t o r s c o n t r i b u t i n g to the s u p e r i o r performance o f these s t u d e n t s . Some d i s t i n c t i v e f e a t u r e s o f E a s t A s i a n mathematics were i d e n t i f i e d i n a paper a d d r e s s i n g t h i s i s s u e (Leung, 2001) . In E a s t A s i a , c o n t e n t , b a s i c s k i l l s , and knowledge are emphasized, w h i l e i n N o r t h A m e r i c a , mathematics tends to be taught u s i n g examples drawn from "everyday l i f e " . The N o r t h American s t y l e o f i n s t r u c t i o n presumes t h a t s tudents are b e t t e r a b l e to grasp mathemat ica l concepts i f they can r e l a t e them to the w o r l d around them. M e m o r i z a t i o n , r e p e a t e d p r a c t i c e , and even r o t e l e a r n i n g are p o p u l a r ways o f l e a r n i n g i n E a s t A s i a , i n c o n t r a s t to Western pedagogy where r o t e l e a r n i n g i s c r i t i c i z e d as not mean ing fu l to s t u d e n t s . E a s t A s i a n s view e d u c a t i o n as hard work r a t h e r than p l e a s u r e or f u n , w h i l e 'the l a t t e r d e s c r i p t o r s are viewed as e s s e n t i a l to the l e a r n i n g p r o c e s s among Western educators who f a v o r " c h i l d - c e n t e r e d e d u c a t i o n " . Academic achievement and c o n c r e t e success - i n the form of h i g h grades , p a s s i n g exams, or b e i n g a c c e p t e d to a p r e s t i g i o u s school or program - always have been valued h i g h l y i n East A s i a . Both East Asian teachers and parents have high expectations f o r t h e i r c h i l d r e n : academic success i s a means to b r i n g honor to one's f a m i l y and ancestors, and i s l i n k e d d i r e c t l y to success i n s o c i e t y . In c o n t r a s t , Western educators have a tendency to value i n t r i n s i c over e x t r i n s i c m o t i v a t i o n . Western pedagogy emphasizes i n d i v i d u a l l e a r n i n g , while more communal East Asian s o c i e t i e s treasure group l e a r n i n g with a s o c i a l o r i e n t a t i o n . F i n a l l y , an American teacher i s viewed as a f a c i l i t a t o r of l e a r n i n g r a t h e r than an expert i n the subject matter or even a s c h o l a r , while the opposite i s true i n the case of an East Asian teacher (Leung, 2001). When observations of teaching methods of grade one and f i v e mathematics were conducted i n Japanese, Chinese and US classrooms, l a r g e c r o s s - c u l t u r a l d i f f e r e n c e s were found regarding classroom i n s t r u c t i o n s and management ( S t i g l e r , Lee, & Stevenson, 1987). In each country, 20 f i r s t and 20 f i f t h grade classrooms were s e l e c t e d from at l e a s t 10 schools representing various p o i n t s on the socio-economic spectrum. (There were 240 students at each grade i n each country.). US teachers devoted l e s s time to mathematics than to language a r t s , compared to approximately equal d i v i s i o n of time between these two subjects i n Japan and Taiwan. The percentage of time spent i n academic a c t i v i t i e s was higher i n both Chinese and Japanese classrooms 38 than i n US classrooms, and i n t e r e s t i n g l y , the time devoted to academics increased between f i r s t and f i f t h grade only i n Asian c o u n t r i e s . US classrooms showed the opposite p a t t e r n . US c h i l d r e n were more o f f - t a s k ( i nappropriate a c t i v i t i e s during c l a s s time) than Chinese and Japanese c h i l d r e n i n mathematics c l a s s e s . US c h i l d r e n a l s o spent more time working on t h e i r own or i n small groups than i n whole c l a s s a c t i v i t i e s , while Japanese and Chinese c h i l d r e n were working, watching and l i s t e n i n g together as a c l a s s f o r a m a j o r i t y of the time. S i m i l a r l y , US teachers worked more with i n d i v i d u a l students and l e s s with the whole c l a s s than Chinese and Japanese teachers. There was a p a r a l l e l r e l a t i o n s h i p between the classroom management s t r a t e g i e s and achievement d i f f e r e n c e s among the three c o u n t r i e s ( S t i g l e r , Lee & Stevenson, 1987). S i m i l a r l y , US mathematical c u r r i c u l a , i n comparison to c u r r i c u l a i n Japan, China, and Taiwan, are po o r l y organized and much l e s s advanced ( i . e . , second or t h i r d grade m a t e r i a l taught i n A s i a i s introduced i n the f i f t h or s i x t h grade i n the United States (Fuson, S t i g l e r , & Bartsch, 1988). The study described above a l s o found that US teachers g e n e r a l l y valued mathematics l e s s than Chinese teachers, p r e f e r r e d l e s s to teach i t , and- were l e s s confident i n t h e i r s k i l l s teaching mathematics compared to teaching language a r t s (Stevenson et a l . , 1990). The authors concluded that the performance of US c h i l d r e n may be n e g a t i v e l y i n f l u e n c e d by the comparatively small amount of time devoted to the subject i n the United States, low expectations held among US parents f o r t h e i r c h i l d r e n ' s mathematical achievement, and lower i n t e r e s t i n the subject among US teachers of mathematics. C r o s s - c u l t u r a l , d i f f e r e n c e s in. mathematical achievement are l i k e l y to be a f f e c t e d by the above-described d i f f e r e n c e s i n sch o o l i n g . In a d d i t i o n , s c h o o l i n g patterns do not e x i s t i n i s o l a t i o n and are l i k e l y i n t e r t w i n e d with other c u l t u r a l and f a m i l y p a t t e r n s , which are described i n the f o l l o w i n g s e c t i o n s . Homework. As shown i n previous s e c t i o n s , the achievement of immigrant students may be i n f l u e n c e d by the time devoted to homework, since i n a number of s t u d i e s , d i f f e r e n c e s regarding homework were found between students with recent immigrant backgrounds and native-born American students. There were a l s o found c r o s s - c u l t u r a l d i f f e r e n c e s i n the amount of time devoted to mathematical homework between East Asian and North American students. For example, i t was found that US c h i l d r e n devote much l e s s time to homework than do Chinese and Japanese students (Stevenson, Lee & S t i g l e r , 1986). In a d d i t i o n , both US educators and parents do not h i g h l y value homework (Stevenson et a l . , 1986) . In another c r o s s - c u l t u r a l examination of the r e l a t i o n s h i p between homework-and achievement, i n t e r e s t i n g d i f f e r e n c e s between Chinese, Japanese and US students were found (Chen & 40 Stevenson, 1989). Three thousand five-hundred elementary school c h i l d r e n and t h e i r parents, l i v i n g i n B e i j i n g , Chicago, Minneapolis, Sendai and T a i p e i p a r t i c i p a t e d i n t h i s study. US f i r s t , t h i r d and f i f t h graders obtained s i g n i f i c a n t l y lower scores on achievement t e s t s i n mathematics s p e c i f i c a l l y designed f o r t h i s study than t h e i r counterparts i n China and Japan. I t was a l s o found that US c h i l d r e n were assigned s i g n i f i c a n t l y smaller amounts of homework, and spent l e s s time doing homework than both Japanese and Chinese students. When the r e l a t i o n s h i p between the amount of time spent doing homework and achievement was analyzed, there seemed to be a p o s i t i v e r e l a t i o n s h i p between these f a c t o r s when the performance between c u l t u r e s was considered; however, no s i g n i f i c a n t r e l a t i o n s h i p was found between the amount of time spent doing homework and achievement w i t h i n each country. This may be due to the f a c t that c h i l d r e n who devote the l a r g e s t time to homework are not l i k e l y to be the best students. This was confirmed by the f i n d i n g that c h i l d r e n w i t h i n each c u l t u r e who received the highest l e v e l of p a r e n t a l a s s i s t a n c e were l i k e l y to have lower achievement. P a r e n t a l a s s i s t a n c e i s i n general b e n e f i c i a l ; however, students who have l e a r n i n g d i f f i c u l t i e s are l i k e l y to be i n need of more p a r e n t a l support with academic work than students who f i n d l e a r n i n g easy (Chen & Stevenson, 1989). I t appears t h a t , i n comparison to East Asian c h i l d r e n , US c h i l d r e n devote l e s s time to doing homework, which may be a f f e c t i n g t h e i r general achievement i n mathematics. One may wonder i f t h i s has not changed i n the l a s t twenty years, p a r t i c u l a r l y c o n s i d e r i n g how much one hears i n the popular American media about primary school age c h i l d r e n being overwhelmed by homework. Unfortunately, c r o s s - c u l t u r a l research addressing t h i s issue seems to be r a r e . P a r e n t a l i n f l u e n c e s . As i n the case of homework, there are p a r a l l e l s between s p e c i f i c parenting behaviors and achievement found i n s t u d i e s of immigrant f a m i l i e s and i n c r o s s - c u l t u r a l s t u d i e s . In the case of Asian versus American parents and sch o o l i n g , there are a number of c r o s s - c u l t u r a l d i f f e r e n c e s i n p a r e n t a l b e l i e f s and expectations about t h e i r c h i l d r e n ' s achievement i n mathematics. One of the most s a l i e n t c h a r a c t e r i s t i c s i s that East Asian parents are much more c r i t i c a l of t h e i r c h i l d r e n ' s performance i n mathematics compared to US parents (Stevenson et a l . , 1986; Stevenson et a l . , 1990; Stevenson, Chen, & Lee, 1993). For example, when mothers of elementary school students i n Minneapolis, Sendai, and T a i p e i were asked to ra t e t h e i r c h i l d r e n ' s achievement i n mathematics, the US mothers c o n s i s t e n t l y showed the best s a t i s f a c t i o n with t h e i r c h i l d r e n ' s performance compared to both Chinese and Japanese mothers (Stevenson et a l . , 1986; Stevenson et a l . , 1993) . 42 In another c r o s s - c u l t u r a l study, mothers' b e l i e f s about t h e i r sixth-grade c h i l d r e n ' s performance i n mathematics were examined i n the Republic of China and the United States. The sample c o n s i s t e d of 51 Chinese-American mothers, 67 native-born Caucasian American mothers and 47 native-born Chinese mothers from a range of socio-economic backgrounds (Hess, Chih-Mei, & McDevitt, 1987). There were marked d i f f e r e n c e s i n b e l i e f s among the three groups. Mothers from the People's Republic of China saw l a c k of e f f o r t as the main reason f o r poor mathematical performance. The Chinese-American mothers a l s o viewed l a c k of e f f o r t as the main c o n t r i b u t o r to low performance, but assigned considerable r e s p o n s i b i l i t y to other f a c t o r s such as a l a c k of n a t u r a l a b i l i t y , and poor home and school t r a i n i n g . The Caucasian-American group d i s t r i b u t e d the r e s p o n s i b i l i t y f o r low performance across l a c k of e f f o r t , a b i l i t y , poor home and school t r a i n i n g and bad luck much more evenly compared to the other two groups (Hess et a l . , 1987). S i m i l a r l y , i n a study from Minneapolis, Sendai and T a i p e i , US mothers emphasized the impact of innate a b i l i t i e s on school success to a greater extent than Asian mothers (Stevenson, Chen, & Lee, 1993). S i m i l a r l y , when mathematical education i n Japan, Germany and the United States was compared using data from the TIMSS, d i f f e r e n c e s i n n a t i o n a l standards, teacher t r a i n i n g , and a t t i t u d e s towards d e a l i n g with d i f f e r e n c e s i n a b i l i t y were found (Stevenson, 1998). For 43 example, US respondents a t t r i b u t e d i n d i v i d u a l d i f f e r e n c e s i n mathematics to f a m i l y f a c t o r s such as f a m i l y s t a b i l i t y and support, German respondents a t t r i b u t e d d i f f e r e n c e s to inborn c h a r a c t e r i s t i c s of students such as t a l e n t and i n t e l l i g e n c e , and Japanese respondents emphasized e f f o r t (Stevenson, 1998). These r e s u l t s imply that East Asian parents are more l i k e l y to s t r e s s e f f o r t when t h e i r c h i l d r e n l e a r n mathematics, as w e l l as be more concerned about t h e i r c h i l d r e n ' s performance than US parents. This i s again one of the p o s s i b l e s o c i o - c u l t u r a l f a c t o r s a f f e c t i n g i n t e r n a t i o n a l and c u l t u r a l ( i . e . , i n the case of immigrant c h i l d r e n ) d i f f e r e n c e s i n mathematical achievement. Students' perception. Studies i n v e s t i g a t i n g c r o s s - c u l t u r a l aspects of the i n f l u e n c e of students' m o t i v a t i o n on t h e i r achievement i n mathematics are r e l a t i v e l y r a r e , and t h e i r f i n d i n g s are i n c o n s i s t e n t . As described i n the previous s e c t i o n , there appears to be a d i f f e r e n t emphasis on e f f o r t versus innate a b i l i t y among Asian and US parents. This i s a l s o r e f l e c t e d i n students' a t t i t u d e s . For example, eleventh graders i n China and Japan e x h i b i t e d a strong b e l i e f that e f f o r t i s the main f a c t o r i n school success i n co n t r a s t to US students, who s t r e s s e d the importance of innate a b i l i t y (Stevenson et a l . , 1993). In a d d i t i o n , i t was a l s o found that US students, despite t h e i r r e l a t i v e l y low achievement, reported the most frequent f e e l i n g s of academic anxi e t y (Stevenson et a l . , 1993). 44 US students appear to be more o p t i m i s t i c about t h e i r i n d i v i d u a l performance i n mathematics. A study of 353 Asi a n -American and non-Asian f o u r t h , f i f t h and s i x t h graders i n the San Francisco Bay area found that Asian-American students had a lower self-concept of t h e i r mathematical a b i l i t i e s than non-Asian American students, and b e l i e v e d . t h a t t h e i r parents held the same b e l i e f s (Whang & Hancock, 1994). Results of another study suggested that US students, despite t h e i r low achievement scores, enjoy mathematics. For example, when interviewed, US c h i l d r e n i n d i c a t e d that they enjoy mathematics, want to l e a r n more about mathematics, are s a t i s f i e d with t h e i r performance i n t h i s subject, and again b e l i e v e d that they are meeting t h e i r parents' expectations i n regards to t h e i r performance i n mathematics. Authors hypothesized that these p o s i t i v e a t t i t u d e s of US c h i l d r e n may be due to the f a c t that US c h i l d r e n consider mathematics a r e l a t i v e l y easy subject (Stevenson et a l . , 1990). O v e r a l l , i n comparison to Asian students, US students seem to emphasize innate a b i l i t y more than e f f o r t i n mathematical achievement. US c h i l d r e n enjoy mathematics, and are more s a t i s f i e d with t h e i r performance than t h e i r Asian peers. Students' s e l f - p e r c e p t i o n s i n terms of t h e i r mathematical achievement seem to r e f l e c t b e l i e f s of t h e i r parents. In a d d i t i o n , Asian students show the same c h a r a c t e r i s t i c s regarding t h e i r mathematical achievement when compared to nations other 45 than the United States. For example, when 1487 eleventh grade students from L e i p z i g (Germany) and Sendai (Japan) were asked to complete a questi o n n a i r e , the German students were l e s s c r i t i c a l of t h e i r mathematical a b i l i t y , h e ld lower standards f o r t h e i r performance, and were l e s s l i k e l y to a t t r i b u t e e x c ellence i n mathematical achievement to t h e i r own e f f o r t s such as studying than Japanese students (Randel, Stevenson, & Witruk, 2000). Present Study and Hypotheses In the present study, the r e l a t i o n s h i p s between p a r e n t a l i n f l u e n c e s , parents' a t t i t u d e s towards sc h o o l i n g , language, immigrant s t a t u s , and the performance of c h i l d r e n were examined. Data on the numeracy, memory and l i t e r a c y performance of students p a r t i c i p a t i n g i n t h i s study have been c o l l e c t e d i n each grade from kindergarten to grade 6. The main focus of t h i s study i s mathematical performance. Performance on memory and v i s u a l -s p a t i a l measures r e l a t e d to numeracy s k i l l s was considered to gain a more comprehensive p i c t u r e of c h i l d r e n ' s numerical a b i l i t i e s . The l i t e r a c y data were c o l l e c t e d i n order to determine the E n g l i s h p r o f i c i e n c y of the ESL sample. The performance of c h i l d r e n with f o r e i g n born parents and who come from f a m i l i e s where language(s) other than E n g l i s h are used (immigrant/ESL group) was compared to the performance of c h i l d r e n with Canadian born parents who come from E n g l i s h speaking f a m i l i e s (Canadian born p a r e n t s / E n g l i s h group). A questionnaire addressing a t t i t u d e s towards sc h o o l i n g , mathematics and the home support c h i l d r e n r e c e i v e (e.g., t u t o r i n g , help with homework), was administered to grade 5 and 6 c h i l d r e n and to t h e i r parents. The questionnaire responses of c h i l d r e n and t h e i r parents of f i r s t - g e n e r a t i o n immigrant backgrounds (foreign-born), and those of Canadian born parents, were compared. The p o s s i b l e existence of absolute d i f f e r e n c e s between the performances of these two groups on mathematical and other measures was i n v e s t i g a t e d . A l s o , the d i f f e r e n c e s between performances of various immigrant groups were examined and the f u n c t i o n of the country of o r i g i n as a p o s s i b l e v a r i a b l e impacting school achievement was considered. The goal of t h i s research was to i n v e s t i g a t e the impact of second language and immigrant status on mathematical achievement, and to assess how some a t t r i b u t e s of the parents of students - i n c l u d i n g a t t i t u d e s towards schooling, immigrant s t a t u s , and language - might a f f e c t mathematical achievement. One may wonder why the sample was not simply d i v i d e d i n t o immigrant versus Canadian f a m i l i e s when r e f e r r i n g to our research groups. The d i s t i n c t i o n between immigrants and Canadians i s perhaps not as simple as one might t h i n k i n a s o c i e t y as di v e r s e as Canada. The m a j o r i t y of Canadian f a m i l i e s have immigrant roots and many recent immigrants accept Canadian c i t i z e n s h i p w i t h i n a few years of t h e i r a r r i v a l to Canada. 47 F a m i l i e s l i v i n g i n Canada f o r generations do d i f f e r from f a m i l i e s who were born i n a country other than Canada. The most evident f a c t o r i s t h e i r E n g l i s h p r o f i c i e n c y . There i s a l s o the d i f f e r e n t c u l t u r a l i d e n t i t y a s s o c i a t e d with each of these groups and the a b i l i t y to " f i t " i n t o mainstream Canadian s o c i e t y . The focus of t h i s study was the immigrant st a t u s of parents rather than of c h i l d r e n i n e x p l o r i n g the mathematical performance of elementary school c h i l d r e n . As described i n the i n t r o d u c t o r y s e c t i o n , i t appears that immigrant status of parents i s a strong determinant of the school success of c h i l d r e n (Kao & Tienda, 1995). C h i l d r e n of immigrants are a very d i v e r s e group. Besides coming from d i f f e r e n t c u l t u r a l and l i n g u i s t i c backgrounds, these c h i l d r e n d i f f e r i n terms of age upon a r r i v a l i n t h e i r new country, and some are born i n the new country. In a d d i t i o n , t h e i r home exposure to t h e i r mother tongue and E n g l i s h , as w e l l as t h e i r language p r o f i c i e n c y i n these two languages V a r i e s widely; however, i t i s recognized that c h i l d r e n coming from f a m i l i e s where parents are f i r s t generation immigrants have much i n common despite the d i v e r s i t y w i t h i n t h i s group. The immigrant status of parents i n r e l a t i o n to t h e i r c h i l d r e n ' s school achievement and general adjustment i s i n c r e a s i n g l y an object of i n t e r e s t i n the current research (e.g., Aldous, 2006; Aroian, 2006; Boyod, 2002; Caplan, et a l . , 1991; 1992; Gibson, 1991; 48 F u l i g n i , 1997; Kao, 2004; Kao & Tienda, 1995; f o r review see A l l e n , 2005). 1. I t was hypothesized that immigrant/ESL c h i l d r e n w i l l perform as w e l l or b e t t e r on numeracy and r e l a t e d memory measures across grades compared to c h i l d r e n coming from E n g l i s h speaking households with Canadian born parents. In a d d i t i o n , i t i s expected that the performance of the immigrant/ESL group w i l l improve i n l a t e r grades. 2. When the f u n c t i o n of the country of o r i g i n as a p o s s i b l e v a r i a b l e impacting school achievement was considered, i t was expected that East Asian students w i l l have higher scores than other immigrant groups on numeracy measures. 3. With respect to p a r e n t a l questionnaire responses, i t was expected that immigrant/ESL parents w i l l have higher educational a s p i r a t i o n s f o r t h e i r c h i l d r e n , w i l l care more about t h e i r c h i l d r e n ' s grades and school achievement, and w i l l provide more t u t o r i n g and a s s i s t a n c e with mathematics at home than Canadian born parents. 4. I t was hypothesized that immigrant/ESL c h i l d r e n w i l l care more about t h e i r mathematical achievement and 49 have higher educational a s p i r a t i o n s than c h i l d r e n with Canadian born parents. 5. I t was expected that questionnaire responses w i l l be r e l a t e d to c h i l d r e n ' s performance on numeracy measures. Method Participants Some of the students i n our study p a r t i c i p a t e d l o n g i t u d i n a l l y ; however, the rat e of a t t r i t i o n w i t h i n our l o n g i t u d i n a l sample increased with each year. The sample s i z e changed throughout grades, as some c h i l d r e n were missing during the t e s t i n g , and some c h i l d r e n came to these schools i n l a t e r grades. In a d d i t i o n , every year, some students dropped out of the study, or d i d not p a r t i c i p a t e i n some years. I n c l u d i n g a l l students p a r t i c i p a t i n g i n t h i s study since i t s beginning, there were 481 students. There were two cohorts with d i f f e r e n t s t a r t i n g dates of p a r t i c i p a t i o n . One of these cohorts s t a r t e d to p a r t i c i p a t e i n the study a year l a t e r (N = 200) than the other (N = 281). I n c l u d i n g both cohorts, there were 282 students who had E n g l i s h as a f i r s t language and Canadian born parents ( i n c l u d i n g 51 F i r s t Nation students) and 199 students who had recent immigrant backgrounds and ESL. There were 215 g i r l s and 266 boys. The drop out rat e was high, and some students d i d not p a r t i c i p a t e i n c e r t a i n grades (e.g., a student was present i n 50 kindergarten, grades 2, 4 and 5, but not i n grades 1 and 6). Of the 306 students p a r t i c i p a t i n g i n the study i n kindergarten, 138 p a r t i c i p a t e d i n grade one, 240 i n grade two, 217 i n grade three, 191 i n grade four, and 113 i n grade f i v e . Only one cohort had reached grade 6; of these students, 50 p a r t i c i p a t e d since kindergarten. Each year, new students were added to the study. The sample s i z e i n each grade i s described i n Table 1 below. Table 1 Sample D i s t r i b u t i o n across Grades: Numeracy Performance Grade T o t a l Canadian/ Immigrant/ E n g l i s h ESL G i r l s Boys Mean age SD K 306 211 95 141 165 70.55 3 .53 1 164 110 54 80 84 83. 01 3 . 60 2 273 177 96 126 147 92.15 6 . 77 3 290 192 98 136 154 103.19 3 . 67 4 269 178 91 124 145 117.27 4 .24 5 205 110 95 103 102 130.15 4 . 92 6* 86 49 37 48 38 141.14 3 .82 * In the f i n a l year of the study, only cohort 1 had reached grade 6. In the f i n a l year of the study, 177 students answered a questionnaire addressing t h e i r a t t i t u d e s towards mathematics (84 with immigrant/ESL backgrounds, 93 with Canadian born parents/ E n g l i s h backgrounds). The same year, parents of these p a r t i c i p a t i n g students were asked to answer questionnaires 51 addressing t h e i r a t t i t u d e s towards mathematics and the home support i n mathematics t h e i r c h i l d r e n r e c e i v e (described i n the f o l l o w i n g s e c t i o n s ) . Of 177 parents, 102 returned the qu e s t i o n n a i r e s . Over h a l f [N = 52) of these f a m i l i e s had immigrant/ESL backgrounds and some (N = 39) of the immigrant/ESL f a m i l i e s answered a d d i t i o n a l questions regarding t h e i r language and c u l t u r a l background. The sample d i s t r i b u t i o n of c h i l d r e n and parents answering questionnaire i s described i n Table 2 below. Table 2 Sample D i s t r i b u t i o n i n the F i n a l Year of Study: Questionnaire C h i l d r e n answering questionnaire Grade Canadian/ Immigrant/ Frequency E n g l i s h ESL G i r l s Boys 5 91 44 ' 47 43 48 6 86 49 37 48 38 T o t a l 177 93 84 91 86 Parents answering questionnaire Grade Canadian/ Immigrant/ Frequency E n g l i s h ESL Parents of g i r l s Parents of boys 5 55 24 31 24 31 6 47 26 21 29 18 T o t a l 102 50 52 53 49 The immigrant/ESL background sample was very d i v e r s e . The language d i s t r i b u t i o n of the immigrant/ESL background sample across grades i s described i n Table 3 below. Table 3 Language D i s t r i b u t i o n of the Sample with Immigrant Background Language o r i g i n group Language Frequency East Asians Mandarin 5 Cantonese 9 Japanese 8 Korean 38 South East Asian Tagalog 25 Elocano 1 Ilongo 1 South A s i a H i n d i 2 Guj a r a t i 1 Urdu 1 Middle Eastern Persian 59 Albanian 1 Kurdish 1 A r a b i c 3 Turkish 2 European P o l i s h 2 Russian 6 Rumanian 2 Serbian 3 Bul g a r i a n 2 Czech 2 Norwegian 1 Swedish 1 Greek 1 French 3 Estonian 1 South American Spanish 10 A f r i c a n A f r i k a a n 1 C u t c h i - S w a h i l i 1 Two languages i n family- Thai and Swedish 1 Tagalog and Spanish 1 Persian and Korean 1 Persian and German 1 Bu l g a r i a n and Russian 1 Chechen and Russian 1 T o t a l number of c h i l d r e n 199 53 Besides E n g l i s h , there were 31 languages spoken i n the p a r t i c i p a t i n g f a m i l i e s with immigrant backgrounds. The l a r g e s t group was Persian speakers from Iran, followed by Korean f a m i l i e s , Tagalog speakers from the P h i l i p p i n e s , and Mandarin and Cantonese speakers from China. In a d d i t i o n , among F i r s t Nation f a m i l i e s , 15 f a m i l i e s spoke some Squamish and one f a m i l y spoke some Kwakwaka'wakw language i n a d d i t i o n to Squamish. These f a m i l i e s were not inc l u d e d i n our ESL sample, as E n g l i s h i s t h e i r f i r s t language. There are only a few n a t i v e Squamish speakers a l i v e , and Squamish i s very n e a r l y an e x t i n c t language; however, as we can see i n our study, there are f a m i l i e s who are t r y i n g to r e - l e a r n i t and to expose t h e i r c h i l d r e n to t h i s language. Schools and Socio-Economic Status The p a r t i c i p a t i n g f a m i l i e s of t h i s study came from d i v e r s e e t h n i c , language, c u l t u r a l and s o c i a l backgrounds. O r i g i n a l l y , f i v e elementary schools i n North Vancouver p a r t i c i p a t e d i n t h i s study. Two years ago (2005), one of the schools was clos e d . In the f o l l o w i n g years, some students from t h i s school moved to three other schools i n North Vancouver and continued to p a r t i c i p a t e i n t h i s study. Our p a r t i c i p a t i n g schools are c h a r a c t e r i z e d by high immigrant populations. In a d d i t i o n , three p a r t i c i p a t i n g schools have high F i r s t Nation populations. 54 The incomes of f a m i l i e s i n these North Vancouver neighborhoods are g e n e r a l l y known to be spread across a spectrum ranging from very a f f l u e n t to very modest. According to the school s t a f f , t h e i r students come from very d i v e r s e c u l t u r a l and economic backgrounds. The d i s t r i b u t i o n of the immigrant/ESL p o p u l a t i o n was even across schools. In other words, immigrant c h i l d r e n attended schools known to have mostly middle c l a s s populations and lo c a t e d i n a f f l u e n t neighborhoods, as w e l l as schools known to have a high s p e c i a l needs po p u l a t i o n and l o c a t e d i n l e s s a f f l u e n t neighborhoods. Parents answering numeracy questionnaires provided i n f o r m a t i o n about t h e i r educational l e v e l and occupation. This i n f o r m a t i o n helped to c o n t r o l f o r socio-economic status when comparing immigrant and Canadian born parents. There were no s i g n i f i c a n t d i f f e r e n c e s between f o r e i g n born and Canadian born parents i n terms of t h e i r education, d i s t r i b u t i o n of job types and f a m i l y s i z e . Students' Performance Data c o l l e c t e d from kindergarten to Grade 6 were used i n the present study. The measures were administered by t r a i n e d graduate and undergraduate students i n i n d i v i d u a l and group s e t t i n g s . The main purpose of the study was numeracy performance. L i t e r a c y measures were not administered to research the d i f f e r e n c e between the groups i n t h i s area, but rather to gain inf o r m a t i o n about the E n g l i s h p r o f i c i e n c y of the immigrant/ESL sample. Measures Used in Kindergarten The f o l l o w i n g t e s t s , from standardized and experimental measures, were administered i n kindergarten. Numeracy. 1. Wide Range Achievement Test - I I I (WRAT-III): Computational A r i t h m e t i c t e s t (Wilkinson, 1993). This t e s t r e q u i r e s c h i l d r e n to count, perform b a s i c c a l c u l a t i o n s o r a l l y , and perform w r i t t e n c a l c u l a t i o n s . This t e s t r e q u i r e s both o r a l and w r i t t e n responses and i t i s timed. 2. Number I d e n t i f i c a t i o n . In t h i s experimental task, c h i l d r e n are presented with a page of randomly arranged numbers ranging from 1 to 9, and are asked to i d e n t i f y a l l the numbers as f a s t as they can. This task i s timed. 3. Woodcock-Johnson I I I Achievement (WJ-III ACH): Q u a n t i t a t i v e Concepts t e s t (Woodcock, McGrew, Mather, 2001). In t h i s i n d i v i d u a l l y administered measure, a c h i l d i s asked to i d e n t i f y various math terms, number pa t t e r n s , and formulae (e.g., "Point to the l a r g e s t duck"). In the number s e r i e s part of the t e s t , a c h i l d i s asked to f i l l i n a missing number ("What number belongs i n t h i s s e r i e s : 2 _ 6 8?"). 4. Woodcock-Johnson I I I Achievement (WJ-III ACH): C a l c u l a t i o n t e s t (Woodcock, McGrew, Mather, 2001). This measure 56 was administered i n a group s e t t i n g . I t r e q u i r e s a c h i l d to perform various mathematical c a l c u l a t i o n s , ranging from simple a d d i t i o n to more complex equations (e.g., "2 + 4 = _" or "3x + 3y = 15") (Mather & J a f f e , 2002) . The C a l c u l a t i o n t e s t i s a normed measure of computational s k i l l s . 5. Rapid Automatized Naming (RAN): This task i s i n d i v i d u a l l y administered. The c h i l d i s presented with the numbers 1 to 9 randomly placed on the page. The c h i l d i s asked to name the numbers as f a s t as p o s s i b l e (the exact counting time i s recorded). This task measures the e f f i c i e n c y of l e x i c a l r e t r i e v a l . Visual-spatial integration. 1. Beery-Buktenica Developmental Test of V i s u a l Motor I n t e g r a t i o n (VMI) (Beery & Buktenica, 1989). The Berry-Buktenica Developmental Test of Visual-Motor I n t e g r a t i o n i s an i n d i v i d u a l l y administered t e s t . C h i l d r e n are r e q u i r e d to copy various two-dimensional f i g u r e s . 2. SATZ R e c o g n i t i o n - D i s c r i m i n a t i o n (Satz & F l e t c h e r , 1982). In t h i s task, c h i l d r e n are presented with a p i c t u r e of a p a t t e r n and then are asked to i d e n t i f y the same p a t t e r n among others. Memory. 1. Working Memory f o r Numbers (Sieg e l & Ryan, 1989). This experimental task i s administered i n d i v i d u a l l y . A c h i l d i s asked to count the number of yellow dots presented among blue dots on 57 a 5 x 8 i n . index card. There are sets of cards. In each set, there are three t r i a l s , and the number of cards per set increases as the task progresses, s t a r t i n g with two cards and ending with f i v e cards. For each t r i a l , the c h i l d i s asked to r e c a l l the number of yellow dots counted on each card i n the order i n which they were presented (e.g., r e c a l l numbers of yellow dots on two car d s ) . I f a c h i l d f a i l s a l l the items of a given set, then the task i s discontinued. 2. Wechsler I n t e l l i g e n c e Scale f o r C h i l d r e n - I I I (WISC-I I I ) : D i g i t Span t e s t (Wechsler, 1991). This t e s t r e q u i r e s a c h i l d to repeat a sequence of numbers that an examiner reads aloud. I t has two p a r t s : r e p e t i t i o n of numbers forward (sequences of numbers ranging i n length from 2 to 9 numbers) and r e p e t i t i o n of numbers backward (sequences ranging i n length from 2 to 8) . Literacy. 1. L e t t e r I d e n t i f i c a t i o n . In t h i s experimental task, c h i l d r e n are presented with a page on which 26 l e t t e r s are randomly arranged, and are asked to i d e n t i f y as many as they can. 2. Phoneme D e l e t i o n . (Muter, Hulme & Snowling, 1998). C h i l d r e n are shown a p i c t u r e representing word (e.g. bus) and then are asked to de l e t e an i n i t i a l or f i n a l phoneme from the 58 word. For example, an examiner would say, "Bus without Ab' says ?" The c o r r e c t response would be "us".. 3. Woodcock-Johnson I I I Achievement (WJ-III ACH): L e t t e r -Word I d e n t i f i c a t i o n t e s t (Research E d i t i o n ) (Woodcock, McGrew, Mather, 2001). An i n d i v i d u a l l y administered measure, i n which a c h i l d i d e n t i f i e s and pronounces i s o l a t e d l e t t e r s and words (g, r, cat, palm). I t i s a measure of b a s i c decoding s k i l l s . Measures Used in Grades 1 to 6 The f o l l o w i n g t e s t s , from standardized and experimental measures, were administered i n Grades 1 to 6. Numeracy. 1. Wide Range Achievement Test - I I I (WRAT-III): Computational A r i t h m e t i c t e s t (Wilkinson, 1993). This measure i s described i n the kindergarten measures. 2. Rapid Automatized Naming (RAN): This measure i s described i n the kindergarten measures. 3. Woodcock-Johnson I I I Achievement (WJ-III ACH): Q u a n t i t a t i v e Concepts t e s t (Woodcock, McGrew, Mather, 2001). This measure i s described i n the kindergarten measures. 4. Woodcock-Johnson I I I Achievement (WJ-III ACH): C a l c u l a t i o n t e s t (Woodcock, McGrew, Mather, 2001). This measure i s described i n the kindergarten measures. 5. Woodcock-Johnson I I I Achievement (WJ-III ACH): A p p l i e d Problems t e s t (Woodcock, McGrew, Mather, 2001): In t h i s task, a 59 c h i l d i s asked to analyze and solve o r a l l y - p r e s e n t e d mathematical problems (e.g., B i l l had $7.00. He bought a b a l l f o r $3.95 and a comb f o r $1.20. How much money d i d he have l e f t ? ) , which may be repeated i f needed (Mather & J a f f e , 2002). 6. Woodcock-Johnson I I I Achievement (WJ-III ACH): Math Fluency t e s t (Woodcock, McGrew, Mather, 2001). In t h i s task, c h i l d r e n are re q u i r e d to r a p i d l y c a l c u l a t e simple ( s i n g l e d i g i t ) s u b t r a c t i o n , m u l t i p l i c a t i o n and a d d i t i o n problems (e.g., 3 + 4 ) (Mather & J a f f e , 2002). This t e s t was administered only i n grades two and three. Vi sual-spatial integration. 1. Woodcock-Johnson I I I Diagnostic Supplement: Block Rotation t e s t (Research E d i t i o n ) : (Woodcock, McGrew, Mather, 2001). In t h i s task, a c h i l d i s presented with a p i c t u r e of a three-dimensional p a t t e r n of blocks followed by f i v e sets of s i m i l a r block p a t t e r n s . Two of the f i v e are i d e n t i c a l to the ta r g e t p a t t e r n but r o t a t e d . The c h i l d must then choose which two sets of blocks are r o t a t e d versions of the ta r g e t p a t t e r n . This task r e q u i r e s the c h i l d to be able to mentally manipulate three-dimensional o b j e c t s . Memory. 1. Working Memory f o r Numbers (Sieg e l & Ryan, 1989). This measure i s described i n the kindergarten measures. 60 2. Wechsler I n t e l l i g e n c e Scale f o r C h i l d r e n - I I I (WISC-I I I ) : D i g i t Span t e s t (Wechsler, 1991) . This measure i s described i n the kindergarten measures. Literacy. 1. Woodcock-Johnson I I I Achievement (WJ-III ACH): Word Attack t e s t (Woodcock, McGrew, Mather, 2001): In t h i s i n d i v i d u a l l y administered t e s t , a c h i l d i s asked to read o r a l l y non-words that conform to E n g l i s h s p e l l i n g r u l e s (e.g. f l i b , bungic). I t i s a good measure of decoding s k i l l s . 2. Woodcock-Johnson I I I Achievement (WJ-III ACH): L e t t e r -Word I d e n t i f i c a t i o n t e s t (Research E d i t i o n ) (Woodcock, McGrew, Mather, 2001). This measure i s described i n the kindergarten measures. 3. Wide Range Achievement Test - I I I (WRAT-III): S p e l l i n g t e s t ( W i l k i n s o n , 1993). This task was administered i n a group s e t t i n g . C h i l d r e n were,asked to s p e l l o r a l l y - p r e s e n t e d words. 4. Stanford Diagnostic Reading Test (SDRT): Reading Comprehension t e s t (Karlsen & Gardner, 1994). This t e s t was administered i n a group s e t t i n g , and i t was administered only to grades two and three. In t h i s t e s t , c h i l d r e n are r e q u i r e d to read short passages, and then answer m u l t i p l e - c h o i c e questions t a r g e t i n g various forms of comprehension. There i s a time l i m i t on t h i s t e s t . 61 5. Verbal Reasoning. This t e s t was adapted from one s e c t i o n of the Verbal Comprehension t e s t i n Woodcock-Johnson I I I Tests of C o g n i t i v e A b i l i t i e s (Research E d i t i o n ) (Woodcock, McGrew, Mather, 2001). Verbal analogies such as "Eye i s to see, as ear i s to... (hear)" are administered o r a l l y i n an i n d i v i d u a l s e t t i n g . C h i l d r e n are presented with an analogy which i s read aloud by the examiner, and they are asked to f i n i s h i t ( i . e . , to f i l l i n the missing word). Students' Performance among Different Immigrant Groups I t i s important to acknowledge heterogeneity w i t h i n immigrant populations when numerical reasoning i s considered. For example, Chinese c h i l d r e n use s p e c i f i c number techniques when p e r c e i v i n g numbers (e.g., 23 i s 2 tens and 3 ones). These techniques are l i k e l y very b e n e f i c i a l f o r the development of general mathematical reasoning. From an e a r l y age, Chinese c h i l d r e n i n t e r n a l i z e elementary c h a r a c t e r i s t i c s of numerals, g i v i n g them an advantage l a t e r i n s o l v i n g more complex mathematical problems. However, when t h e i r numerical a b i l i t i e s are t e s t e d i n a language and c u l t u r e where d i f f e r e n t number techniques are used, i t may be c h a l l e n g i n g f o r them to adjust. Whenever c r o s s - c u l t u r a l performance i n mathematics i s i n v e s t i g a t e d , the l e a r n i n g techniques unique to c e r t a i n c u l t u r a l groups should be kept i n mind, as w e l l as other unique c u l t u r a l c h a r a c t e r i s t i c s a s s o c i a t e d with mathematics l e a r n i n g . 62 In order to determine i f there i s any d i f f e r e n c e i n numeracy performance between various immigrant groups, the sample was d i v i d e d i n t o four c u l t u r a l groups: East Asians (Mandarin, Cantonese, Japanese and Korean speakers), Middle Easterners (Iranians speaking P e r s i a n , one Albanian speaker a l s o from Iran, Kurdish, A r a b i c and Turkish speakers), Southeast Asians - F i l i p i n o s (Tagalog, Elocano and Ilongo speakers from P h i l i p p i n e s ) and Europeans (Russians, Serbians, Bulgarians, Poles, Romanians and Czechs, Greek, Estonian, Swedish, Norwegian and French). Some languages could not be inc l u d e d i n the analyses since they d i d not belong to any of these groups and were not present i n s u f f i c i e n t numbers to c o n s t i t u t e a group themselves (e.g., A f r i k a a n s and C u t c h i - S w a h i l i ) . These somewhat a r b i t r a r y groupings were intended to provide s u f f i c i e n t subjects i n each group to permit the d e s i r e d s t a t i s t i c a l analyses to be undertaken, while having s u f f i c i e n t commonality w i t h i n groups to provide u s e f u l observations. While some languages were represented i n s u f f i c i e n t numbers to c o n s t i t u t e a group themselves ( i . e . , F i l i p i n o ) , other language groups needed to be created by grouping together subjects with some r e l a t e d languages and c u l t u r a l commonality ( i . e . , European, East Asian, Middle Eastern). In a d d i t i o n , these groups were created according to the d i v i s i o n of immigrant samples i n previous s t u d i e s . For example, 63 F u l i g n i (1997) i n h i s study i n v e s t i g a t i n g academic achievement among students from recent immigrant f a m i l i e s a l s o used the East Asian (Chinese, Koreans and Japanese), F i l i p i n o and European groups. The European group was a l s o one of the main e t h n i c groups i n a study of educational achievement among immigrant youth (Aldous, 2006). In a comparative study of the school performance of c h i l d r e n of immigrants, East Asian and F i l i p i n o groups were used as w e l l (Rumbaut, 1996). The achievement of East Asian students i s a frequent subject of i n t e r e s t i n research. For example, an East Asian group was used i n a c r o s s -c u l t u r a l study of mo t i v a t i o n and mathematics achievement (Chen & Stevenson, 1995) and various aspects of high achievement among East Asian students i n mathematics - such as t h e i r i d e n t i t y and f a c t o r s behind t h e i r high achievement - were i n v e s t i g a t e d i n previous s t u d i e s (Leung, 2001, 2002). Children's Questionnaire In the f i n a l year of t h i s study, c h i l d r e n were asked some questions r e l a t e d to t h e i r a t t i t u d e s towards mathematics and mathematical school achievement (see Figure 1). The questionnaire was designed by the author of t h i s study. Some c h i l d r e n p r e f e r r e d to f i l l i n the questionnaire on t h e i r own and some d i d i t with the a s s i s t a n c e of a t e s t e r . The time f i l l i n g i n the q u e stionnaire v a r i e d from c h i l d to c h i l d . L a t e r , parents of these c h i l d r e n were asked to f i l l i n a s i m i l a r questionnaire 64 Figure 1: Questionnaire f o r c h i l d r e n . Questionnaire for Children 1. Why do you want to do well in school? (please choose only one answer) a. To get a good job later b. To be well educated c. To earn lots of money d. To please my parents and family e. To be happy 2. What influences how you do in school? (please choose only one answer) a. Your talent and skills b. Your work and trying c. Help which you get from your teachers, tutors, parents and friends 3. How well do you do in mathematics compared to other children? (please choose only one answer) a. You do better than other kids. b. You do about same as other kids. c. You are not as good as other kids. 4. Do you receive help with mathematics outside school (e.g., tutor, friends, parents, siblings)? If yes, from who and how much? 5. Is it very important for you to get high grades in mathematics? Yes No 6. Do you think that mathematics is an important subject at school? Yes No 7. Do you like mathematics? Yes No 8. Do you think that you will need mathematics later in life? Yes No 9. Do you learn useful things in mathematics classes? Yes No 10. Do you think that it is important to do your homework in mathematics? Yes No 11. Could you do better in mathematics i f you tried harder? Yes No 12. Do you want to do better in mathematics than you do now? Yes No 13. Do your parents practice mathematics with you? Yes No 14. Do you use mathematics outside school? Yes No 15. Would you be happy i f someone cancelled all mathematics classes? Yes No 65 addressing the same i s s u e s , i n c l u d i n g a t t i t u d e s towards mathematics and school achievement. The r e l a t i o n s h i p between c h i l d r e n ' s performance, t h e i r responses on the questionnaire and the responses of t h e i r parents was i n v e s t i g a t e d . Parents' Questionnaire In a previous study, where the same data from e a r l i e r years (kindergarten to grade 3) were used, i t was found that parents with recent immigrant backgrounds were s i g n i f i c a n t l y more l i k e l y to t u t o r t h e i r c h i l d r e n i n mathematics at home than Canadian born parents (Kerr, • 2004) . Immigrant f a m i l i e s are n a t u r a l l y concerned that t h e i r c h i l d r e n not s u f f e r any disadvantage i n t h e i r education a r i s i n g out of language d e f i c i t s , c u l t u r a l d i f f e r e n c e , d i s c r i m i n a t i o n , and other f a c t o r s a s s o c i a t e d with immigrant/ESL backgrounds. This may e x p l a i n the greater tendency to t u t o r among these parents. A l s o , i n conversation with the author, many parents who received t h e i r education i n other c o u n t r i e s expressed d i s t r u s t of Canadian schools, remarking that Canadian schools e x e r c i s e d l a x d i s c i p l i n e , and had lower academic expectations of students than d i d schools i n t h e i r home co u n t r i e s . Immigrant parents f r e q u e n t l y commented that they wanted t h e i r c h i l d r e n to enjoy some of the b e n e f i t s of the schoolin g t y p i c a l i n t h e i r country of o r i g i n , t h i n g s that they thought might be l a c k i n g i n the Canadian system. 66 I n t h e p r e s e n t s t u d y , a q u e s t i o n n a i r e ( s e e F i g u r e 2 b e l o w ) , d e s i g n e d b y t h e a u t h o r o f t h i s s t u d y , w a s a d m i n i s t e r e d t o t h e p a r e n t s o f g r a d e 5 a n d 6 s t u d e n t s . T h i s q u e s t i o n n a i r e w a s m o d e l e d a f t e r a q u e s t i o n n a i r e u s e d i n a p r e v i o u s s t u d y , w h i c h w a s a d m i n i s t e r e d t o t h e p a r e n t s o f g r a d e 3 s t u d e n t s f r o m t h e s a m e s c h o o l s ( K e r r , 2 0 0 4 ) . I n a d d i t i o n , t h i s q u e s t i o n n a i r e w a s c r e a t e d a f t e r c o n s u l t a t i o n w i t h r e s e a r c h e r s i n t h e f i e l d w h o p r o v i d e d f e e d b a c k . A l s o , a s m a l l p i l o t s t u d y w a s r u n t o o b t a i n f e e d b a c k r e g a r d i n g t h e q u e s t i o n n a i r e . I n t h i s p i l o t s t u d y , t h e q u e s t i o n n a i r e w a s a d m i n i s t e r e d t o 14 f o r e i g n b o r n p a r e n t s w i t h y o u n g c h i l d r e n . T h e p a r e n t s w e r e a s k e d t o f i l l o u t t h e q u e s t i o n n a i r e a n d t o p r o v i d e c r i t i c i s m a f t e r w a r d s . T h e m a i n f o c u s o f t h e q u e s t i o n n a i r e w a s t h e e x a m i n a t i o n o f p a r e n t s ' a t t i t u d e s t o w a r d s m a t h e m a t i c s a n d o f t h e l e a r n i n g e n v i r o n m e n t a t h o m e . I n a d d i t i o n , f a c t o r s s u c h a s c o u n t r y o f o r i g i n , p a r e n t a l i n c o m e a n d e d u c a t i o n , a n d f a m i l y d y n a m i c s w e r e c o n s i d e r e d . F a m i l i e s w i t h r e c e n t i m m i g r a n t b a c k g r o u n d s w e r e a s k e d t o a n s w e r s o m e a d d i t i o n a l q u e s t i o n s r e l a t e d t o t h e i r c u l t u r e o f o r i g i n , l a n g u a g e b a c k g r o u n d a n d t h e w a y t h e i r c h i l d r e n a r e e x p o s e d t o t h e c u l t u r e a n d l a n g u a g e o f t h e i r h o m e c o u n t r y . P a r e n t s w e r e g i v e n a n o p t i o n t o b e i n t e r v i e w e d i n s t e a d o f f i l l i n g i n t h e q u e s t i o n n a i r e , b u t a l l t h e p a r e n t s p r e f e r r e d t o p r o v i d e w r i t t e n r e s p o n s e s . T h e m a j o r i t y o f t h e q u e s t i o n n a i r e s w e r e a n s w e r e d b y m o t h e r s ( 8 4 % ) ; h o w e v e r , i n s o m e f a m i l i e s 67 Figure 2 : Questionnaire f o r parents. Questionnaire for Parents A: Background Information 1. W h a t is y o u r c h i l d ' s n a m e ? 2. W h a t is y o u r r e l a t i o n s h i p to t h i s c h i l d ? P l e a s e c h e c k o n e . Mother Father Other (please specify) 3. P l e a s e use t h i s t a b l e to d e s c r i b e the a d u l t s l i v i n g i n y o u r h o m e . Relationship to the child (e.g., mother, father, grandmother, aunt, friend) *Country where this person was born "Total number of years this person has lived in English speaking countries (including Canada) 4. P l e a s e use th i s t a b l e to d e s c r i b e the o t h e r c h i l d r e n l i v i n g i n y o u r h o m e . Relationship to the child (e.g., brother, sister, cousin, friend) *Country where this child was born Age of this child "Total number of years this child has lived in English speaking countries (including Canada) 5. W h a t is y o u r o c c u p a t i o n a l t r a i n i n g , a n d y o u r h i ghes t l eve l o f e d u c a t i o n ? Please include your education/training from your home country and from Canada. 6. W h a t is y o u r p a r t n e r ' s o c c u p a t i o n a l t r a i n i n g , a n d h i s / h e r h i ghes t l e v e l o f e d u c a t i o n ? Please, include his/her education/training from his/her home country and from Canada. 7. W h a t is y o u r p r e s e n t p r o f e s s i o n / w o r k ? (e .g . , s t a y - a t - h o m e m o t h e r , d o c t o r ) 8. W h a t is y o u r p a r t n e r ' s p r e s e n t p r o f e s s i o n / w o r k ? 9. W h a t k i n d o f w o r k d i d y o u d o i n y o u r h o m e c o u n t r y ? * 10. W h a t k i n d o f w o r k d i d y o u r p a r t n e r d o i n h i s / h e r h o m e c o u n t r y ? * 68 *B: Lanuuase Exposure 1. Are any languages other than English spoken in your home? 2. What languages do the adults and children living in your home speak? 3. What language(s) did your child first learn? 4. What language does your child primarily use at home? 5 . With what family members does your child use a language other than English? 6. Does your child do any school-related work in any languages other than English? \fyes, what language(s)? 7. Does your child attend any language school? 8. Does your child read in any language other than English? If yes, what language(s)? 9. Does your child write in any language other than English? If yes, what language(s)? 10. Does your child attend any after-school activities where a language other than English is spoken? * C: Cultural Exposure 1. Is it important for you that your child knows about the culture of your family's country of origin? 2. If yes, why? 3. Please describe how your child is exposed to the culture of your family's country of origin (e.g., reading books, attending cultural events, groups, learning songs). 4. Please describe how you teach your child about the culture of his/her country of origin. D: School Success of Your Child Please indicate your response by circling the number that best describes your opinion. Strongly Disagree Disagree Agree Strongly Agree 16. It is important to me that my child gets good school grades. 1 2 3 4 17. It is important to me that my child gets a university education. 1 2 3 4 18. Why do you want your child to do well in school? (please choose only one answer) a. To get a good job later b. To be well educated c. To have a high income d. To honor the family e. To be happy 19. What has the most influence on your child's success in school? (please choose only one answer) a. Talent/Inborn skills b. How hard child works and tries c. Opportunities (tutoring, good teacher, good school) 69 E: Mathematics and Your Child Please circle the number or answer that best describes your opinion. Strongly Disagree Disagree Agree Strongly Agree 20. M y child's knowledge of mathematics is important to me. 1 2 3 4 21. It is important for me that my child obtains high grades in mathematics. 1 2 3 4 22. Mathematics is an important subject in school. 1 2 3 4 23. It is important for my child to devote time to mathematics homework and practice. 1 2 3 4 24. Does your child receive any tutoring in mathematics outside of school? Yes No 25. Do you or any other family members tutor your child in mathematics? Yes No 26. Is your child exposed to any other-than-school mathematical exercises (e.g., worksheets, practice books, textbooks)? Yes No 27. Does your child receive any help with mathematics homework? Yes No 28. Do you practice mathematics with your child at home? Yes No 29. Does your child play mathematics-related games with the family (e.g., Monopoly, family games)? Yes No 30. Does your child have any opportunity to use mathematics in real life settings (e.g., shopping, saving money, games)? Yes No 31. Do you think that your child can do better in mathematics than now? Yes No 32. Do you want your child do better in mathematics than he/she does now? Yes No 33. How does your child to do in mathematics compared to other children? Very good About the same Not as good as other children Note: Sections/questions marked with * are only for parents with immigrant backgrounds 70 f a t h e r s (13%), grandmothers (2%) or both parents (1%) responded to the questi o n n a i r e . I t was hypothesized that parents of recent immigrant backgrounds w i l l d i f f e r i n t h e i r responses from parents born i n Canada by being more concerned about t h e i r c h i l d r e n ' s education and grades, having higher educational a s p i r a t i o n s f o r t h e i r c h i l d r e n , o f f e r i n g more support - such as t u t o r i n g and p r a c t i c i n g mathematics at home - and by mot i v a t i n g t h e i r c h i l d r e n to do w e l l i n school. I t was hypothesized that p a r e n t a l a t t i t u d e s w i l l have an impact on the c h i l d r e n ' s mo t i v a t i o n and school success. Results Performance of the Children The research question of whether the performance of immigrant/ESL c h i l d r e n d i f f e r s from n a t i v e E n g l i s h speaking c h i l d r e n of parents born i n Canada was answered by using m u l t i p l e independent t - t e s t analyses. The independent t - t e s t was chosen as a method of a n a l y s i s because both samples had normally d i s t r i b u t e d populations, and the standard d e v i a t i o n s were equal. The equal variance was assumed i n the case of the m a j o r i t y of the t e s t s . When the variance was not equal, the highest p-value of the t - t e s t was used to reduce the chance of Type I and I I e r r o r s . P values of <.01 and <.05 were considered to be s t a t i s t i c a l l y s i g n i f i c a n t . These conventional p-values were adopted to balance concerns f o r Type I and I I e r r o r s . The sample 71 s i z e was la r g e enough that the r i s k of Type I or I I e r r o r s was l i m i t e d to a s a t i s f a c t o r y degree. The r e s u l t s are presented i n t a b l e s on the f o l l o w i n g pages. Whenever p o s s i b l e , p e r c e n t i l e s were used; however, on some measures i n the e a r l y grades, s i g n i f i c a n t d i f f e r e n c e s between the two groups were found only i n standard and/or raw scores, but not i n p e r c e n t i l e s . In these instances, these s i g n i f i c a n t d i f f e r e n c e s i n standard and/or raw scores were inc l u d e d along with p e r c e n t i l e s . There was d i v e r s i t y i n sample s i z e s i n some grades, since some measures were administered to only one cohort of c h i l d r e n i n a given grade (e.g., i n kindergarten) and some c h i l d r e n were present only f o r some measures (e.g., only f o r group measures). Kindergarten. In kindergarten, immigrant/ESL c h i l d r e n had lower performance on the D i g i t Span t e s t (scaled score) than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents, t(302) = 2.05, p<.05. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the r e s t of the measures. The r e s u l t s of kindergarten measures are presented i n Table 4 below. Grade 1. In grade one, as a group, the immigrant/ESL c h i l d r e n performed s i g n i f i c a n t l y b e t t e r than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on the WRAT-III Computational A r i t h m e t i c t e s t (raw score), t(162) = 2.63, p<.01, 72 Table 4 Kindergarten Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents C a n a d i a n / I m m i g r a n t / E n g l i s h ESL T -M e a s u r e Mean SD Mean SD t e s t p (n = 209) (n = 96) W R A T - I I I A r i t h m e t i c 57.38 29.20 55.65 28.52 0.49 ns ( p e r c e n t i l e ) L e t t e r i d e n t i f i c a t i o n 22.29 4.89 22.75 3.82 0.82 ns (RS, max 2 6) W I S C - I I I D i g i t s p a n 9.44 3.11 8.67 3.00 2.05 <.05 [ s c a l e d s c o r e ) (n = 186) (n = 91] W o r k i n g memory f o r 2.10 0.73 2.25 0.99 1.29 ns numbers (RS, max 4) (n = 129) (n = 58) B e e r y - B u k t e n i c a t e s t o f VMI ( p e r c e n t i l e ) Phoneme d e l e t i o n (RS, max 16) Number i d e n t i f i c a t i o n (RS, max 10) R e c o g n i t i o n - d i s c r i m i n a t i i (RS,max 15) 55 .28 29.37 60 .22 32.87 1 .03 ns 6. 99 6.10 6. 50 5.80 0 .52 ns 9. 59 1.43 9. 84 0.56 1 .75 ns 12 .02 2.52 12 .17 2.85 0 .36 ns (n = 80) (n = 37) W J - I I I Q u a n t i t a t i v e 65.03 26.03 60.49 28.32 0.85 ns c o n c e p t s ( p e r c e n t i l e ) W J - I I I C a l c u l a t i o n 52.83 38.38 56.14 39.00 0.43 ns ( p e r c e n t i l e ) W J - I I I L e t t e r w o r d 63.09 25.41 65.97 25.53 0.58 ns i d e n t i f i c a t i o n ( p e r c e n t i l e ) R a p i d a u t o m a t i z e d n a m i n g 26.45 13.37 24.35 13.16 0.79 ns ( t i m e i n s e c o n d s ) N o t e 1. C a n a d i a n / E n g l i s h = Ca n a d i a n b o r n p a r e n t s and E n g l i s h as a f i r s t l a n g u a g e ; Immigrant/ESL = f o r e i g n b o r n p a r e n t s and ESL; RS = raw s c o r e N o t e 2 . Sample s i z e v a r i e d a c r o s s k i n d e r g a r t e n measures. For example, W J - I I I measures and RAN were a d m i n i s t e r e d o n l y t o one c o h o r t ( s t a r t i n g a y e a r l a t e r t h a n t h e f i r s t c o h o r t ) . 73 the WRAT-III Computational A r i t h m e t i c t e s t ( w r i t t e n p a r t , raw score), t(162) = 2.70, p<.01, the WJ-III C a l c u l a t i o n t e s t (raw score), t(156) = 2.58, p<.05, the WJ-III Block Rotation t e s t (standard s c o r e ) , t(162) = 2.24, p<.05, the WJ-III Block Rotation t e s t (raw sc o r e ) , t(162) = 2.16, p<.05, and Working Memory f o r Numbers t e s t (any order, raw score), fc(162) = 2.13, p<.05. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the r e s t of the measures. Results of grade 1 measures are presented i n Table 5 below. Grade 2. The r e s u l t s of the t - t e s t analyses of Grade 2 measures are summarized i n Table 6 below. In grade two, the immigrant/ESL c h i l d r e n performed s i g n i f i c a n t l y b e t t e r than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on the WRAT-III Computational A r i t h m e t i c t e s t ( p e r c e n t i l e ) , t(243) = 2.16, p<.05. The Canadian born p a r e n t s / E n g l i s h group had s i g n i f i c a n t l y higher scores on the Verbal Reasoning t e s t (raw scor e ) , t(271) = 2.29, p<.05. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the r e s t of the measures. Grade 3 . In grade three, the immigrant/ESL c h i l d r e n performed s i g n i f i c a n t l y b e t t e r than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on the WRAT-III Computational A r i t h m e t i c t e s t ( p e r c e n t i l e ) , t(285) = 1.99, p<.05, the WJ-III C a l c u l a t i o n t e s t ( p e r c e n t i l e ) , t(285) = 3.30, 74 Table 5 Grade 1 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents Canadian / E n g l i s h (n = 110) Immigrant /ESL (n = 54) Measure Mean SD Mean SD T-t e s t WRAT-III A r i t h m e t i c ( p e r c e n t i l e ) WRAT-III A r i t h m e t i c (RS, max 40) WRAT-III A r i t h m e t i c ( W r i t t e n Part) WRAT-III A r i t h m e t i c ( Oral Part) WJ-III Q u a n t i t a t i v e concepts ( p e r c e n t i l e ) WJ-III C a l c u l a t i o n ( p e r c e n t i l e ) WJ-III C a l c u l a t i o n (RS, max 28) WJ-III A p p l i e d problems (p e r c e n t i l e ) WJ-III Block r o t a t i o n ( p e r c e n t i l e ) WJ-III Block r o t a t i o n (SS) WJ-III Block r o t a t i o n (RS, max 48) Rapid automatized naming (time i n sec) Working memory (exact) (RS, max 12) Working memory(any order) (RS, max 12) WISC-III D i g i t span (scaled score) WJ-III Word attack ( p e r c e n t i l e ) WJ-III L e t t e r word i d e n t i f i c a t i o n ( p e r c e n t i l e ) WRAT-III S p e l l i n g ( p e r c e n t i l e ) 50.18 17.38 4.22 13.20 54 .88 54 . 60 7 . 59 52.77 56.04 103.25 26.31 17.06 3.56 4.11 10.06 76.91 69. 79 27.71 3.16 1.76 1.86 28.71 26.17 2.54 30.52 30.74 19.99 8.22 6.48 2.17 2.26 3.27 21.26 26. 34 55. 94 18.74 5.07 13. 67 59.37 67 . 48 8.73 59.30 63.78 110.98 29.13 16.26 4.17 4.89 10.85 78.41 77 .41 27.99 3.00 2 .17 1.33 27 . 57 24 . 45 2.73 26. 67 29.87 22.22 7 .12 9.02 2.18 2.07 3.19 22.12 24.45 1.19 2.63 2.70 1.64 0.95 1.82 2.58 1.34 1.53 2.24 2.16 0. 65 1. 67 2.13 1.46 0.43 1.78 64.31 26.03 62.08 25.19 0.51 ns <. 01 <. 01 ns ns ns <. 05 ns ns <. 05 <. 05 ns ns <. 05 ns ns ns ns N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL; SS = standard score; RS = raw score 75 Table 6 Grade 2 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents Canadian/ English (n = 177 *n = 157) Immigrant/ ESL (n = 96 i) Measure Mean SD Mean SD T-test p WRAT-III Arithmetic (percentile)* WJ-III Quantitative concepts (percentile) WJ-III Calculation (percentile)* WJ-III Applied problems (percentile) WJ-III Block rotation (percentile) WJ-III Math fluency (percentile)* Rapid automatized naming (time i n seconds) Working memory for numbers (RS, max 12) WISC-III Digit span (scaled score) WJ-III Word attack (percentile) WJ-III Letter word i d e n t i f i c a t i o n (percentile) WRAT-III Spelling (percentile)* SDRT: Reading comprehension (percentile)* Verbal reasoning (RS, max 15) 55.06 23.91 61.95 24.14 2.16 <.05 60.72 28.46 60.46 26.63 0.09 61.81 26.10 62.43 25.69 0.18 59.04 29.89 59.47 30.26 0.15 59.18 34.74 56.63 31.23 0.62 13.62 3.68 4.15 2.15 13.09 4.38 10.85 3.12 11.13 70.12 23.20 73.08 67.47 26.45 70.08 24.27 0.80 ns ns ns ns 49.88 26.07 53.89 26.17 1.15 ns 3.38 1.16 ns 2.19 0.81 ns 2.95 0.72 ns 20.00 1.06 ns ns 61.34 24.89 63.66 23.03 0.72 ns 41.73 28.13 37.85 26.05 1.06 ns 5.70 1.99 5.14 1.86 2.29 <.05 N o t e 1. Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL; RS = raw score N o t e 2 . In t h i s grade, sample siz e was smaller for group than i n d i v i d u a l measures. Group sample sizes and measures are marked with*. 76 p<.01, the WJ-III Math Fluency t e s t ( p e r c e n t i l e ) , t(285) = 3.22, p<.01, the Working Memory f o r Numbers t e s t (raw sco r e ) , t(285) = 2.05, p<.05 , and the Number Seri e s part i n the WJ-III Q u a n t i t a t i v e Concepts t e s t (raw score), t(285) = 2.22, p<.05. The Canadian born p a r e n t s / E n g l i s h group had s i g n i f i c a n t l y higher scores on the Verbal Reasoning t e s t (raw score), t(285) = 2.18, p<.05 than the immigrant/ESL group. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the r e s t of the measures. The r e s u l t s of the t - t e s t analyses of Grade 3 measures are summarized i n Table 7 below. Grade 4. The r e s u l t s of the t - t e s t analyses of the grade 4 measures are i n Table 8 below. Immigrant/ESL c h i l d r e n had higher performance than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on a l l numeracy group measures and on one l i t e r a c y measure: the WRAT-III Computational A r i t h m e t i c t e s t ( p e r c e n t i l e ) , t(264) = 4.55, p<.001, the WJ-III C a l c u l a t i o n t e s t ( p e r c e n t i l e ) , t(264) = 4.74, p<.001, the WJ-III Math Fluency t e s t ( p e r c e n t i l e ) , t(264) = 3.07, p<.01, and the WRAT-I I I S p e l l i n g t e s t ( p e r c e n t i l e ) , t (264) = 2.57, p<.05. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the r e s t of the measures. Grade 5 . Immigrant/ESL c h i l d r e n had higher performance than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on a l l numeracy group measures and on some numeracy and memory 77 Table 7 Grade 3 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents Canadian/ Immigrant/ English ESL (n = 190) (n = 97) Measure Mean SD Mean SD T-test WRAT-III Arithmetic (percentile) WJ-III Quantitative concepts (percentile) WJ-III Q.C. Number series (RS, max 23) •WJ-III Calculation (percentile) WJ-III Applied problems (percentile) WJ-III Block rotation (percentile) WJ-III Math fluency (percentile) Rapid automatized naming (time i n seconds) Working memory for numbers (RS, max 12) •WISC-III Digit span (scaled score) WJ-III Word attack (percentile) WJ-III Letter word i d e n t i f i c a t i o n (percentile) WRAT-III Spelling (percentile) SDRT: Reading comprehension (percentile) Verbal reasoning (RS, max 15) 43.45 25.46 49.81 26.09 1.99 <. 05 55.24 25.78 60.03 25.40 1.50 11.45 12.17 ns 2.16 12.04 2.11 2.22 <.05 46.96 24.54 56.97 23.77 3.30 <. 01 62.59 30.17 63.05 29.75 0.12 ns 64.14 30.97 63.96 30.92 0.05 ns 40.41 28.10 51.84 29.10 3.22 <.01 3.14 11.75 2.83 1.11 62.82 23.06 64.15 19.97 0.48 ns 4.93 2.56 5.42 2.34 2.05 <. 05 10.28 3.07 10.23 2.86 0.15 ns ns 60.67 28.12 62.54 23.64 0.59 ns 55.32 24.12 61.48 26.36 1.91 ns 38.84 25.96 37.65 25.54 0.37 ns 6.59 1.88 6.09 1.79 2.18 <. 05 N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL; RS = raw score 78 Table 8 Grade 4 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents Canadian/ English (n = 179) Immigrant/ ESL (n = 91) Measure Mean SD Mean T-SD test P WRAT-III Arithmetic (percentile) WJ-III Quantitative concepts (percentile) WJ-III Calculation (percentile) WJ-III Applied problems (percentile) WJ-III Block rotation (percentile) WJ-III Math fluency (percentile) Rapid automatized naming (time i n seconds) Working memory for numbers (RS, max 12) WISC-III Digit span (scaled score) WJ-III Word attack (percentile) WJ-III Letter word i d e n t i f i c a t i o n (percentile) WRAT-III Spelling (percentile) SDRT: Reading comprehension (percentile) Verbal reasoning (RS, max 15) 38.49 54.97 39.72 61.94 62.55 38.23 10.80 5.94 9.30 60.52 59.38 27.45 54.88 28.00 4.55 <.001 23.86 57.68 25.73 1.10 ns 23.15 54.10 23.53 4.74 <.001 29.15 60.70 29.64 0.33 29.94 65.04 28.64 1.05 29.60 50.53 32.77 3.07 <. 01 2.47 10.59 2.12 0.62 2.40 6.15 2.29 1.07 2.84 9.74 2.91 1.46 20.77 61.74 19.88 0.61 26.96 60.35 23.45 0.65 ns ns ns ns ns ns ns 57.13 29.60 66.83 27.67 2.57 <. 05 42.08 27.01 40.30 25.81 0.52 ns 7.17 1.71 7.08 1.66 0.09 ns N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL; RS = raw score i n d i v i d u a l l y administered measures: the WRAT-III Computational A r i t h m e t i c t e s t ( p e r c e n t i l e ) , t(200) = 5.40, p<.001, the WJ-III C a l c u l a t i o n t e s t ( p e r c e n t i l e ) , t ( 2 0 0 ) = 4.50, p<.001, the WJ-III Math Fluency t e s t ( p e r c e n t i l e ) , t (200) = 3.47, p<.01, the WJ-III Q u a n t i t a t i v e Concepts t e s t ( p e r c e n t i l e ) , t(203) = 2.23, p<.05, and the Working Memory f o r Numbers t e s t (raw score), t(203) = 2.79, p<.05. The Canadian born p a r e n t s / E n g l i s h group had s i g n i f i c a n t l y higher scores than the immigrant/ESL group on the SDRT: Diagnostic Reading Comprehension t e s t ( p e r c e n t i l e ) , t(200) = 3.13, p<.05. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the r e s t of the measures. For r e s u l t s of grade 5 measures see Table 9 below. Grade 6 . For r e s u l t s of t - t e s t a n a l y s i s of grade 6 measures see Table 10 below. Only one cohort was present i n grade 6; th e r e f o r e , the sample s i z e was smaller i n t h i s grade than i n the previous grades. When the performance of the two groups was compared, some s i g n i f i c a n t d i f f e r e n c e s were found. Immigrant/ESL c h i l d r e n had higher scores than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on the WRAT-III Computational A r i t h m e t i c t e s t ( p e r c e n t i l e ) , t(84) = 3.62, p<.001, the WJ-III C a l c u l a t i o n t e s t ( p e r c e n t i l e ) , t(84) = 2.15, p<.05, and the WJ-I I I Math Fluency t e s t ( p e r c e n t i l e ) , t(84) = 2.28, p<.05. There were no s i g n i f i c a n t d i f f e r e n c e s between the two groups on the re s t of the measures. 80 Table 9 Grade 5 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents Canadian/ English (n = 110) Immigrant/ ESL (n = 95) Measure Mean SD T-Mean SD test p WRAT-III Arithmetic (percentile) WJ-III Quantitative concepts (percentile) WJ-III Calculation (percentile) WJ-III Applied problems (percentile) WJ-III Block rotation (percentile) WJ-III Math fluency (percentile) Rapid automatized naming (time i n seconds) Working memory for numbers (RS, max 12) WISC-III d i g i t span (scaled score) WJ-III Word attack (percentile) WJ-III Letter word i d e n t i f i c a t i o n (percentile) WRAT-III Spelling (percentile) SDRT: Reading comprehension (percentile) Verbal reasoning (RS, max 15) 41.20 26.81 55.89 21.36 44.79 26.15 61.46 28.18 74.30 23.10 41.93 31.64 10.12 2.53 7.07 2.43 10.48 3.31 66.36 20.37 67.45 26.16 61.35 26.03 5.40 <.001 62.81 23.42 2.23 <. 05 61.53 26.64 4.50 <.001 67.14 27.54 1.45 ns 71.52 27.28 0.79 ns 57.57 32.33 3.47 <. 01 9.87 2.44 0.72 ns 7.99 2.25 2.79 <.05 10.35 3.14 0.27 ns 65.34 20.69 0.36 ns 64.76 27.45 0.72 ns 65.48 28.92 69.41 27.02 0.99 7.95 2.06 7.53 1.83 1.56 ns 53.73 26.24 42.33 25.39 3.13 <.01 ns N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL; RS = raw score 81 Table 10 Grade 6 Performance of Immigrant/ESL and Native E n g l i s h Speaking C h i l d r e n with Canadian Born Parents Canadian/ English (n = 49) Immigrant/ ESL (n = 37) Measure Mean SD Mean T-SD test WRAT-III Arithmetic 42.72 24.12 (percentile) WJ-III Quantitative 57.04 23.66 concepts (percentile) WJ-III Calculation 47.44 28.34 (percentile) WJ-III Applied problems 64.67 28.01 (percentile) WJ-III Block rotation 72.31 27.63 (percentile) WJ-III Math fluency 44.02 30.89 (percentile) Rapid automatized naming 9.4 7 2.22 (time i n seconds) Working memory for 8.44 2.05 numbers (RS, max 12) WISC-III Digit span 11.43 3.54 (scaled score) WJ-III Word attack 71.06 19.85 (percentile) WJ-III Letter word 71.95 27.74 i d e n t i f i c a t i o n (percentile) WRAT-III Spelling (percentile) SDRT: Reading comprehension (percentile) Verbal reasoning 8.69 1.72 (RS, max 15) 62.84 26.81 3.62 <. 001 66.46 25.55 1.77 ns 61.40 31.43 2.15 <.05 69.54 25.77 0.83 75.72 26.33 0.58 8.51 2.33 0.14 11.25 3.52 0.24 69.30 19.99 0.41 75.89 26.74 0.66 66.81 26.44 71.68 24.89 0.87 48.86 25.97 46.03 27.75 0.49 8.30 1.71 1.06 ns ns 59.48 31.35 2.28 <.05 9.12 1.80 0.80 ns ns ns ns ns ns ns ns N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL; RS = raw score Country of Origin and Numeracy Performance The immigrant sample was d i v i d e d i n t o four c u l t u r a l groups: East Asians, Middle Easterners, Southeast Asians and Europeans, as described i n methods s e c t i o n . In order to determine i f there i s any d i f f e r e n c e i n numeracy performance between immigrant groups w i t h i n our sample, a one-way a n a l y s i s of variance (ANOVA) was c a l c u l a t e d on c h i l d r e n ' s performance on the WRAT-III Computational A r i t h m e t i c , WJ-III C a l c u l a t i o n and WJ-III Math Fluency t e s t s with four language groups as the independent v a r i a b l e . P e r c e n t i l e s were used f o r t h i s a n a l y s i s . These three numeracy measures were s e l e c t e d because, i n the previous analyses, they appear to be most s e n s i t i v e i n cap t u r i n g d i f f e r e n c e s between the two language groups. In a d d i t i o n , these three measures are very r e l i a b l e and provide a good sample of d i f f e r e n t aspects of c h i l d r e n ' s numeracy s k i l l s . I n d i v i d u a l mean d i f f e r e n c e s between the four language groups were assessed by F i s h e r ' s l e a s t s i g n i f i c a n t d i f f e r e n c e t e s t . WRAT-III computational arithmetic: S i g n i f i c a n t d i f f e r e n c e s i n performance on the WRAT-III Computational A r i t h m e t i c were found f o r the four language groups i n grade 2, F(3,80) = 4.20, p<.001; grade 3, F(3,84) = 6.66, p<.01; grade 4, F(3,78) = 4.24, p<.001 and grade 5, F(3,84) = 9.39, p<.001. Members of the European group were not present i n the grade 6 sample. Excluding the European group, there was a s i g n i f i c a n t d i f f e r e n c e f o r the 83 remaining three groups, F(2,32) = 6.15, p<.01. The European group was not included i n t h i s a n a l y s i s because there were only a few Europeans i n the grade 6 sample. This was p a r t l y due to the dropout r a t e among t h i s group, and p a r t l y because only one cohort had reached grade 6 i n the f i n a l year of the study. There was no s i g n i f i c a n t d i f f e r e n c e between the four groups i n kindergarten and grade 1. Table 11 summarizes the a n a l y s i s of variance among the four language groups' performance on the WRAT-III Computational A r i t h m e t i c across seven grades. I t was shown that the East Asian group had the highest scores compared to the other three groups. For r e s u l t s see Table 12. In kindergarten, East Asian had s i g n i f i c a n t l y higher scores than F i l i p i n o s (p<.05). In grade 1, there was not any s i g n i f i c a n t d i f f e r e n c e . In Grade 2, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.01), Europeans (p<.05) and F i l i p i n o s (pK.Ol). In grade 3, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.001)r F i l i p i n o s {p<.05) and Europeans (p<.001). In grade 4, East Asians (p<.01) and Middle Easterners (pK.Ol) had s i g n i f i c a n t l y higher scores than F i l i p i n o s . In grade 5, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.001), Europeans (p<.05), and F i l i p i n o s (p<.01). In grade 6, East Asians had s i g n i f i c a n t l y higher scores than F i l i p i n o s (p<.01) and Middle Easterners (p<. 05) . 8 4 Table 11 ANOVA of Four Language Groups' Performance on the WRAT-III Computational A r i t h m e t i c ( P e r c e n t i l e ) , across Seven Grades Grade Language group N Mean SD test P K Middle Easterners 35 54. 66 29.83 1.72 ns F i l i p i n o s 17 47 .12 23.42 East Asians 16 67.44 28 .19 Europeans 18 62.28 29.04 G 1 Middle Easterners 23 50.78 25.95 0.81 ns F i l i p i n o s 5 51.80 35.32 East Asians 11 66.00 28 . 04 Europeans 10 59.00 29.31 G 2 Middle Easterners 34 57.24 23.70 4.20 <. 01 F i l i p i n o s 18 53.44 22 .46 East Asians 16 78.50 17 .21 Europeans 16 60.63 24.77 G 3 Middle Easterners 36 44.00 23. 60 6. 66 <. 001 F i l i p i n o s 17 49.82 18.30 East Asians 22 69.91 27.75 Europeans 13 37.23 28.72 G 4 Middle Easterners 34 59.15 24.71 4.24 <. 001 F i l i p i n o s 13 35.62 26.81 East Asians 24 66.92 25.43 Europeans 11 53.18 30.28 G 5 Middle Easterners 29 51.10 23.56 9.39 <. 001 F i l i p i n o s 13 54.62 19.42 East Asians 36 77.61 19.99 Europeans 10 59.00 21.78 G 6 Middle Easterners 15 56.27 21.05 6.15 <. 01 F i l i p i n o s 7 42 .71 29.15 East Asians 13 79. 57 24.49 Europeans 0 - -85 Table 12 Mean D i f f e r e n c e : F i s h e r ' s LSD WRAT-III A r i t h m e t i c Grade Language K Gl G2 G3 G4 G5 G6 Group F i l i p i n o -7.54 1.02 -3.79 5.82 -23.53* 3.51 -13.55 Middle Easterner East 20.32 14.20 25.06* 20.09* 31.30* 22.99* 36.85* Asian F i l i p i n o East 12.78* 15.22 21.26* 25.91* 7.77 26.51* 23.30* Asian Middle Easterner East 5.16 7.00 17.88* 32.68* 13.73 18.61* Asian European European 7.62 8.22 3.39 -6.77 -5.97 7.90 Middle Easterner European 15.16 7.20 7.18 -12.59 17.57 4.38 F i l i p i n o *p<. 05 86 WJ-III calculation. Table 13 summarizes the a n a l y s i s of variance among the four language groups' performance on the WJ-I I I C a l c u l a t i o n t e s t across seven grades. There was a s i g n i f i c a n t d i f f e r e n c e i n the performances of the four language groups on the WJ-III C a l c u l a t i o n t e s t i n grade 3, F(3,84) = 7.82, pK.OOl, grade 4, F(3,79) = 2.91, p<.05 and grade 5, F(3,84) = 8.52, p<.001. In grade 6, excluding the European group (not present i n grade 6), there was a s i g n i f i c a n t d i f f e r e n c e f o r the remaining three groups, F(2,31) = 8.00, p<.01. There was no s i g n i f i c a n t d i f f e r e n c e between the four groups i n kindergarten, grade 1 and grade 2. I t was shown that the East Asian group had the highest scores compared to the other three groups. For r e s u l t s see Table 14. In kindergarten, grade 1 and grade 2, there was no s i g n i f i c a n t d i f f e r e n c e between i n d i v i d u a l groups. In grade 3, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners (p<.001), F i l i p i n o s (p<.001) and Europeans (p<.001). In grade 4, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners (p<.05), Europeans (p<.05) and F i l i p i n o s (p<.05). In grade 5, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners (p<.001), Europeans {p<.05) and F i l i p i n o s (p<.01). In grade 6, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.01) and F i l i p i n o s (p<. 01) . Table 13 ANOVA of Four Language Groups' Performance on the WJ-III C a l c u l a t i o n ( P e r c e n t i l e ) across Seven Grades F-Grade Language group N Mean SD test P K Middle Easterners 10 59.40 43.80 0.36 ns F i l i p i n o s 10 44.50 42.36 East Asians 5 66.00 37.95 Europeans 8 53.88 40.59 G 1 Middle Easterners 22 61. 05 26.95 0.83 ns F i l i p i n o s 5 68.83 32.11 East Asians 11 75. 09 19.66 Europeans 10 68 . 60 20.97 G 2 Middle Easterners 28 62.96 26.70 2 . 63 ns F i l i p i n o s 18 53.67 23.78 East Asians 16 76.69 18.44 Europeans 16 59.06 27.28 G 3 Middle Easterners 36 52.81 23.41 7.82 <. 001 F i l i p i n o s 17 48.06 20.24 East Asians 22 76.68 18.79 Europeans 13 48 . 62 25. 40 G 4 Middle Easterners 34 50.85 19. 91 2.91 <. 05 F i l i p i n o s 13 49.15 24.52 East Asians 25 66.08 24.70 Europeans 11 48.36 25.48 G 5 Middle Easterners 29 49.44 22.59 8.53 <. 001 F i l i p i n o s 13 58.31 26.59 East Asians 36 77.23 22.00 Europeans 10 60.30 17.85 G 6 Middle Easterners 15 50.35 27.49 8.00 <. 01 F i l i p i n o s 7 40.29 33.01 East Asians 13 83.75 21.90 Europeans 0 - -88 Table 14 Mean D i f f e r e n c e : F i s h e r ' s LSD WJ-III C a l c u l a t i o n Grade Language K GI G2 G3 G4 G5 G6 Group F i l i p i n o -14.90 7.75 -9.30 -4.75 -1.70 8.86 -10.06 Middle Easterner East 21.50 6.29 23.02* 28.62* 16.93* 18.93* 43.46* Asian F i l i p i n o East 6.60 14.05 13.72 23.88* 15.23* 27.79* 33.40* Asian Middle Easterner East 12.13 6.49 17.63* 28.07* 17.72* 16.93* Asian European European -5.52 7.55 -3.90 -4.19 -2.49 10.85 Middle Easterner European 9.38 -.20 5.40 0.59 -0.79 1.99 F i l i p i n o *p<. 05 89 WJ-III math fluency. The a n a l y s i s of variance among the four language groups' performance on the WJ-III Math Fluency t e s t was performed. The WJ-III Math Fluency t e s t was not administered i n kindergarten and grade 1. There were s i g n i f i c a n t d i f f e r e n c e s i n the performance of the four language groups on the WJ-III Math Fluency t e s t i n grade 2, F(3,80) = 5.70 p<.01; grade 3, F(3,83) = 5.41, p<.01; grade 4, F(3,79) = 3.82, p<. 05; and grade 5, F(3,84) = 8.57, p<.001. In grade 6, excluding the European group (not present i n grade 6), there was a s i g n i f i c a n t d i f f e r e n c e f o r the remaining three groups, F(2,32) = 6.97, p<.01. For r e s u l t s , see Table 15. I t was shown that the East Asian group had the highest scores compared to the other three groups. For r e s u l t s , see Table 16 below. In Grade 2, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners (p<.01) and F i l i p i n o s (p<.001). In grade 3, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.01), Europeans (p<.05) and F i l i p i n o s (p<.02). In grade 4, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners (p<.01) and F i l i p i n o s (p<.01). In grade 5, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.001) and F i l i p i n o s (p<.05). In grade 6, East Asians had s i g n i f i c a n t l y higher scores than Middle Easterners {p<.001) and F i l i p i n o s (p<.05). Table 15 ANOVA of Four Language Groups' Performance on the WJ-III Math Fluency- ( P e r c e n t i l e ) across Five Grades Grade Language group N Mean SD F-test P G 2 Middle Easterners 34 49.44 22.76 5.70 <. 01 F i l i p i n o s 18 40.17 28 . 61 East Asians 16 73.63 15. 90 Europeans 16 56.44 30.31 G 3 Middle Easterners 36 47.83 23.91 5.41 <. 01 F i l i p i n o s 16 41.44 29.04 East Asians 22 72.82 26.05 Europeans 13 50.31 33. 69 G 4 Middle Easterners 34 44. 60 30.55 3.81 <. 05 F i l i p i n o s 13 37.15 31.48 East Asians 25 68.39 31.84 Europeans 11 48.09 35.39 G 5 Middle Easterners 29 40.64 33. 08 8.57 <. 002 F i l i p i n o s 13 52.54 25.47 East Asians 36 76.13 25.90 Europeans 10 57 . 60 26. 57 G 6 Middle Easterners 15 46.29 31.90 6.97 <. 01 F i l i p i n o s 7 46.29 31.90 East Asians 13 81.40 22.83 Europeans 0 - -Note. This measure was not administered i n kindergarten and grade 1 Table 16 Mean D i f f e r e n c e : F i s h e r ' s LSD WJ-III Math Fluency Grade Language G2 G3 G4 G5 G6 Group F i l i p i n o -9.27 -6.40 -7.44 11.90 -0.56 Middle Easterner East 33.46* 31.38* 31.23* 23.59* 35.11* Asian F i l i p i n o East 24.18* 24.98* 23.79* 35.48* 34.55* Asian Middle Easterner East 17.19 22.51* 20.29 18.52 Asian European European 7.00 2.47 3.49 16.96 Middle Easterner European 16.27 8.87 10.94 5.06 F i l i p i n o *p<. 05 92 Correlation among Measures in Early and Later Grades. To c a l c u l a t e the r e l a t i o n s h i p between kindergarten and grade 6 measures i n our l o n g i t u d i n a l sample, a Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t was used. The sample s i z e of c h i l d r e n present i n both of these grades was sm a l l , and i n the case of some numeracy measures (e.g., Math Fluency, Q u a n t i t a t i v e Concepts and RAN) not s u f f i c i e n t to c a l c u l a t e these c o r r e l a t i o n s . Therefore, the c o r r e l a t i o n between grade one and f i v e measures with l a r g e sample s i z e s was incl u d e d as w e l l . The c o r r e l a t i o n s were computed between measures w i t h i n the same areas. A l s o , c o r r e l a t i o n between kindergarten and grade one memory measures and numeracy measures administered i n grades s i x and f i v e was computed. Wherever p o s s i b l e , p e r c e n t i l e s were used. Kindergarten and grade 6 numeracy and memory correlations. For r e s u l t s see Table 17 below. In kindergarten, the l a r g e s t number of s i g n i f i c a n t c o r r e l a t i o n s were between the WRAT-III Computational A r i t h m e t i c t e s t and grade 6 measures. The WRAT-III Computational A r i t h m e t i c t e s t administered i n kindergarten was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d with f o l l o w i n g grade 6 t e s t s : WRAT-III Computational A r i t h m e t i c t e s t , r(50) = .34, p<.05, the WJ-III Q u a n t i t a t i v e Concepts t e s t , r(44) = .32, p<.05, the WJ-III C a l c u l a t i o n t e s t , r(49) = .33, p<.05, the WJ-I I I A p p l i e d Problems t e s t , r(50) = .46, p<.01, and the WJ-III Math Fluency t e s t , r(50) = .33, p<.05. 93 Table 17 The I n t e r c o r r e l a t i o n among Numeracy and Memory Measures Administered i n Kindergarten and Grade 6 (Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t s ) Grade 6 measure Kindergarten measure c CD CD o u CD i—H r H - H - H > - H c - H • P o - P • H +J o - P CO a CD -rH a - P CD CD e ro CD 4-> CD O N 4-> U ro Ti O r H - H -p - H r4 r H a> u MH 4-1 • H — +J CD —- - H CD — — . rO u CD C Cu o CD r H a CD X ! CD 6 < <—1 CO -— r H r H Cu — O r H 4-> r H O • H rC - H a r H - H CO - H 4-> M - P d CO O +J sC CO PQ S 4-> l-l C 4-> C a C (0 1—1 CD 1—1 I—I CD M CD I—I CD i—i CD 1 O 1—1 CD H O 1—1 r H n O H O • d r4 1—1 o 1—1 U H X ! I—I M M U - H CD 1 1 CD 1 O 1 CD 1 CD a a I"} o l-D l-D U a a rO — ' o 3= — s a •—- - — PC CO Ti G O U CD CO C - H £ CD •H e e -H WRAT-III Arithmetic (percentile) .34t .32t .33t .46* .04 .33t .10 Number i d e n t i f i c a t i o n (raw score) .33t .15 .31t .46* .25 .31t -.10 SATZ (raw score) .32t .25 .33t .31t .27 .20 -.02 Beery-Buktenica VMI test (percentile) .16 .17 . 11 .25 .28t .24 -.33t Working memory (raw score) . 14 .11 .31t .19 .18 .18 -.10 WISC-III Digit span (scaled score) .33t .22 .27 .36t .27 .13 -.24 * C o r r e l a t i o n i s s i g n i f i c a n t at the .01 l e v e l t C o r r e l a t i o n i s s i g n i f i c a n t at the .05 l e v e l 94 The Number I d e n t i f i c a t i o n t e s t administered i n kindergarten was p o s i t i v e l y c o r r e l a t e d with these grade 6 t e s t s : the WRAT-III Computational A r i t h m e t i c t e s t , r(50) = .33, p<.05, the WJ-III C a l c u l a t i o n t e s t , r(49) = .31, p<.05, the WJ-III A p p l i e d Problems t e s t , r(50) = .46, p<.01 and the WJ-III Math Fluency t e s t , r(50) = .31, p<.05. The SATZ R e c o g n i t i o n - D i s c r i m i n a t i o n t e s t (kindergarten) was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d with these grade 5 measures: the WRAT-III Computational A r i t h m e t i c t e s t , r(50) = .31, p<.05, the WJ-III the WJ-III C a l c u l a t i o n t e s t , r(49) = .33, p<.05, and the WJ-III A p p l i e d Problems t e s t , r(50) = .31, p<.05. The Beery-Buktenica Developmental Test of V i s u a l Motor I n t e g r a t i o n t e s t (kindergarten) was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d with WJ-III Block Rotation t e s t s , r(50) = .28, p<.05 (grade 5) . From memory measures, the Working Memory t e s t (kindergarten) was s i g n i f i c a n t l y c o r r e l a t e d with the WJ-III C a l c u l a t i o n t e s t (grade 5), r(43) = .31, p<.05, and the D i g i t Span (kindergarten) was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d to the WRAT-III Computational A r i t h m e t i c t e s t , r(50) = .33, p<.05 and the WJ-III A p p l i e d Problems t e s t , r(50) = .36, p<.05 (grade 6) . Grade 1 and 5 numeracy and memory correlations. For r e s u l t s see Table 18 below. The WJ-III numeracy measures (Q u a n t i t a t i v e Concepts, C a l c u l a t i o n and Math Fluency) and the WRAT-III 95 Table 18 The I n t e r c o r r e l a t i o n among Numeracy and Memory Measures Administered i n Grades 1 and 5 (Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t s ) Grade 5 measure a CD CD o u CD r H r H - H - H > - H c • H 4-1 o 4-1 - H 4-> o 4 J cO c T J ~ CD 4-1 a • H 4-1 CD CD CO e m a) 4-> (D O N TJ) 4-> o CO T J O r H • H C -p - H M r H CD M m 4-1 O • H - — 4-1 CD - H CD CO O U CD c a r H a o (!) X ! CD £ CD <C r H r H r H o- — O r H 4-> r H O CO - H CO - H (X r H - H CO - H 4-> 1—1 4-1 CH co O 4 J <C co OQ 4-1 2 4-1 3 C I—I c 4-> C e C C CO -iH H CD H H 0) i—i ai t—I CD 1—1 CD 1 u 1—1 CD 1—1 o M r H 1—I O t—1 O T J a CD EH U I—t o 1—1 n M , Q I—I U 1—1 U • H - H g <=£ CD 1 c 1 cu 1 o 1 CD 1 CD Grade 1 measure « a r o o h 3 r4 l-D a, H> a, CO CO 4-1 is — S O is a !S is — WRAT-III Arithmetic .38* .50* .33* .46* 04 .38* - . 1 2 (percentile) WJ-III Quantitative .49* .46* .41* . 51* 17 .46* - . 3 1 * concepts (percentile) WJ-III Calculation .37* .43* .30t . 42* 60 .44* - . 2 7 t (percentile) WJ-III Applied .44* .57* .32* .56* 19 .43* - . 2 7 t problems (percentile) WJ-III Block .19 .19 - . 0 1 .28t — # 01 .16 - . 0 1 rotation (percentile) Rapid automatized - . 2 1 - . 1 8 - . 1 1 - . 2 1 16 - . 3 3 * - . 5 8 naming (time i n seconds) Working memory .33* . 31* .19 .31t 05 .29t - . 2 7 t (raw score) WISC-III Digit span . 15 .30t . 14 .12 11 . 15 - . 0 7 (scaled score) * C o r r e l a t i o n i s s i g n i f i c a n t at the .01 l e v e l t C o r r e l a t i o n i s s i g n i f i c a n t at the .05 l e v e l 96 Computational A r i t h m e t i c were s i g n i f i c a n t l y c o r r e l a t e d to each other i n grades 1 and 5. The WRAT-III Computational A r i t h m e t i c t e s t administered i n Grade 1 was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d with the f o l l o w i n g grade 5 t e s t s : WRAT-III Computational A r i t h m e t i c t e s t , r(65) = .38, p<.05, the WJ-III Q u a n t i t a t i v e Concepts t e s t , r(65) = .50, p<.01, the WJ-III C a l c u l a t i o n t e s t , r(65) = .33, p<.05, the WJ-III A p p l i e d Problems t e s t , r(65) = .46, p<.01, and the WJ-III Math Fluency t e s t , r(65) = .38, p<.05. The WJ-III Q u a n t i t a t i v e Concepts t e s t administered i n grade 1 was s i g n i f i c a n t l y c o r r e l a t e d to the f o l l o w i n g grade 5 measures: WRAT-III Computational A r i t h m e t i c t e s t , r(67) = .49, p<.01, the WJ-III Q u a n t i t a t i v e Concepts t e s t , r(67) = .46, p<.01, the WJ-III C a l c u l a t i o n t e s t , r(67) = .41, p<.01, the WJ-I I I A p p l i e d Problems t e s t , r(67) = .51, p<.01, and the WJ-III Math Fluency t e s t , r(67) = .46, p<.01. The WJ-III C a l c u l a t i o n t e s t administered i n grade 1 was s i g n i f i c a n t l y c o r r e l a t e d to the f o l l o w i n g grade 5 measures: the WRAT-III Computational A r i t h m e t i c t e s t , r(65) = .37, p<.01, the WJ-III Q u a n t i t a t i v e Concepts t e s t , r(65) = .43, p<.01, the WJ-I I I C a l c u l a t i o n t e s t , r(65) = .30, p<.05, the WJ-III A p p l i e d Problems t e s t , r(65) = .42, p<.01, and the WJ-III Math Fluency t e s t , r(65) = .44, p<.01. 97 The WJ-III A p p l i e d Problems t e s t administered i n grade 1 was s i g n i f i c a n t l y c o r r e l a t e d to the f o l l o w i n g grade 5 measures: the WRAT-III Computational A r i t h m e t i c t e s t , r(67) = .44, p<.01, the WJ-III Q u a n t i t a t i v e Concepts t e s t , r(67) = .57, p<.01, the WJ-III C a l c u l a t i o n t e s t , r(67) = .33, p<.01, the WJ-III A p p l i e d Problems t e s t , r(67) = .56, p<.01, and the WJ-III Math Fluency t e s t , r(67) = .43, p<.01. In a d d i t i o n , there was s i g n i f i c a n t c o r r e l a t i o n between the WJ-III Block Rotation t e s t (grade 1) and the WJ-III A p p l i e d Problems t e s t (grade 5), r(67) = .28 p<.05; the Working Memory f o r Numbers t e s t (gradel) and the WRAT-III Computational A r i t h m e t i c t e s t , r(67) = .33, p<.05, the WJ-III Q u a n t i t a t i v e Concepts t e s t , r(67) = .31, p<.05, the WJ-III A p p l i e d Problems t e s t , r(67) = .31, p<.05, and the WJ-III Math Fluency t e s t , r(67) = .29, p<.05; and WISC-III D i g i t Span (grade 1) and the WJ-III Q u a n t i t a t i v e Concepts t e s t (grade 5), r(67) = .30, p<.05. Kindergarten and grade 6 memory correlations. For r e s u l t s see Table 19 below. In kindergarten, the WISC-III D i g i t Span t e s t s i g n i f i c a n t l y c o r r e l a t e d with grade 6's Working Memory f o r Numbers t e s t , r(50) = .47, p<.0l, and the WISC-III D i g i t Span, r(50) = .47, p<.01. In a d d i t i o n , the kindergarten Working Memory f o r Numbers t e s t s i g n i f i c a n t l y c o r r e l a t e d with grade 6 WISC-III D i g i t Span t e s t , r(44) = .34, p<.05. Table 19 The I n t e r c o r r e l a t i o n among Memory Measures Administered i n K and Grade 6 (Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t s ) Grade 6 measure Working memory for WISC-III Digit Kindergarten measure numbers (raw score) span(scaled score) Working memory for .34t .08 numbers (raw score) WISC-III Digit span .47* .47* (scaled score) * Correlation i s s i g n i f i c a n t at the .01 l e v e l t Correlation i s s i g n i f i c a n t at the .05 l e v e l Grade 1 and 5 memory correlations. In grade 1, the WISC-III D i g i t Span t e s t s i g n i f i c a n t l y c o r r e l a t e s w i t h grade 5's Working Memory f o r Numbers t e s t , r(67) = .39, p<.01, and the WISC-III D i g i t Span, r(67) = .49, p<.01. The grade 1 Working Memory f o r Numbers t e s t s i g n i f i c a n t l y c o r r e l a t e d with the grade 5 WISC-III D i g i t Span t e s t , r(44) = .30, p<.05. For r e s u l t s see Table 20 below. Kindergarten and grade 6 literacy correlations. In kindergarten, the Phoneme De l e t i o n t e s t was s i g n i f i c a n t l y c o r r e l a t e d to the grade 6 WRAT-III S p e l l i n g t e s t , r(50) = .28, p<.05. For r e s u l t s see Table 21 below. 99 Table 20 The I n t e r c o r r e l a t i o n among Memory Measures Administered i n Grades 1 and 5 (Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t s ) Grade 5 measure Working memory for WISC-III Digit span Grade 1 measure numbers (raw score) (scaled score) Working memory for .21 .30t numbers (raw score) WISC-III Digit span .39* .49* (scaled score) * Correlation i s s i g n i f i c a n t at the .01 l e v e l t Correlation i s s i g n i f i c a n t at the .05 l e v e l Table 21 The I n t e r c o r r e l a t i o n among L i t e r a c y Measures Administered i n Kindergarten and Grade 6 (Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t s ) Grade 6 Measure (percentile) Kindergarten measure Letter i d e n t i f i c a t i o n (raw score) Phoneme deletion (raw score) WJ-III Word attack .21 WJ-III Letter word i d e n t i f i c a t i o n -.01 WRAT-III Spelling .28t SDRT: Reading comprehension . 11 .15 .02 .21 .12 * C o r r e l a t i o n i s s i g n i f i c a n t at the .01 l e v e l t C o r r e l a t i o n i s s i g n i f i c a n t at the .05 l e v e l 100 Grade 1 and 5 literacy correlations. There was s i g n i f i c a n t c o r r e l a t i o n between a l l grade 1 l i t e r a c y measures and a l l l i t e r a c y measures administered i n grade 5. For r e s u l t s see Table 22 below. Table 22 The I n t e r c o r r e l a t i o n among L i t e r a c y Measures Administered i n Grades 1 and 5 (Pearson-Product Moment C o r r e l a t i o n C o e f f i c i e n t s ) Grade 5 measure ( p e r c e n t i l e ) WJ-III WJ-III WRAT-III SDRT: Reading Word L e t t e r S p e l l i n g comprehension Grade 1 measure attack word (p e r c e n t i l e ) WJ-III Word at t a c k .49* .57* WJ-III L e t t e r word .55* .56* i d e n t i f i c a t i o n WRAT-III S p e l l i n g .29t .42* * C o r r e l a t i o n i s s i g n i f i c a n t at the .01 l e v e l t C o r r e l a t i o n i s s i g n i f i c a n t at the .05 l e v e l The grade 1 WJ-III Word Attack t e s t s i g n i f i c a n t l y c o r r e l a t e d with the f o l l o w i n g grade 5 measures: the WJ-III Word Attack t e s t , r(67) = .49, p<.01, the WJ-III L e t t e r I d e n t i f i c a t i o n t e s t , r(67) = .57, p<.01, the WRAT-III S p e l l i n g t e s t , r(65) = .50, p<.01 and the SDRT: Diagnostic Reading Comprehension t e s t , r(65) = .34, p<.01. The grade 1 WJ-III L e t t e r I d e n t i f i c a t i o n t e s t s i g n i f i c a n t l y c o r r e l a t e d with the .50* .34* .58* .33* .43* .30t 101 f o l l o w i n g grade 5 measures: the WJ-III Word Attack t e s t , r(67) = .55, p<.01, the WJ-III L e t t e r I d e n t i f i c a t i o n t e s t , r(67) = .56, p<.01, the WRAT-III S p e l l i n g t e s t , r(65) = .58, p<.01 and the SDRT: Diagnostic Reading Comprehension t e s t , r(65) = .33, p<.01. The grade 1 WRAT-III S p e l l i n g t e s t s i g n i f i c a n t l y c o r r e l a t e d with these grade 5 measures: the WJ-III Word Attack t e s t , r(64) = .29, p<.05, the WJ-III L e t t e r I d e n t i f i c a t i o n t e s t , r(64) = .42, p<.01, the WRAT-III S p e l l i n g t e s t , r(63) = .43, p<.01 and the SDRT: Diagnostic Reading Comprehension t e s t , r(63) = .30, p<.05. Summary of Children's Performance Results Independent T-test analysis. A t - t e s t a n a l y s i s revealed some s i g n i f i c a n t d i f f e r e n c e s between the immigrant/ESL and Canadian born p a r e n t s / E n g l i s h groups across the range of grades. These d i f f e r e n c e s were mainly i n numeracy group measures, and were stronger i n l a t e r grades. In kindergarten, there was no d i f f e r e n c e i n the performance of the two groups on almost any measures. The only exception was the D i g i t Span t e s t , on which immigrant/ESL c h i l d r e n had lower scores than n a t i v e E n g l i s h speaking c h i l d r e n . In grade 1, ESL c h i l d r e n had s i g n i f i c a n t l y higher scores on the WRAT-III Computational A r i t h m e t i c t e s t , the WJ-III C a l c u l a t i o n t e s t , the WJ-III Block Rotation t e s t s and the Working Memory t e s t ; however, these d i f f e r e n c e s were mainly i n raw scores. The main d i f f e r e n c e between the groups was not evident u n t i l l a t e r grades. Immigrant/ESL c h i l d r e n had 102 s i g n i f i c a n t l y higher scores than the Canadian born p a r e n t s / E n g l i s h group on the WRAT-III Computational A r i t h m e t i c t e s t ( p e r c e n t i l e s ) i n each grade from grade 2 to grade 6. Immigrant/ESL c h i l d r e n a l s o obtained higher scores on the WJ-III C a l c u l a t i o n ( p e r c e n t i l e ) and the WJ-III Math Fluency ( p e r c e n t i l e ) t e s t s than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents from grade 3 to grade 6. In a d d i t i o n , immigrant/ESL c h i l d r e n had s i g n i f i c a n t l y higher scores on the Working Memory f o r Numbers t e s t and the Number Seri e s t e s t (part of the WJ-III Q u a n t i t a t i v e Concepts t e s t ) i n grade 3 and the WJ-I I I Q u a n t i t a t i v e Concepts t e s t ( p e r c e n t i l e ) i n grade 5. L i t e r a c y measures were not part of the research purpose of t h i s study, but were administered to gain info r m a t i o n about the language p r o f i c i e n c y of the immigrant sample compared to c h i l d r e n from E n g l i s h speaking households. Immigrant/ESL c h i l d r e n had lower performance on some l i t e r a c y measures than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents, such as Verbal Reasoning i n grades 2 and 3, and on the SDRT: Diagnostic Reading Comprehension t e s t ( p e r c e n t i l e ) i n grade 5. This i s not s u r p r i s i n g , c o n s i d e r i n g the language disadvantage of ESL c h i l d r e n i n t h i s sample. However, i n grade 4, immigrant/ESL c h i l d r e n had s u r p r i s i n g l y s i g n i f i c a n t l y higher scores than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents on the WRAT-III S p e l l i n g t e s t ( p e r c e n t i l e ) . O v e r a l l , immigrant/ESL 103 c h i l d r e n had higher scores on a number of measures i n a l l grades except kindergarten. The d i f f e r e n c e was small i n grades one and two, but became much more evident i n l a t e r grades. ANOVA analysis of four language groups. On three s e l e c t e d measures (WRAT-III Computational A r i t h m e t i c , WJ-III C a l c u l a t i o n and WJ-III Math Fluency) the performance of four language groups (Middle Easterners, F i l i p i n o s , East Asians, and Europeans) was analyzed. O v e r a l l , on a l l three numeracy measures (WRAT-III Computational A r i t h m e t i c , WJ-III C a l c u l a t i o n and WJ-III Math Fluency), c h i l d r e n with East Asian o r i g i n s had the highest scores compared to other groups. The d i f f e r e n c e between groups was s i g n i f i c a n t i n grades 2 to 6, with the exception of the WJ-I I I C a l c u l a t i o n t e s t i n grade 3. Correlation among early and later measures. When the l o n g i t u d i n a l data were analyzed, a strong p o s i t i v e r e l a t i o n s h i p was found between many numeracy and r e l a t e d memory measures administered i n kindergarten and grade 6. The c o r r e l a t i o n i n these grades was not strong f o r l i t e r a c y measures. This i s l i k e l y due to the e a r l y i n t e r v e n t i o n l i t e r a c y programs i n the p a r t i c i p a t i n g schools. Many c h i l d r e n who st r u g g l e i n reading and l i t e r a c y i n kindergarten are average by grade 6 due to the high q u a l i t y of education i n these schools. A l s o , immigrant c h i l d r e n who have l i m i t e d E n g l i s h p r o f i c i e n c y i n kindergarten are a l s o weak i n l i t e r a c y , but are l i k e l y to improve t h e i r E n g l i s h and general l i t e r a c y s k i l l s i n l a t e r grades. The r e l a t i o n s h i p between performance i n lower and higher grades i s even more evident when c o r r e l a t i n g grade 1 and 5 measures i n a l l three areas (numeracy, memory and l i t e r a c y ) with l a r g e r sample s i z e s . This i m p l i e s that c h i l d r e n who had higher scores i n lower grades were l i k e l y to have higher scores i n l a t e r grades. A l s o , there appears to be a r e l a t i o n s h i p between memory and numeracy measures. E a r l y memory measures, e s p e c i a l l y the Working Memory t e s t , seem to be p r e d i c t i v e of the l a t e r numeracy measures. Numeracy Questionnaires In the f i n a l year of our study (grades 5 and 6), c h i l d r e n were asked to answer questions r e l a t e d to t h e i r a t t i t u d e s towards mathematics. Parents of these c h i l d r e n were given a questionnaire addressing s i m i l a r i s s u e s . Most of the questions r e q u i r e d "yes or no" answers. Some of the questions were answered i n m u l t i p l e choice forms. In p a r e n t a l q u e s t i o n n a i r e s , parents were asked to rat e some statements from 1 to 4 (s t r o n g l y disagree to s t r o n g l y agree). The data were analyzed using a c r o s s - t a b u l a t i o n (chi-square) t e s t and a nonparametric t e s t . Children's questionnaire. In Tables 23 and 24 below, the c h i l d r e n ' s numeracy questionnaire was analyzed using a c r o s s -t a b u l a t i o n (chi-square) t e s t . A s i g n i f i c a n t l y higher p r o p o r t i o n 105 Table 23 Chil d r e n ' s Questionnaire (Part 1) Canadian/ Immigrant/ English ESL Question Answer (n = 93) (n = 84) P • Do you receive help with yes 61 (65.6%) 71 (84.5%) <. 01 mathematics outside of school? no 32 (34.4%) 13 (15.5%) • Is i t very important for you yes 81 (87.1%) 80 (95.2%) ns to get high grades i n no 12 (12.9%) 4 (4.8%) mathematics? • Do you think that mathematics yes 89 (95.7%) 82 (97.6%) ns i s an important subject at no 4 (4.3%) 2 (2.4%) school? • Do you l i k e mathematics? yes 61 (65.6%) 68 (81%) <. 05 no 32 (34.4%) 16 (19%) • Do you think that you w i l l yes 86 (92.5%) 84 (100%) <. 05 need mathematics l a t e r i n no 7 (7.5%) 0 (0%) l i f e ? • Do you learn useful things i n yes 93 (100%) 77 (91.7%) <. 01 mathematics classes? no 0 (0%) 7 (8.3%) • Do you think that i t i s yes 88 (94.6%) 77 (91.7%) ns important to do your homework no 5 (5.4%) 7 (8.3%) i n mathematics? • Could you do better i n yes 81 (87.1%) 80 (95.2%) ns mathematics i f you t r i e d no 12 (12.9%) 4 (4.8%) harder? • Do you want to do better i n yes 74 (79.6%) 78 (92.9%) <. 05 mathematics than you do now? no 19 (20.4%) 6 (7.1%) • Do your parents practice yes 55 (59.1%) 56 (66.7%) ns mathematics with you? no 38 (40.9%) 28 (33.3%) • Do you use mathematics outside yes 72 (77.4%) 67 (79.8%) ns of school? no 21 (22.6%) 17 (20.2%) • Would you be happy i f someone yes 37 (39.8%) 54 (65.1%) ns cancelled a l l math classes? no 56 (60.2%) 29 (34.9%) 106 Table 24 Child r e n ' s Questionnaire Responses (Part 2) Answer Canadian/ English (n = 93) Immigrant/ ESL (n = 84) P Question: Why well do you want to do in school? • To get a good job l a t e r 37 (39.8%) 23 (27.4%) ns • To be well educated 34 (36.6%) 38 (45.2%) • To earn l o t s of money 6 (6.4%) 6 (7.2%) To please your parents and family To be happy 7 (7.5%) 9 (9.7%) 9 8 (10.7%) (9.5%) Question: What influences how you do i n school? • Your talent and s k i l l s 12 (12.9%) 15 (17.9%) ns • 'Your work and tryi n g 61 (65.6%) 52 (61.9%) • Help which you get from your teachers, tutors, parents and friends 20 (21.5%) 17 (20.2%) Question: How well do mathematics compared children? you do i n to other • • You do better than other kids You do about the same 21 (22.6%) 58 (62.4%) 40 38 (47.6%) (45.2%) <. 01 • You are not as good as other kids 14 (15.0%) 6 (7.2%) Note . Canadian/English = Canadian born parents and English as a f i r s t l a n g u a g e ; Immigrant/ESL = f o r e i g n b o r n p a r e n t s and ESL 107 of immigrant/ESL c h i l d r e n than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents i n d i c a t e d that they r e c e i v e help with mathematics outside school (mostly from f a m i l y i n c l u d i n g s i b l i n g s , but a l s o from f r i e n d s and t u t o r s ) , t hat they l i k e mathematics, that they t h i n k that they w i l l need mathematics l a t e r i n l i f e and that they want to do b e t t e r i n mathematics than they do now. When they were asked to compare t h e i r own performance to other c h i l d r e n , immigrant/ESL c h i l d r e n were more l i k e l y to i n d i c a t e that they do b e t t e r than other kids than were na t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents. In c o n t r a s t , n a t i v e E n g l i s h speaking c h i l d r e n were more l i k e l y to s t a t e that they do about the same as other c h i l d r e n . Native E n g l i s h speaking c h i l d r e n with Canadian born parents a l s o i n d i c a t e d more than the immigrant/ESL group that they l e a r n u s e f u l things i n mathematics c l a s s e s . Children's questionnaire and different immigrant groups. In Tables 25 and 2 6 below, the answers of immigrant c h i l d r e n belonging to one of three language groups (East Asian, F i l i p i n o , and Middle Eastern) were analyzed using a c r o s s - t a b u l a t i o n ( c h i -square) t e s t . The European group was not i n c l u d e d i n t h i s a n a l y s i s due to i t s small sample, s i z e . A s i g n i f i c a n t l y higher p r o p o r t i o n of East Asian and Middle Eastern c h i l d r e n than F i l i p i n o c h i l d r e n i n d i c a t e d that they l i k e mathematics. East Asian c h i l d r e n were most l i k e l y to i n d i c a t e 108 Table 25 Children's Questionnaire: Immigrant Groups (Part 1) Question Answer East Asian (n = 31) F i l i p i n o (n = 17) Middle Eastern (n = 27) P Do you r e c e i v e help with math outside of school? yes 25 (80.6%) 16 (94.1%) 21 (77.8%) no 6 (19.4%) 1 (5.9%) 6 (22.2%) ns Is i t very important for you to get high grades i n mathematics? yes 29 (93.5%) 16 (94.1%) 26 (96.3%) no 2 (6.5%) 1 (5.9%) 1 (3.7%) ns Do you think that mathematics i s an important subject at school? yes 30 (96.8%) 17 (100%) 26 (96.3%) no 1 (3.2%) 0 (0%) 1 (3.7%) ns Do you l i k e mathematics? Do you think that you w i l l need mathematics l a t e r i n l i f e ? yes no yes no 28 (90.3%) 10 (58.8%) 23 (85.2%) 3 (9.7%) 7 (41.2%) 4 (14.8%) <. 05 31 (100%) 0 (0%) 17 (100%) 0 (0%) 27 (100%) 0 (0%) Do you learn useful things i n mathematics classes? yes 27 (87.1%) 16 (94.1%) 25 (92.6%; no 4 (12.9%) 1 (5.9%) 2 (7.4%) ns Do you think that i t i s important to do your homework i n mathematics? yes 28 (90.3%) 15 (88.2%) 25 (92.6%) no 3 (9.7%) 2 (11.8%) 2 (7.4%) ns Could you do better i n mathematics i f you t r i e d harder? yes 30 (96.8%) 17 (100%) 24 (88.9%; no 1 (3.2%) 0 (0%) 3 (11.1%; ns 109 Table 25 (Continued) Question Answer East Asian (n = 31) F i l i p i n o (n = 17) Middle Eastern (n = 27) Do you want to do better i n mathematics than you do now? Do your parents practice mathematics with you? Do you use mathematics outside of school? Would you be happy i f someone cancelled a l l math classes? yes no yes no yes no yes no 29 (93.5%) 2 (6.5%) 18 (58.1%) 13 (41.9%) 25 (80.6%) 6 (19.4%) 12 (38.7%) 19 (61.3%) 15 (88.2%) 2 (11.8%) 12 (70.6%) 5 (29.4%) 12 (70.6%) 5 (29.4%) 8 (47.1%; 9 (52.9%; 25 (92.6%) 2 (7.4%) 18 (66.7%) 9 (33.3%) 22 (81.5%) 5 (18.5%) 7 (26.9%) 19 (73.1%) ns ns ns ns 110 Table 26 Child r e n ' s Questionnaire Responses: Immigrant Groups (Part 2) Answer East Asian F i l i p i n o (n = 31) (n = 17) Middle Eastern (n = 27) P • To get a good job la t e r • To be well educated Question: Why do you want to do well i n school? 5 (16.1%) 6 (35.3%) 10 (37.0%) ns 16 (51.6%) 7 (41.1%) 10 (37.0%; To earn l o t s of money 1 (3.2%) 2 (11.8%) 2 (7.4%; To please your parents and family To be happy 5 (16.1%) 0 (0%) 4 (14.8%) 4 (13.0%) 2 (11.8%) 1 (3.8%) Question: What influences how you do i n school? Your talent and s k i l l s 5 (16.1%) 4 (23.5%) 5 (18.5%) ns • Your work and trying 20 (64.5%) 9 (53.0%) 15 (55.6%) • Help which you get from your teachers, tutors, parents and friends • You do better than other kids 6 (19.4%) 4 (23.5%) 7 (25.9%) Question: How well do you do i n mathematics compared to other children? 21 (67.7%) 4 (23.5%) 12 (44.4%) <.01 • You do about the same 9 (29.1%) 9 (53.0%) 14 (51.9%) • You are not as good as 1 (3.2%) 4 (23.5%) 1 (3.7%) other kids I l l that they do b e t t e r than other k i d s , f o llowed by Middle Eastern c h i l d r e n . A higher p r o p o r t i o n of F i l i p i n o c h i l d r e n i n d i c a t e d that they are not as good as other kids i n mathematics than East Asian and Middle Eastern c h i l d r e n . The d i f f e r e n c e between groups was s i g n i f i c a n t f o r t h i s item. Parents' questionnaire. Using the c r o s s - t a b u l a t i o n a n a l y s i s , i t was demonstrated that immigrant/ESL parents a t t r i b u t e d s i g n i f i c a n t l y more importance than Canadian born/native E n g l i s h speaking parents to t h e i r c h i l d r e n g e t t i n g a u n i v e r s i t y education and to t h e i r c h i l d r e n o b t a i n i n g high grades i n mathematics. For r e s u l t s see Table 27 below. In the c r o s s - t a b u l a t i o n analyses, there were no s i g n i f i c a n t d i f f e r e n c e s revealed between the two groups (immigrant/ESL and Canadian born parents/English) i n the p a r e n t a l m u l t i p l e choice responses to the quest i o n n a i r e . For r e s u l t s , see Table 28 below. The questions r e q u i r i n g "yes" and "no" answers on the p a r e n t a l questionnaire were analyzed using c r o s s - t a b u l a t i o n (chi-square). The r e s u l t s are presented i n Table 29 below. A s i g n i f i c a n t l y higher p r o p o r t i o n of immigrant/ESL parents than Canadian born/native E n g l i s h speaking parents i n d i c a t e d that t h e i r c h i l d r e n r e c e i v e t u t o r i n g i n mathematics outside of school, that they or other f a m i l y members t u t o r t h e i r c h i l d r e n i n mathematics, that t h e i r c h i l d r e n are exposed to other-than-112 Table 27 Cross-Tabulation A n a l y s i s of Parent Questionnaire Responses: Mathematics and School Success (part 1) Canadian/English Immigrant/ESL Answer (n = 50) (n = 52) p Statement that my : I t i s important to me c h i l d gets good school grades. • • • • Strongly Disagree Agree Strongly disagree agree 3 (6.0%) 1 (2.0%) 21 (42.0%) 25 (50.0%) 0 (0%) 1 (2.0%) 17 (33.3%) 33 (64.7%) ns Statement: I t i s important to me that my c h i l d gets a university education. • • • • Strongly Disagree Agree Strongly disagree agree 2 (4.0%) 3 (6.0%) 24 (48.0%) 21 (42.0%) 0 (0%) 0 (0%) 11 (21.6%) 40 (78.4%) <. 01 Statement: My child's knowledge of mathematics i s important to me. • • Strongly Disagree disagree 0 (0%) 2 (4.0%) 0 (0%) 1 (1.9%) ns • Agree 22 (44.0%) 17 (32.7%).. • Strongly agree 26 (52.0%) 34 (65.4%) Statement: I t i s important for me that my c h i l d obtains high grades i n mathematics. • Strongly disagree 0 (0%) 0. (0%) <. 01 • Disagree 10 (20.4%) 2 (3.8%) • Agree 27 (55.1%) 21 (40.4%) • Strongly agree 12 (24.5%) 29 (55.8%) 113 Table 27 (continued) Canadian/English Immigrant/ESL Answer (n = 50) (n = 52) P Statement: Mathematics i s an important subject at school. • Strongly disagree 0 (0%) 0 (0%) ns • Disagree 0 (0%) 0 (0%) • Agree 17 (34.7%) 15 (28.8%) • Strongly agree 32 (65.3%) 37 (71.2%) Statement: I t i s important for my c h i l d to devote time to mathematics homework and practice. Strongly disagree Disagree Agree Strongly agree 1 (2.1%) 3 (6.1%) 28 (57.1%; 17 (34.7%; 1 (1.9%) 0 (0%) 24 (46.2%) 27 (51.9%) ns N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL 114 Table 28 Cross-Tabulation A n a l y s i s of Parent Questionnaire Responses: Mathematics and School Success (part 2) Canadian/ Immigrant/ English ESL Answer (n = 50) (n = 52) Question: Why do you want your c h i l d to do well i n school? To get a good job l a t e r 18 (36.7%) 18 (35.3%) ns To be well educated 17 (34.7%) 24 (47.0%) To have a high income 1 (2.0%) 1 (2.0%) To honor family 1 (2.0%) 0 (0%) To be happy 12 (24.6%) 8 (15.7%) Question: What has the most influence on your child's success i n school? Talent/inborn S k i l l s 9 (18.4%) 4 (8.0%) ns How hard c h i l d works and 22 (44.9%) 28 (56.0%) t r i e s Opportunities (tutoring, 18 (36.7%) 18 (36.0%) teacher, school) Very good About the same Not as good as other children Question: How does your c h i l d do i n mathematics compared to other children? 24 (49.0%) 17 (34.7%) 8 (16.3%) 23 (44.2%) 24 (46.2%) 5 (9.6%) ns N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL 115 Table 29 Cross-Tabulation A n a l y s i s of Parent Questionnaire Responses: Mathematics Canadian/ Immigrant/ English ESL Question Answer (n = 50) (n = 52) p Does your c h i l d receive any tutoring i n mathematics outside of school? yes no 6 44 (12.0%) (88.0%) 18 34 (34.6%) (65.4%) <. 05 Do you or any other family members tutor your c h i l d i n mathematics? yes no 21 29 (42.0%) (58.0%) 33 19 (63.5%) (36.5%) <. 05 Is your c h i l d exposed to any other-than-school mathematical exercises? yes no 15 35 (30.0%) (70.0%) 29 23 (55.8%) (44.2%) <. 05 Does your c h i l d receive any help with mathematics homework? yes no 39 11 (78.0%) (22.0%) 35 17 (67.3%) (32.7%) ns Do you practice mathematics with your c h i l d at home? yes no 31 19 (62.0%) (38.0%) 40 12 (76.9%) (23.1%) ns Does your c h i l d play mathematics-related games with the family? yes no 47 3 (94.0 %) (6.0 %) 31 ( (59.6%) 21 40.4%) <. 001 Does your c h i l d have any opportunity to use mathematics i n real l i f e settings? yes no 49 1 (98.0%) (2.0%) 48 4 (92.3%) (7.7%) ns Do you think that your c h i l d can do better i n mathematics than now? yes no 34 16 (68.0%) (32.0%) 50 2 (96.2%) (3.8%) <. 001 Do you want your c h i l d to do better i n mathematics than he/she does now? yes no (56. 21 27 2%) (43.8%) 49 3 (94.2%) (5.8%) <. 001 N o t e . Canadian/English = Canadian born parents and English as a f i r s t language; Immigrant/ESL = foreign born parents and ESL 116 school mathematical e x e r c i s e s , that they b e l i e v e that t h e i r c h i l d r e n can do b e t t e r i n mathematics and that they want t h e i r c h i l d r e n do b e t t e r i n mathematics. A s i g n i f i c a n t l y higher number of Canadian born/native E n g l i s h speaking parents than immigrant/ESL parents i n d i c a t e d that t h e i r c h i l d r e n p l a y mathematics-related games with the f a m i l y . Parents' questionnaire and different immigrant groups. In Tables 30, 31 and 32 below, the answers of immigrant parents belonging to one of three language groups (East Asian, F i l i p i n o , and Middle Eastern) were analyzed using a c r o s s - t a b u l a t i o n ( c h i -square) t e s t . The European group was not in c l u d e d i n t h i s a n a l y s i s due to i t s i n s u f f i c i e n t sample s i z e . In the c r o s s - t a b u l a t i o n a n a l y s i s (chi-square), a s i g n i f i c a n t d i f f e r e n c e between the three language groups was found f o r the statement: " I t i s important to me that my c h i l d gets a u n i v e r s i t y education". A l l Middle Eastern parents s t r o n g l y agreed with t h i s statement. In c o n t r a s t , some of the East Asian and F i l i p i n o parents choose "agree" i n s t e a d of " s t r o n g l y agree" when r a t i n g t h i s statement. A s i g n i f i c a n t l y higher p r o p o r t i o n of East Asian parents s a i d that t h e i r c h i l d r e c e i v e t u t o r i n g i n mathematics outside of school compared to F i l i p i n o and East Asian parents. There were no s i g n i f i c a n t d i f f e r e n c e s between the three groups on the r e s t of the statements. 117 Table 30 Parent Questionnaire Responses: Immigrant Groups Mathematics and School Success (part 1) Middle East Asian F i l i p i n o Eastern Answer (n = 17) (n.= 15) (n = 16) P Statement: I t i s important to me that my c h i l d gets good school grades. • Strongly disagree 0 (0%) 0 (0%) 0 (0%) ns • Disagree 1 (6.2%) • 0 (0%) 0 (0%) • Agree 8 (50.0%) 5 (33.3%) 3 (18.8%) • Strongly agree 7 (43.8%) 10 (66.7%) 13 (81.2%) Statement: I t i s important to me that my c h i l d gets a university education. • Strongly disagree 0 (0%) 0 (0%) 0 (0%) <. 05 • Disagree 0 (0%) 0 (0%) 0 (0%) • Agree 6 (37.5%) 4 (26.7%) 0 (0%) • Strongly agree 10 (62.5%) 11 (73.3%) 16 (100%) Statement: My child's knowledge of mathematics i s important to me. • Strongly disagree 0 (0%) 0 (0%) 0 (0%) ns • Disagree 1 (5.9%) 0 (0%) 0 (0%) • Agree 7 (41.2%) 5 (35.7%) 3 (18.8%) • Strongly agree 9 (52.9%) 9 (64.3%) 13 (81.2%) Statement: I t i s important for me that my c h i l d obtains high grades i n mathematics. • Strongly disagree 0 (0%) 0 (0%) 0 (0%) ns • Disagree 2 (11.8%) 0 (0%) 0 (0%) • Agree 8 (47.0%) 4 (25.0%) 6 (42.9%) • Strongly agree 7 (41.2%) 12 (75.0%) 8 (57.1%) 118 Table 30 (continued) Middle East Asian F i l i p i n o Eastern Answer (n = 17) (n = 15) (n = 16) p Statement: Mathematics i s an important subject at school. • Strongly disagree 0 (0%) 0 (0%) 0 (0%) • Disagree 0 (0%) 0 (0%) 0 (0%) • Agree 5 (29.4%) 4 (28.6%) 5 (31.2%) • Strongly agree 12 (70.6%) 10 (71.4%) 11 (68.8%) Statement: I t i s important for my c h i l d to devote time to mathematics homework and practice. • Strongly disagree 0 (0%) 0 (0%) 0 (0%) • Disagree 0 (0%) 1 (7.1%) 0 (0%) • Agree 10 (58.8%) 4 (28.6%) 8 (50.0%) • Strongly agree 7 (41.2%) 9 (64.3%) 8 (50.0%) 119 Table 31 Parent Questionnaire Responses: Immigrant Groups Mathematics and School Success (part 2) Middle East Asian F i l i p i n o Eastern Answer (n = 17) (n = 15) (n = 16) p Question: Why do you want your c h i l d to do well i n school? • To get a good job 4 (25.0%) 7 (46.7%) 6 (37.5%) l a t e r • To be well educated 8 (50.0%) 7 (46.7%) 7 (43.8%) • To have a high income 0 (0%) 1 (6.6%) 0 (0%) • To honor family 0 (0%) 0 (0%) 0 (0%) • To be happy 4 (25.0%) 0 (0%) 3 (18.7%) Question: What has the most influence on your child's success i n school? • Talent/inborn S k i l l s 0 (0%) 1 (7.1%) 3 (18.8%) • How hard c h i l d works 10 (62.5%) 7 (50.0%) 8 (50.0%) and t r i e s • Opportunities 6 (37.5%) 6 (42.9%) 5 (31.2%) (tutoring, teacher, school) Question: How does your c h i l d do i n mathematics compared to other children? • Very good 10 (58.8%) 3 (21.4%) 7 (43.8%) • About the same 6 (35.3%) 8 (57.2%) 9 (56.2%) • Not as good as other 1 (5.9%) 3 (21.4%) 0 (0%) children 120 Table 32 Parent Questionnaire Responses: Immigrant Groups, Mathematics Question East (n Asian = 17) F i l i p i n o (n = 14) Middle Eastern (n = 16) P • Does your c h i l d yes 10 58.8 %) 3 (21.4%) 3 (18.8%) <. 05 receive any no 7 41.2%) 11 (78.6%) 13 (81.3%) tutoring i n math outside of school? • Do you or any other yes 13 76.5%) 10 (71.4%) 7 (43.8%) ns family members no 4 23.5%) 4 (28.6%) 9 (56.2%) tutor your c h i l d i n mathematics? • Is your c h i l d yes 10 58.8%) 10 (71.4%) 5 (31.2%) ns exposed to any no 7 41.2%) 4 (28.6%) 11 (68.8%) other-than-school math exercises? • Does your c h i l d yes 9 52.9%) 11 (78.6%) 11 (68.8%) ns receive any help no 8 47.1%) 3 (21.4%) 5 (31.2%) with mathematics homework? • Do you practice yes 11 64.7%) 11 (78.6%) 13 (81.3%) ns mathematics with no 6 35.3%) 3 (21.4%) 3 (18.8%) your c h i l d at home? • Does your c h i l d yes 13 76.5%) 8 (57.1%) 6 (37.5%) ns play mathematics- no 4 23•5 %) 6 (42.9%) 10 (62.5%) related games with the family? • Does your c h i l d yes 15 88 . 2 %) 12 (85.7%) 16 (100%) ns have any no ' 2 11.8%) 2 (14.3%) 0 (0%) opportunity to use mathematics i n real l i f e settings? • Do you think that yes 17 100%) 14 (100%) 15 (93.8%) ns your c h i l d can do no 0 0%) 0 (0%) 1 (6.2%) better i n math than now? • Do you want your yes 17 100%) 13 (92.9%) 15 (93.8%) ns c h i l d to do better no 0 0%) 1 (7.1%) 1 (6.3%) i n math than he/she does now? 121 Correlation among parental and children's responses on questionnaires. To c a l c u l a t e the r e l a t i o n s h i p between c h i l d r e n ' s and p a r e n t a l responses on quest i o n n a i r e s , a Spearman's Rho c o r r e l a t i o n c o e f f i c i e n t was used. Only matching questions with yes and no answers were chosen f o r t h i s a n a l y s i s . These r e s u l t s are i n Table 33 below. There was a s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n between a l l c h i l d r e n ' s and p a r e n t a l answers to the d i r e c t l y matching questions: there was a s i g n i f i c a n t c o r r e l a t i o n between c h i l d r e n ' s and parents' answers to the question about wanting c h i l d r e n to do b e t t e r i n mathematics than now, r(96) = .20, p<. 05, the questions about the c h i l d r e n ' s a b i l i t y to do b e t t e r i n mathematics than now, r(98) = .35, p<.001, and the question about parents p r a c t i c i n g mathematics with t h e i r c h i l d r e n , r(98) = .33, p<.05. In a d d i t i o n , there was a s i g n i f i c a n t c o r r e l a t i o n between the c h i l d r e n ' s responses about r e c e i v i n g help outside of school and the parents' responses to the question about p r a c t i c i n g mathematics with t h e i r c h i l d r e n , r(98) = .24, p<.05 and c h i l d r e n ' s responses about t h e i r parents p r a c t i c i n g mathematics with them and p a r e n t a l responses i n d i c a t i n g that they helped t h e i r c h i l d r e n with homework, r(98) =, .30, p<.01 and tuto r e d them, r(98) = .25, p<.01. A l s o , there was a s i g n i f i c a n t c o r r e l a t i o n between parents' answers regarding wanting t h e i r c h i l d r e n to do b e t t e r i n mathematics and t h e i r c h i l d r e n ' s 122 Table 3 3 The I n t e r c o r r e l a t i o n among Chil d r e n ' s and P a r e n t a l Questionnaire Responses (Spearman's Rho C o e f f i c i e n t ) Children's question CO 4-1 o u o ft - H >i CD - H r H o O o 4-1 M-H r>. 4-1 CD r H 4-1 Ti TS a 4-> - r H U rO X ! CO O rO C rO CD CD CO 6 o o X O - H o X Xi co T5 4-> CD CD - H x 4-1 4-1 4-> 4-1 O M a X! > 4-1 U O - H rO CD 4-> - H rO CO 4-) M r>. 4-> tn TS 4-) Xi S-l CO CD e a C O CO C o rO rO B O CD M H - H rO 3 o ro 3 S Ti ft r- CD X O X 4-> CD • r H 3 - r H 4-> O CD CD CD 3 U 4-1 4-> M e 4-1 rO c- >i Xi - H M O O rO CD O O m u B 3 4-> r H 3 - H > 3 B X) ft X B o CD 0) o Ti rO 4-> O 4-1 O - r H O CD a >! O Xi >i Xi C O >1 - r H U X Parents question 4-1 4-> rO 4-1 4-1 4-1 3 4-1 o CD ro o O c o O U - r H O - H 3 o CO o rO Q Xi B • a O - H >i Q ft 3 Q 3 O Q - H > 6 Do you want your c h i l d to .20t .27* .10 .19 .04 do b e t t e r i n mathematics than now? Do you t h i n k that your .36* .35* .20t .19 -.01 c h i l d could do b e t t e r i n mathematics than now? Do you p r a c t i c e 18 .12 .33* 24t .02 mathematics wi t h your c h i l d ? Does your c h i l d r eceive .27 .12 -.02 .18 .14 any t u t o r i n g i n mathematics outside of school? Do you or any f a m i l y .12 .13 .25t .09 , . 11 members t u t o r your c h i l d i n mathematics? Is your c h i l d exposed to .12 .11 .19 .16 . 13 any other-than-school mathematical e x e r c i s e s ? Does your c h i l d r eceive .09 • 23t .30* .06 -.15 any help w i t h mathematics homework? * Correlation i s s i g n i f i c a n t at the . 01 le v e l (2 -tailed) t Correlation i s s i g n i f i c a n t at the .05 le v e l (2 -tailed) responses regarding being able to do b e t t e r i f they t r i e d harder, r(98) = .27, p<.01 and the parents' responses regarding b e l i e v i n g that t h e i r c h i l d r e n are able to do b e t t e r i n mathematics and the c h i l d r e n ' s responses regarding wanting to do b e t t e r i n mathematics , r(98) = .36, p<.01. There was a l s o a s i g n i f i c a n t c o r r e l a t i o n between c h i l d r e n ' s responses about t h e i r a b i l i t y to do b e t t e r i n mathematics i f they t r i e d harder and the pa r e n t a l responses about h e l p i n g t h e i r c h i l d r e n with homework i n mathematics, r(98) = .23, p<.05. Cultural and Social Background of Families Based on the Questionnaire Parents' answers to the questionnaire provided some info r m a t i o n regarding t h e i r f a m i l y dynamics, education and p r o f e s s i o n a l background. There were 50 Canadian born parents and 52 f o r e i g n born parents r e t u r n i n g q u e s t i o n n a i r e s . Using c r o s s -t a b u l a t i o n (chi-square) a n a l y s i s , there was not any s i g n i f i c a n t d i f f e r e n c e between two groups on any socio-economic f a c t o r s . Most of the f a m i l i e s had 2 c h i l d r e n (61% of Canadian and 51% of immigrant f a m i l i e s ) , some had only one c h i l d (21% of Canadian and 37% of immigrant f a m i l i e s ) and only a few had 3 or more c h i l d r e n (18% of Canadian and 12% of immigrant f a m i l i e s ) . These frequencies were not s i g n i f i c a n t l y d i f f e r e n t , % (3, N = 100) = 5.18, n s . 124 In terms of education, the m a j o r i t y of parents had u n i v e r s i t y (44% of Canadian and 66% of immigrant parents) or other post-secondary education (34% of Canadian and 22% of immigrant p a r e n t s ) . Only a small m i n o r i t y of parents had high-school equivalent (18% of Canadian and 7% of immigrant parents) or l e s s (4% of Canadian and 5% of immigrant p a r e n t s ) . These frequencies were not s i g n i f i c a n t l y d i f f e r e n t : f o r the parent f i l l i n g out the questionnaire ( u s u a l l y the mother): x (3, N = 91) = 8.35, ns and f o r the partner ( u s u a l l y the. f a t h e r ) : x 2 (3, N = 81) = 6.15, ns. When asked about t h e i r p r o f e s s i o n a l background, 27% of Canadian and 21% of immigrant parents had p r o f e s s i o n a l careers, 26% of Canadian and 12% of immigrant parents had s k i l l e d t r a d e s / t e c h n i c a l jobs, 10% of Canadian and 9% of immigrant parents worked i n business, 28% of Canadian and 41% of immigrant parents had u n s k i l l e d jobs, and 9% of Canadian and 17% of immigrant parents were unemployed or stay-home parents. These frequencies were not s i g n i f i c a n t l y d i f f e r e n t : f o r the parent f i l l i n g out the questionnaire ( u s u a l l y the mother): % (4, N = 99) = 5.17, ns and f o r the partner ( u s u a l l y the father) : %2 (4, N = 79) = 8.33, ns. When comparing the occupations of immigrant parents i n t h e i r home cou n t r i e s and i n Canada, i t i s estimated that about h a l f of immigrant parents have lower status work i n Canada than they had i n t h e i r home country. T h i r t y nine parents who were f o r e i g n born answered a questionnaire about t h e i r c u l t u r a l and language background. With one exception, a l l parents i n d i c a t e d that t h e i r c h i l d r e n l i v e d i n homes where a language other than E n g l i s h was spoken. In t h i s one instance, the f a t h e r was born i n Hong Kong, but the mother was Canadian born. About 67% of c h i l d r e n were born i n t h e i r parents' home country. Seventy two percent of f a m i l i e s used e x c l u s i v e l y t h e i r mother tongue when communicating with t h e i r c h i l d r e n , 15% used both t h e i r mother tongue and E n g l i s h , and 13% used mostly E n g l i s h . According to t h e i r parents, 69% of c h i l d r e n learned t h e i r mother tongue before they learned E n g l i s h , 8% learned both languages simultaneously, and 23% learned E n g l i s h f i r s t , although they were exposed to another language at home. F i f t y nine percent of the c h i l d r e n used t h e i r mother tongue as t h e i r primary language at home, 10% used both E n g l i s h and t h e i r mother tongue e q u a l l y , and 31% used p r i m a r i l y E n g l i s h . Twenty s i x percent of parents s t a t e d that t h e i r c h i l d r e n attended language schools, and 55% s a i d that t h e i r c h i l d r e n are able to w r i t e and read i n t h e i r mother tongue. According to t h e i r parents, only 5% of c h i l d r e n attended a f t e r - s c h o o l a c t i v i t i e s where a language other than E n g l i s h was spoken, but 21 % d i d s c h o o l - r e l a t e d work i n languages other than E n g l i s h . 126 With two exceptions, a l l f a m i l i e s agreed that i t i s important f o r them that t h e i r c h i l d r e n know about the c u l t u r e of t h e i r f a m i l y ' s country of o r i g i n . Parents i n d i c a t e d that they want t h e i r c h i l d r e n to know about the c u l t u r e of t h e i r home country so that they know t h e i r r o o t s , understand t h e i r c u l t u r a l i d e n t i t y , can r e l a t e to f a m i l y and f r i e n d s , and because the c u l t u r e of t h e i r home country i s s t i l l p art of who the f a m i l y i s (e.g. "...because we are Korean"). Most of the parents s a i d that t h e i r c h i l d r e n are exposed to the c u l t u r e of t h e i r home country by attending c u l t u r a l events, t a l k i n g to t h e i r parents, and s o c i a l i z i n g with the members of that c u l t u r e . Some parents s a i d t hat t h e i r c h i l d r e n watch t h e i r home country's t e l e v i s i o n and are exposed to i n t e r n e t content from t h e i r home country, read books i n t h e i r n a t i v e language, v i s i t the home country, and t a l k to f a m i l y and f r i e n d s on the phone. According to t h e i r parents, c h i l d r e n l e a r n about the c u l t u r e of t h e i r parents through these a c t i v i t i e s and by p a r e n t a l guidance arid encouragement. Relationship between Children's Questionnaire Responses and Their Performance on Selected Numeracy Measures In the f i n a l year of the study (grades 5 and 6), c h i l d r e n f i l l e d i n a questionnaire addressing t h e i r a t t i t u d e s towards mathematics and the t u t o r i n g which they r e c e i v e . Children's answers were r e l a t e d to t h e i r grade 5 and 6 numeracy performance on three s e l e c t e d measures (WRAT-III Computational A r i t h m e t i c , WJ-III C a l c u l a t i o n and WJ-III Fluency). P e r c e n t i l e s were used f o r t h i s a n a l y s i s . These three measures were s e l e c t e d because they are very good i n d i c a t o r s of numeracy s k i l l s . A l s o , on these three measures the immigrant/ESL group d i f f e r e d most from Canadian born p a r e n t s / E n g l i s h group across grades i n the previous analyses. T-test a n a l y s i s was used to see i f there i s any d i f f e r e n c e between c h i l d r e n answering "yes" and c h i l d r e n answering "no" on s e l e c t e d grade 5 and 6 numeracy measures. Not a l l the questions were i n c l u d e d i n t h i s a n a l y s i s . In some instances, the sample s i z e s were very unequal (e.g., only a few c h i l d r e n answered "no"), or some questions were not s u i t a b l e f o r t h i s kind of a n a l y s i s . Grade 5. For r e s u l t s see Table 34 below. The d i f f e r e n c e i n grade 5 performance on s e l e c t e d numeracy measures between c h i l d r e n answering "yes" and "no" on the numeracy questionnaire was most s i g n i f i c a n t f o r the question " I s i t very important f o r you to get high grades i n mathematics?". The d i f f e r e n c e i n grade 5 performance on s e l e c t e d numeracy measures between c h i l d r e n answering "yes" and "no" on the numeracy questionnaire was most s i g n i f i c a n t f o r the question " Is i t very important f o r you to get high grades i n mathematics?". The c h i l d r e n who answered "yes" had s i g n i f i c a n t l y higher scores on a l l three measures: the WRAT-III A r i t h m e t i c , t(152) = 2.60, 128 Table 34 R e l a t i o n s h i p between Grade 5 Numeracy Performance of C h i l d r e n and Their Questionnaire Responses Answer/Question Yes No T-test Measure (percentile) Mean SD Mean SD p Do you receive help with mathematics outside of school? (n = 112) (n = 42) WRAT-III Arithmetic 54.11 26.53 50.41 28.55 0 .69 ns WJ-III Calculation 53.51 27.20 54.48 24.44 0 .20 ns WJ-III Math fluency 48.68 31.86 49.95 32.65 0 .22 ns Is i t very important for you to get high grades i n mathematics? (n = 143) (n = 11) WRAT-III Arithmetic 54.73 26.96 33.09 21.39 2 . 60 <. 05 WJ-III Calculation 54.90 27.46 39.18 18.47 2 . 61 <. 05 WJ-III Math fluency 51.62 31.38 15.27 17.58 6 .15 <. 001 Do you l i k e mathematics? (n = 116) (n = 38) WRAT-III Arithmetic 56.60 26.99 42.76 25.11 2 .79 <. 01 WJ-III Calculation 55.75 24.38 47.74 27.85 1 .59 ns WJ-III Math fluency 51.72 32.43 40.80 29.44 1 .84 ns Do you want to do better i n mathematics than now? (n = 133) (n = 21) WRAT-III Arithmetic 52.83 27.54 55.43 24.80 0 .41 ns WJ-III Calculation 53.29 27.03 56.81 28.62 0 .55 ns WJ-III Math fluency 47.50 31.81 58.67 32.09 1 .49 ns Do your parents practice mathematics with you? (n = 97) (n = 57) WRAT-III Arithmetic 49.72 27.07 59.79 26.40 2 .09 <. 05 WJ-III Calculation 51.32 25.79 57.95 29.15 1 . 47 ns WJ-III Math fluency 46.09 30.11 54.03 34.62 1 .50 ns 129 Table 34 (Continued) Answer/Question Yes No Mean SD Mean SD T-test p Measure(percentile) Would you be happy i f someone cancelled a l l mathematics classes? (n =55) (n = 97) WRAT-III Arithmetic 50. 89 27 .22 54. 22 26. 56 0 .73 ns WJ-III Calculation 56. 62 28 .56 52 . 06 26. 19 1 .00 ns WJ-III Math fluency 48. 80 33 .07 49. 12 31. 84 0 .06 ns p<.05, the WJ-III C a l c u l a t i o n , t(152) = 2.61, p<.05 and the WJ-I I I Math Fluency, t(152) = 6.15, p<.001. C h i l d r e n who s a i d t h a t they l i k e mathematics had higher scores on the WRAT-III A r i t h m e t i c , t(152) = 2.79, p<.01 than c h i l d r e n who s a i d that they didn't l i k e mathematics. C h i l d r e n who s a i d that t h e i r parents p r a c t i c e mathematics had s i g n i f i c a n t l y lower performance on the WRAT-III A r i t h m e t i c , t(152) = 2.09, p<.05 than c h i l d r e n who s a i d that t h e i r parents do not p r a c t i c e mathematics with them. For the r e s t of the questions, the d i f f e r e n c e between the numeracy performance of c h i l d r e n responding "yes" and c h i l d r e n responding "no" was not s i g n i f i c a n t . 130 Grade 6 . For r e s u l t s see Table 35 below. There was a s i g n i f i c a n t d i f f e r e n c e i n grade 6 performance on s e l e c t e d numeracy measures between c h i l d r e n answering "yes" and "no" on the question: "Is i t very important f o r you to get high grades i n mathematics?". The c h i l d r e n who answered "yes" had s i g n i f i c a n t l y higher scores on the WJ-III Math Fluency, t(84) = 2.24, p<.05. C h i l d r e n who s a i d that they l i k e mathematics had s i g n i f i c a n t l y higher scores on the WJ-III Math Fluency, t(84) = 2.20, p<.01 than c h i l d r e n who s a i d that they don't l i k e mathematics. C h i l d r e n who s a i d that t h e i r parents p r a c t i c e mathematics with them had s i g n i f i c a n t l y lower performance on the WJ-III C a l c u l a t i o n , t(89) = 2.61, p<.01 and the WJ-III Math Fluency, t(89) = 2.47, p<.01 than c h i l d r e n who s a i d that t h e i r parents do not p r a c t i c e mathematics with them. C h i l d r e n who s a i d that they would be happy i f someone c a n c e l l e d a l l c l a s s e s i n mathematics had s i g n i f i c a n t l y lower performance on the WJ-III C a l c u l a t i o n , t(83) = 3.42, p<.01 and the WJ-III Math Fluency, t(83) = 2.09, p<.05 than c h i l d r e n who answered no to t h i s question. For the r e s t of the questions, the d i f f e r e n c e between the numeracy performance of c h i l d r e n responding "yes" and c h i l d r e n responding "no" was not s i g n i f i c a n t . 131 Table 35 R e l a t i o n s h i p between Grade 6 Numeracy Performance of C h i l d r e n and Their Questionnaire Responses Answer/Question Yes No T-test Measure(percentile) Mean SD Mean SD WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency Do you receive help with mathematics outside school? (n = 63) (n = 23) WRAT-III Arithmetic 53 .66 28 .58 45. 15 22 .72 1 .29 ns WJ-III Calculation 52 .39 31 .18 56. 73 28 .29 0 .57 ns WJ-III Math fluency 51 .63 31 .78 48. 04 32 .61 0 .46 ns Is i t very important for you to get high grades i n mathematics? (n = 77) (n = 9) 52 .09 26.76 45.33 32.44 0 .70 ns 54 .76 30.48 43.00 28.75 1 .10 ns 53 .24 31.54 28.67 26.78 2 .24 <. 05 Do you l i k e mathematics? (n = 61) (n = 25) 54 .47 27 . 57 43.84 25.50 1 .66 ns 57 .26 30.73 44.52 28.01 1 .79 ns 55 .41 30.87 39.11 31.84 2 .20 <. 01 Do you want to do better i n mathematics than now? (n = 68) (n = 18) WRAT-III Arithmetic 49. 98 27 .89 56. 67 24. 83 0 .41 ns WJ-III Calculation 53. 26 31 . 68 54. 47 25. 27 0 .15 ns WJ-III Math fluency 47. 95 30 .53 60. 89 31. 88 1 .55 ns Do your parents practice mathematics with you? (n = 55) (n = 36) 48.03 27.74 46.56 29.46 43.67 30.54 56.04 26.27 63.45 29.21 60.39 31.46 1.35 2.61 2.47 ns <. 01 <. 01 132 Table 35 (Continued) Answer/Question Yes No T-test Measure(percentile) Mean SD Mean SD p Would you be happy i f someone cancelled a l l mathematics classes? (n = 31) (n = 54) WRAT-III Arithmetic 43.90 26.43 55.90 27.22 1. 98 ns WJ-III Calculation 39.94 30.12 62.03 27.63 3. 42 <. 01 WJ-III Math fluency 41.59 33.52 56.28 30.04 2. 09 <. 05 Relationship between Parental Questionnaire Responses and Children's Performance on Selected Numeracy Measures In the f i n a l year of the study, parents of grade 5 and 6 students were asked to answer questionnaire regarding t h e i r a t t i t u d e s toward t h e i r c h i l d r e n ' s mathematical achievement and the support i n mathematics t h e i r c h i l d r e n r e c e i v e at home. Parents' answers on s e l e c t e d questions were analyzed using t -t e s t s to see i f there i s any d i f f e r e n c e between parents answering "yes" and "no" i n terms of t h e i r c h i l d r e n ' s performance on three numeracy measures (WRAT-III Computational A r i t h m e t i c , WJ-III C a l c u l a t i o n and WJ-III Fluency) administered i n grades 5 and 6. 133 Grade 5 . The numeracy performance on grade 5 measures of c h i l d r e n whose parents answered "yes" on s e l e c t e d questions was compared to that of c h i l d r e n whose parents answered "no". Results are reported i n Table 36 below. Using t - t e s t a n a l y s i s of par e n t a l responses on the questionnaire and t h e i r c h i l d r e n ' s performance on s e l e c t e d grade 5 numeracy measures, some s i g n i f i c a n t d i f f e r e n c e s were found. C h i l d r e n of parents who s a i d that t h e i r c h i l d r e n r e c e i v e t u t o r i n g i n mathematics performed s i g n i f i c a n t l y higher on the WRAT-III A r i t h m e t i c , t(84) = 2.68, p<.01 than c h i l d r e n who, according to t h e i r parents, d i d not r e c e i v e t u t o r i n g . C h i l d r e n who received help with homework had s i g n i f i c a n t l y lower scores on the WJ-III C a l c u l a t i o n , t(84) = 2.14, p<.05 and the WJ-III Math Fluency, t(84) = 2.85, p<.01 than c h i l d r e n who d i d not r e c e i v e help with homework. C h i l d r e n whose parents wanted them to do b e t t e r i n mathematics had s i g n i f i c a n t l y lower scores on the WJ-III Math Fluency, t(82) = 2.44, p<.05 than c h i l d r e n of parents who d i d not want t h e i r c h i l d r e n to do b e t t e r i n mathematics. There were no s i g n i f i c a n t d i f f e r e n c e s between "yes" and "no" groups i n the cases of the remaining questions. Grade 6. Using t - t e s t a n a l y s i s , parents' "yes" and "no" responses on s e l e c t e d questions were r e l a t e d to t h e i r c h i l d r e n ' s performance on three numeracy measures administered i n grade 6. 134 Table 36 Re l a t i o n s h i p between Grade 5 Numeracy Performance of C h i l d r e n and Their Parents' Questionnaire Responses Answer/Question Yes No Measure(percentile) Mean SD Mean SD T-test WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency Does your c h i l d receive any tutoring i n mathematics outside of school? (n =66) (n = 20) 7 1 . 9 5 2 2 . 5 7 5 5 . 6 5 2 3 . 0 6 6 0 . 1 0 2 8 . 1 9 5 7 . 4 2 2 5 . 0 8 5 8 . 3 5 3 6 . 3 0 5 5 . 2 3 2 8 . 4 2 Do you or any other family member tutor your c h i l d i n mathematics? WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency with mathematics homework? (n = 64) (n = 22) 5 7 . 1 7 2 3 . 1 6 6 5 . 0 5 2 5 . 1 1 5 4 . 6 4 2 5 . 5 0 6 7 . 9 5 2 4 . 1 1 5 0 . 7 3 2 9 . 7 3 7 1 . 1 5 2 6 . 8 6 2 . 68 0 . 4 1 0 . 3 5 1 . 5 2 2 . 1 4 2 . 8 5 <. 01 ns ns (n = 47) (n = 39) WRAT-III Arithmetic 6 1 . 8 1 2 3 . 2 6 5 6 . 5 9 2 4 . 5 1 1 . 0 1 ns WJ-III Calculation 5 8 . 7 8 2 5 . 4 5 5 7 . 1 5 2 6 . 2 7 0 . 2 9 ns WJ-III Math fluency 5 4 . 4 4 3 0 . 1 0 5 7 . 7 8 3 0 . 68 0 . 5 1 ns Is your c h i l d exposed to any other-than-school mathematical exercises? (n = 38) (n = 48) WRAT-III Arithmetic 6 1 . 2 1 2 5 . 5 8 5 7 . 2 5 2 2 . 4 0 0 . 9 6 ns WJ-III Calculation 5 8 . 8 9 2 6 . 3 3 5 7 . 3 7 2 5 . 4 2 0 . 2 7 ns WJ-III Math fluency 5 6 . 8 7 3 0 . 9 9 5 5 . 2 3 2 9 . 9 3 0 . 2 5 ns Does your c h i l d receive any help ns <. 05 <. 01 135 Table 36 (Continued) Answer/Question Yes No Measure (percentile) Mean SD Mean SD T-test Does your c h i l d play mathematics-related games with the family? (n = 67) (n = 19) WRAT-III Arithmetic 60 .26 23. 62 59.21 23. 20 0 .17 ns WJ-III Calculation 59 .70 25.00 52.21 27. 89 1 .12 ns WJ-III Math fluency 58 .56 28.24 46.76 35. 74 1 .33 ns Do you think that your c h i l d can do better i n mathematics? (n = 68) (n = 18) WRAT-III Arithmetic 59.04 24.78 60.94 20.45 0. 30 ns WJ-III Calculation 56.47 26.04 64.00 24.06 1. 11 ns WJ-III Math fluency 53.22 30.45 66.27 27.77 1. 65 ns Do you want your c h i l d to do better i n mathematics than now? (n = 62) (n = 22) WRAT-III Arithmetic 58.01 25.82 63.18 15.87 0. 56 ns WJ-III Calculation 57.53 26.33 59. 68 25.44 0. 33 ns WJ-III Math fluency 51.71 30.99 69.50 24.20 2. 44 <. 0 136 Some s i g n i f i c a n t d i f f e r e n c e s were found. C h i l d r e n whose parents s a i d that they r e c e i v e t u t o r i n g i n mathematics had s i g n i f i c a n t l y higher scores on the WRAT-III A r i t h m e t i c , t(46) = 3.11, p<.01 than c h i l d r e n who d i d not r e c e i v e t u t o r i n g . S i m i l a r l y , c h i l d r e n who were exposed to any other-than-school mathematical e x e r c i s e s had s i g n i f i c a n t l y higher scores on the WRAT-III A r i t h m e t i c , t(46) = 3.26, p<.05 than c h i l d r e n who were not. C h i l d r e n who, according to t h e i r parents, received help with mathematics homework had lower scores on a l l three measures than c h i l d r e n who d i d not r e c e i v e help with homework: the WRAT-I I : A r i t h m e t i c , t(46) = 2.98, p<.01, the WJ-III C a l c u l a t i o n , t(46) = 2.89, p<.05 and the WJ-III Math Fluency, t(46) = 2.85, p<.05. C h i l d r e n who could, according to t h e i r parents, do b e t t e r i n mathematics than they do now had s i g n i f i c a n t l y lower scores on the WJ-III C a l c u l a t i o n , t(45) = 2.76, p<.01 than c h i l d r e n whose parents s a i d that they do not b e l i e v e that t h e i r c h i l d r e n could do b e t t e r i n mathematics. S i m i l a r l y , c h i l d r e n whose parents s a i d that they wanted them to do b e t t e r i n mathematics than now had s i g n i f i c a n t l y lower scores on the WJ-III C a l c u l a t i o n , t(45) = 2.53, p<.05 and the WJ-III Math Fluency, t(45) = 2.09, p<.05 than c h i l d r e n whose parents s a i d that they do not want t h e i r c h i l d r e n to do b e t t e r i n mathematics. There were no s i g n i f i c a n t d i f f e r e n c e s between "yes" and "no" groups i n the cases of the remaining questions. For r e s u l t s see Table 37. 137 Table 37 R e l a t i o n s h i p between Grade 6 Numeracy Performance of C h i l d r e n and Their Parents' Questionnaire Responses Answer/Question Yes No Measure (percentile) Mean SD Mean SD T-test WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency Does your c h i l d receive any tutoring i n mathematics outside of school? (n = 9) (n = 39) 74.56 29.91 48.21 21.15 70.41 31.74 51.95 28.10 63.58 41.06 48.67 27.78 Do you or any other family members tutor your c h i l d i n mathematics? WRAT-III Arithmetic WJ-III Calculation WJ-III Math fluency 3.11 1.73 1.04 WRAT-III Arithmetic WJ-III Calculation WJ-III Math Fluency <. 01 ns ns (n = 19) (n = 29) WRAT-III Arithmetic 60 .58 29. 38 48 .28 20.66 1. 58 ns WJ-III Calculation 60 .58 27. 97 52 .03 30.34 0. 98 ns WJ-III Math fluency 57 .30 29. 92 47 .63 31.20 1. 08 ns Is your c h i l d exposed to any other-than-school mathematical exercises ? (n = 16) (n = 32) 69.50 26.71 44.97 19.77 3.26 <.05 64.04 27.26 51.06 29.91 1.50 ns 60.08 33.96 47.15 28.60 1.39 ns Does your c h i l d receive any help with mathematics homework? (n = 31) (n = 17) 45.81 22.24 66.53 24.59 2.98 < . 0 1 47.23 26.43 71.48 28.98 2.89 < . 0 1 43.16 28.28 66.60 30.01 2.69 < . 0 5 138 Table 37 (Continued) Answer/Question Yes No T-Mean SD Mean SD test p Does your c h i l d play mathematics-related games with the family? (n = 45) (n = 3) WRAT-I II Arithmetic 55.00 22.82 45.11 33.01 1 .07 ns WJ-II I Calculation 58.04 28.79 44. 67 31.18 1 .24 ns WJ-II I Math fluency 54.78 28.52 37.07 37.45 1 .58 ns Do you think that your c h i l d can do better i n mathematics than now? (n = 39) (n = 9) WRAT-I II Arithmetic 52.79 26.86 54.67 14.92 0 .20 ns WJ-II I Calculation 50.48 28.91 79.88 18.00 2 .76 <. 01 WJ-II I Math fluency 47.83 30.98 67 .22 25.53 1 .74 ns Do you want your c h i l d to do better i n mathematics than now? (n = 35) (n = 12) WRAT-I II Arithmetic 52.40 28.21 55.83 13.55 0 .88 ns WJ-II I Calculation 48.61 29.90 72.08 19.41 2 .53 <. 05 WJ-II I Math fluency 47.72 33.14 64.25 19.41 2 .09 <. 05 Measure (percentile) 139 Summary of Numeracy Questionnaire Results Children's questionnaire. The c h i l d r e n ' s numeracy-questionnaire was analyzed using a c r o s s - t a b u l a t i o n (chi-square) t e s t . I t was found that a s i g n i f i c a n t l y higher p r o p o r t i o n of immigrant/ESL c h i l d r e n than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents i n d i c a t e d that they r e c e i v e help with mathematics outside school (mostly from f a m i l y i n c l u d i n g s i b l i n g s but a l s o from f r i e n d s and t u t o r s ) , that they t h i n k that they w i l l need mathematics l a t e r i n l i f e , t hat they want to do b e t t e r i n mathematics than they do now and that they l i k e mathematics. East Asian and Middle Eastern c h i l d r e n were more l i k e l y than F i l i p i n o c h i l d r e n to say tha t they l i k e mathematics. E n g l i s h speaking c h i l d r e n with Canadian born parents i n d i c a t e d more than the immigrant/ESL group that they l e a r n u s e f u l things i n mathematics c l a s s e s . In a d d i t i o n , i n the m u l t i p l e choice response s e c t i o n , the immigrant/ESL c h i l d r e n were more l i k e l y to i n d i c a t e that they do b e t t e r i n mathematics compared to other c h i l d r e n than n a t i v e E n g l i s h speaking c h i l d r e n with Canadian born parents. In c o n t r a s t , members of the Canadian born pa r e n t s / E n g l i s h group were more l i k e l y to b e l i e v e that they do about the same as other c h i l d r e n than c h i l d r e n i n the immigrant/ESL group. Among the immigrant groups, East Asian students were most l i k e l y to b e l i e v e that they perform b e t t e r than other c h i l d r e n i n mathematics. In c o n t r a s t , F i l i p i n o c h i l d r e n were most l i k e l y to say that they do not do as w e l l as other c h i l d r e n . Parent questionnaire. Using the c r o s s - t a b u l a t i o n ( c h i -square) analyses, i t was shown that immigrant/ESL parents rated the importance of t h e i r c h i l d r e n g e t t i n g a u n i v e r s i t y education and o b t a i n i n g high grades i n mathematics higher than d i d Canadian born/English speaking parents. Of the immigrant groups, Middle Eastern parents rated highest the importance of t h e i r c h i l d r e n g e t t i n g a u n i v e r s i t y education. Using c r o s s - t a b u l a t i o n (chi-square), i t was shown that a s i g n i f i c a n t l y higher p r o p o r t i o n of immigrant/ESL parents than Canadian born/English speaking parents i n d i c a t e d that t h e i r c h i l d r e n r e c e i v e t u t o r i n g i n mathematics outside of school. Among immigrant parents, East Asian parents were more l i k e l y to say that t h e i r c h i l d r e n r e c e i v e t u t o r i n g outside of school than F i l i p i n o and Middle Eastern parents. A s i g n i f i c a n t l y higher p r o p o r t i o n of immigrant parents than Canadian born parents i n d i c a t e d that they or other f a m i l y members t u t o r t h e i r c h i l d r e n i n mathematics, that t h e i r c h i l d r e n are exposed to any other-than-school mathematical e x e r c i s e s , that they b e l i e v e that t h e i r c h i l d r e n can do b e t t e r i n mathematics than now and that they want t h e i r c h i l d r e n to do b e t t e r i n mathematics than they do now. A s i g n i f i c a n t l y higher number of Canadian born/English speaking parents than immigrant/ESL parents i n d i c a t e d that t h e i r c h i l d r e n p l a y mathematics-related games with the f a m i l y . Correlation among parents' and children questionnaire responses. Using a Spearman's Rho c o r r e l a t i o n c o e f f i c i e n t , a s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n between a l l d i r e c t l y matching c h i l d r e n ' s and p a r e n t a l questions ( i . e . , wanting c h i l d r e n to do b e t t e r i n mathematics, c h i l d r e n ' s a b i l i t y to do b e t t e r i n mathematics, and parents p r a c t i c i n g mathematics with t h e i r c h i l d r e n ) was found. In a d d i t i o n , there was s i g n i f i c a n t c o r r e l a t i o n between some a d d i t i o n a l c h i l d r e n ' s and p a r e n t a l responses which were not e x a c t l y matching (e.g., c h i l d r e n saying that they r e c e i v e help outside of school and parents saying that they p r a c t i c e mathematics with them; c h i l d r e n saying that they are able to do b e t t e r i n mathematics i f they t r y harder and parents saying that they help t h e i r c h i l d r e n with homework i n mathematics). Numeracy outcomes and questionnaire responses. T-test a n a l y s i s of c h i l d r e n ' s and parents' responses on questionnaires and c h i l d r e n ' s performance on s e l e c t e d grade 5 and 6 numeracy measures) was conducted. The f o l l o w i n g s i g n i f i c a n t d i f f e r e n c e s were found. The c h i l d r e n who answered "yes" to the question: " I s i t very important f o r you to get high grades i n mathematics?" had s i g n i f i c a n t l y higher scores than c h i l d r e n who answered "no" on 142 the WRAT-III A r i t h m e t i c , the WJ-III C a l c u l a t i o n and the WJ-III Math Fluency i n grade 5, and on the WJ-III Math Fluency i n grade 6. C h i l d r e n who s a i d t h a t they l i k e mathematics had higher scores on the WRAT-III A r i t h m e t i c i n grade 5 and on the WJ-III Math Fluency i n grade 6 than c h i l d r e n who s a i d that they don't l i k e mathematics. C h i l d r e n who s a i d that t h e i r parents p r a c t i c e mathematics with them had s i g n i f i c a n t l y lower performance than c h i l d r e n who s a i d that t h e i r parents do not p r a c t i c e mathematics with them on the WRAT-III A r i t h m e t i c i n grade 5, and on the WJ-I I I C a l c u l a t i o n and the WJ-III Math Fluency i n grade 6. In grade 6, c h i l d r e n who s a i d that they would be happy i f someone c a n c e l l e d a l l c l a s s e s i n mathematics had s i g n i f i c a n t l y lower performance on the WJ- I I I C a l c u l a t i o n and the WJ-III Math Fluency than c h i l d r e n who answered "no" to t h i s question. In the cases of parents' responses on the qu e s t i o n n a i r e , c h i l d r e n of parents who s a i d that t h e i r c h i l d r e n r e c e i v e t u t o r i n g i n mathematics performed s i g n i f i c a n t l y higher on the WRAT-III A r i t h m e t i c i n grades 5 and 6 than c h i l d r e n who, according to t h e i r parents, d i d not re c e i v e t u t o r i n g . In grade 6, c h i l d r e n who were exposed to any other-than-school mathematical e x e r c i s e s had s i g n i f i c a n t l y higher scores on the WRAT-III A r i t h m e t i c than c h i l d r e n who were not. C h i l d r e n whose parents reported that they received help with homework had s i g n i f i c a n t l y lower scores than c h i l d r e n who d i d not r e c e i v e help with homework on the WJ-III C a l c u l a t i o n and the WJ-III Math Fluency i n grades 5 and 6, and the WRAT-III A r i t h m e t i c i n grade 6. C h i l d r e n whose parents wanted them to do b e t t e r i n mathematics had s i g n i f i c a n t l y lower scores on the WJ-III Math Fluency i n grades 5 and 6 and the WJ-III C a l c u l a t i o n i n grade 6 than c h i l d r e n of parents who d i d not want t h e i r c h i l d r e n to do b e t t e r i n mathematics. S i m i l a r l y , c h i l d r e n who could, according to t h e i r parents, do b e t t e r i n mathematics than they do now had s i g n i f i c a n t l y lower scores on the WJ-III C a l c u l a t i o n i n grade 6 than c h i l d r e n whose parents s a i d that they do not b e l i e v e that t h e i r c h i l d r e n could do b e t t e r i n mathematics. Discussion/Conclusion The populations i n Canada, the United States, A u s t r a l i a , and many European c o u n t r i e s are becoming more d i v e r s e as the number of immigrants increases i n these c o u n t r i e s . Although t h i s d i v e r s i t y brings many advantages, i t i s a l s o very c h a l l e n g i n g to accommodate newcomers w i t h i n those s o c i e t i e s , and to help them become s u c c e s s f u l c i t i z e n s . P r o v i d i n g good education f o r c h i l d r e n of immigrants i s one of the most important f a c t o r s i n t h e i r o v e r a l l adjustment. C h i l d r e n of newcomers have much to o f f e r . They may b e n e f i t from the c u l t u r a l and language background of t h e i r country of o r i g i n while a d j u s t i n g and blending i n t o t h e i r new s o c i e t y ; but they a l s o may be n e g a t i v e l y a f f e c t e d by t h e i r m i n o r i t y e t h n i c and/or language s t a t u s . In order to promote good school adjustment and outcomes among immigrant students, f a c t o r s such as E n g l i s h p r o f i c i e n c y , f a m i l y i n f l u e n c e s and school i n f l u e n c e s a f f e c t i n g t h e i r educational achievement need to be understood. In the present study, performance on numeracy and r e l a t e d memory measures of kindergarten to grade 6 c h i l d r e n from immigrant/ESL f a m i l i e s was compared to that of c h i l d r e n whose parents were born i n Canada and who came from E n g l i s h speaking households. Numeracy performance among four immigrant groups (East Asian, Middle Eastern, F i l i p i n o and European) was a l s o i n v e s t i g a t e d . In a d d i t i o n , the a t t i t u d e s towards mathematics, educational a s p i r a t i o n s and home environment i n r e l a t i o n to l e a r n i n g mathematics were compared among the two groups (immigrant/ESL and Canadian/English) and among three immigrant groups (East Asian, F i l i p i n o and Middle Eastern). The r e l a t i o n s h i p of parents' and c h i l d r e n ' s a t t i t u d e s towards mathematics and t h e i r home l e a r n i n g environment to the c h i l d r e n ' s mathematical performance was a l s o i n v e s t i g a t e d . To determine the E n g l i s h p r o f i c i e n c y of the immigrant sample, the l i t e r a c y performance of the two groups (immigrant/ESL and Canadian born parents/English) was compared. In order to c o n t r o l f o r d i f f e r e n c e s i n socio-economic status between immigrant and Canadian born parents, a sample of parents provided infor m a t i o n 145 about the occupation and educational l e v e l of both partners and the number of c h i l d r e n i n each f a m i l y . Numeracy Performance I t was shown i n a number of stud i e s that c h i l d r e n with recent immigrant backgrounds perform w e l l i n school (Caplan, et a l . , 1991; 1992; F u l i g n i , 1997; Kao, & Tienda, 1995, Lesaux & S i e g e l , 2003; Rodriquez, 2002; S t i e f e l , et a l . , 2003, Zhang, 2001). In the present study, i t was hypothesized that immigrant/ESL c h i l d r e n would perform as w e l l or b e t t e r on numeracy and r e l a t e d memory measures across grades compared to c h i l d r e n coming from E n g l i s h speaking households with Canadian born parents. In a d d i t i o n , i t was expected that the performance of the immigrant/ESL group would i n c r e a s i n g l y improve i n l a t e r grades. These expectations were supported by our f i n d i n g s . C h i l d r e n with recent immigrant backgrounds performed as w e l l or b e t t e r on a l l numeracy and on almost a l l r e l a t e d memory measures as c h i l d r e n with Canadian born parents. This was most evident i n l a t e r grades, as hypothesized. I t i s w e l l known that age upon a r r i v a l plays a r o l e i n c h i l d r e n ' s achievement (Derwing e t . a l . , 1999; Gibson & Bhachu, 1991; Gonzales, 2003; Spiess et a l . , 2003; Young, 1983). Background inform a t i o n provided by a sample of immigrant parents answering a questionnaire suggests that some immigrant/ESL students who j o i n e d the study i n l a t e r grades were i n Canada f o r an extensive p e r i o d of time. Some of the immigrant/ESL students have p a r t i c i p a t e d l o n g i t u d i n a l l y i n t h i s study since kindergarten. Therefore, i t i s l i k e l y that these c h i l d r e n were i n c r e a s i n g l y s u c c e s s f u l i n school as t h e i r E n g l i s h s k i l l s and i n t e g r a t i o n to the country increased. In kindergarten, the numeracy and memory performance of the immigrant/ESL group d i d not d i f f e r on any of the measures from the Canadian born p a r e n t s / E n g l i s h group, with one exception. On the D i g i t Span t e s t , the immigrant/ESL group had s i g n i f i c a n t l y lower scores than the Canadian born p a r e n t s / E n g l i s h group. However, the a c t u a l d i f f e r e n c e between means was very s m a l l ; t h e r e f o r e , t h i s s i g n i f i c a n t d i f f e r e n c e i s l i k e l y to have l i m i t e d p r a c t i c a l value. In grade 1, there was no d i f f e r e n c e between groups when p e r c e n t i l e s were used; however, some d i f f e r e n c e s s t a r t e d to appear between the two groups when standard and raw scores were considered. S p e c i f i c a l l y , on the WRAT-III Computational A r i t h m e t i c , the WJ-III C a l c u l a t i o n and the WJ-III Block Rotation t e s t s , the immigrant/ESL group had s i g n i f i c a n t l y higher scores than the Canadian born p a r e n t s / E n g l i s h group when raw scores were considered, and i n one instance - the WJ-III Block Rotation t e s t - when the standard score was considered. By that p o i n t , many of the immigrant/ESL students had been i n the Canadian school system f o r more than one f u l l year ( t e s t i n g was always near the end of school year). A f t e r t h i s much time i n school 147 surrounded by E n g l i s h speaking peers, the disadvantages of a d j u s t i n g to a new school system and i n s t r u c t i o n i n a new language would be s i g n i f i c a n t l y diminished. At the same time, the performance of the immigrant/ESL students would be b e n e f i t i n g from p a r e n t a l i n f l u e n c e , and the mo t i v a t i o n to t h r i v e academically and a t t i t u d i n a l d i f f e r e n c e s s p e c i f i c to t h i s group. In t h i s grade, the d i f f e r e n c e s are s u b t l e but begin to emerge, e s p e c i a l l y when aspects of i n d i v i d u a l measures are analyzed. For example, the WRAT-III Computational A r i t h m e t i c has two p a r t s : w r i t t e n and o r a l . The immigrant/ESL group d i d not d i f f e r from the Canadian born p a r e n t s / E n g l i s h group on the o r a l part of t h i s t e s t , but the immigrant/ESL group had higher performance than the Canadian born p a r e n t s / E n g l i s h group on the w r i t t e n part of t h i s t e s t . I t i s p o s s i b l e that demands of the task r e q u i r i n g o r a l responses were higher f o r c h i l d r e n with recent immigrant backgrounds than when w r i t t e n responses were re q u i r e d . The immigrant/ESL group a l s o demonstrated higher performance on the Working Memory t e s t of "any order" r e c a l l of o r a l l y presented numbers than the Canadian born p a r e n t s / E n g l i s h group. In grade 2 and up, the d i f f e r e n c e i n the performance of the two groups on numeracy measures s t a r t e d to be evident using p e r c e n t i l e s . Using p e r c e n t i l e s , the immigrant/ESL group had s i g n i f i c a n t l y higher performance than the Canadian born pa r e n t s / E n g l i s h group on the WRAT-III Computational A r i t h m e t i c 148 i n grades 2 to 6; on the WJ-III C a l c u l a t i o n t e s t i n grades 3 to 5; and on the WJ-III Math Fluency t e s t i n grades 3 to 6. In a d d i t i o n , the immigrant/ESL group demonstrated higher performance on some memory measures, where standard scores were used ( i . e . , the Working Memory t e s t i n grades 3 and 5). The groups d i d not d i f f e r on any other numeracy and memory measures. O v e r a l l , i n grades 1 to 6, the performance of the immigrant/ESL students was as good as or b e t t e r than the performance of n a t i v e E n g l i s h speaking students with Canadian born parents on a l l the numeracy and r e l a t e d memory measures. The m a j o r i t y of s i g n i f i c a n t d i f f e r e n c e s between the two groups a l s o had p r a c t i c a l s i g n i f i c a n c e , c o n s i d e r i n g the la r g e d i f f e r e n c e between the means of the two groups. This was p r i m a r i l y i n the case of numeracy measures; however, i n some instances, such as the Working Memory t e s t s , the d i f f e r e n c e between means was r e l a t i v e l y small d espite the s t a t i s t i c a l s i g n i f i c a n c e . The p r a c t i c a l s i g n i f i c a n c e of these s p e c i f i c f i n d i n g s i s l i k e l y to be l i m i t e d , and they should be i n t e r p r e t e d with c a u t i o n . I t i s i n t e r e s t i n g that the supe r i o r performance of immigrant/ESL students was mainly on the group numeracy measures presented v i s u a l l y and r e q u i r i n g w r i t t e n responses. The numeracy t e s t s administered i n i n d i v i d u a l s e t t i n g s and r e q u i r i n g o r a l responses seem to be more c h a l l e n g i n g f o r immigrant/ESL 149 students. These t e s t s are more language-loaded than v i s u a l l y presented group numeracy t e s t s r e q u i r i n g w r i t t e n responses. O v e r a l l , i t appears that immigrant/ESL students are as a group c h a r a c t e r i z e d by c e r t a i n f a c t o r s p o s i t i v e l y a f f e c t i n g t h e i r mathematical performance. The disadvantages of immigrant students coping with l i m i t e d E n g l i s h p r o f i c i e n c y seem to be evident when t h e i r performance on v i s u a l l y administered t e s t s i s compared to that on the numeracy t e s t s with language demands. Immigrant/ESL students perform very w e l l on a l l the numeracy t e s t s , but e s p e c i a l l y on the ones with minimal language demands. Each c u l t u r a l and language group i s a unique pop u l a t i o n , and t h e i r adjustment to school and a new s o c i e t y may help i n understanding a v a r i e t y of f a c t o r s a f f e c t i n g school achievement. When researching school achievement of immigrant c h i l d r e n as a whole, i t i s important to acknowledge the d i v e r s i t y w i t h i n t h i s p o p u l a t i o n . In order to understand the d i v e r s i t y w i t h i n our immigrant/ESL group i n terms of performance on numeracy and memory measures, four language groups were created according to c o u n t r i e s of o r i g i n : Middle Eastern (mostly Persian speakers from Iran, some Kurdish, A r a b i c , and Turkish speakers), F i l i p i n o s , East Asians (Japanese, Korean, Cantonese and Mandarin speakers), and Europeans (Russian, Serbian, B u l g a r i a n , P o l i s h , Romanian and Czech, Greek, Swedish, French, Estonian and Norwegian speakers). This grouping was i n f l u e n c e d by previous s t u d i e s i n v e s t i g a t i n g the educational attainment of c h i l d r e n of immigrants which d i v i d e d t h e i r subjects i n t o d i f f e r e n t e t h n i c groups (e.g., Aldous, 2006; F u l i g n i , 1997). The hypothesis that East Asian students would have the highest numeracy performance was based on previous research. In both c r o s s - c u l t u r a l and with i n - c o u n t r y s t u d i e s , i t has been shown that East Asian students are high a c h i e v i n g i n mathematics compared to other groups (e.g., Campbell & Xue, 2001; Chen & Stevenson, 1995; R o b i t a i l l e & Gardner, 1989; Stevenson et a l . , 1990; S t i g l e r , Lee, Lucker, & Stevenson, 1982; Wong, 1980; 1998). For t h i s a n a l y s i s , three measures (WRAT-III Computational A r i t h m e t i c , WJ-III C a l c u l a t i o n and WJ-III Math Fluency) that d i s c r i m i n a t e between the immigrant/ESL group and the Canadian born p a r e n t s / E n g l i s h group i n previous analyses were used. The hypothesis that East Asian students would have higher scores than other immigrant groups on numeracy measures was supported by the present f i n d i n g s . C h i l d r e n with East Asian o r i g i n s had the strongest performance compared to other groups on a l l three measures, and these were s i g n i f i c a n t from grades 2 to 6. The super i o r performance of East Asian students i s most l i k e l y due to the strong emphasis on education, school e f f o r t and moti v a t i o n to succeed shared by East Asian nations. Using data from our l o n g i t u d i n a l sample, there was a s i g n i f i c a n t p o s i t i v e r e l a t i o n s h i p between many kindergarten and 151 grade 6 measures, and between many grade 1 and grade 5 measures. This suggests that c h i l d r e n who d i d w e l l i n kindergarten a l s o performed w e l l i n grade 6, and that c h i l d r e n who d i d w e l l i n grade 1 were l i k e l y to do w e l l i n grade 5. In a d d i t i o n , e a r l y memory measures were s i g n i f i c a n t l y c o r r e l a t e d with the l a t e r numeracy measures. For example, the kindergarten Working Memory t e s t was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d with the WJ-III C a l c u l a t i o n t e s t administered i n grade 6, and the kindergarten WISC-III D i g i t Span t e s t c o r r e l a t e d with the WRAT-III Computational A r i t h m e t i c t e s t and the WJ-III A p p l i e d Problems t e s t administered i n grade 6. The Grade 1 Working Memory t e s t was s i g n i f i c a n t l y p o s i t i v e l y c o r r e l a t e d with the WRAT-III A r i t h m e t i c t e s t , the WJ-III Q u a n t i t a t i v e Concepts t e s t , the WJ-I I I A p p l i e d Problems t e s t , and the WJ-III Math Fluency t e s t administered i n grade 5. The grade 1 WISC-III D i g i t span t e s t c o r r e l a t e d with the grade 5 WJ-III Q u a n t i t a t i v e Concepts t e s t . This suggests that e a r l y memory measures are p r e d i c t i v e of l a t e r numeracy performance. Literacy Performance As one might expect, there i s considerable v a r i a b i l i t y i n E n g l i s h p r o f i c i e n c y among those subjects with recent immigrant backgrounds and ESL. When a sample of parents who immigrated to Canada were asked about the language and c u l t u r a l environment they provide to t h e i r c h i l d r e n at home, t h e i r answers v a r i e d 152 considerably, as expected. Some c h i l d r e n were exposed e x c l u s i v e l y to t h e i r mother tongue at home, some were using both E n g l i s h and t h e i r mother tongue, and some f a m i l i e s p r e f e r r e d to use E n g l i s h . In a d d i t i o n , some c h i l d r e n were immigrants themselves, while others were born i n Canada. This d i v e r s i t y was r e f l e c t e d i n the l i t e r a c y performance. C h i l d r e n with recent immigrant backgrounds d i d not perform as w e l l as c h i l d r e n with Canadian born parents on some of the l i t e r a c y measures. On the Verbal Reasoning t e s t s i n grades 2 and 3, and on the Reading Comprehension t e s t i n g grade 5, t h e i r performance was s i g n i f i c a n t l y lower than that of c h i l d r e n with Canadian born parents. Common sense would suggest that tasks i n v o l v i n g v e r b a l analogies or comprehension of t e x t would be more d i f f i c u l t f o r anyone with l i m i t e d E n g l i s h p r o f i c i e n c y . The lower performance of the immigrant/ESL group on some l i t e r a c y measures i s l i k e l y due to the l i m i t e d E n g l i s h p r o f i c i e n c y of some of the c h i l d r e n i n t h i s group. As noted p r e v i o u s l y , our immigrant/ESL sample i s very d i v e r s e , and some of the students w i t h i n t h i s sample are very new i n Canada, while others are more f a m i l i a r with Canada and E n g l i s h than with t h e i r home country and mother tongue. Immigrant parents answering the questionnaire provided an idea of the d i v e r s i t y w i t h i n the immigrant sample of t h i s study i n terms of t h e i r language, exposure to Canadian c u l t u r e , and t h e i r c o n t i n u i n g t i e s to the 153 c u l t u r e s of t h e i r homelands. In each grade, there were some ESL c h i l d r e n who were new not only to the study, but a l s o to Canada. I t i s important to r e a l i z e that these c h i l d r e n are inc l u d e d i n our immigrant/ESL sample, even though t h e i r l i m i t e d E n g l i s h p r o f i c i e n c y c l e a r l y impaired t h e i r o v e r a l l performance during t e s t i n g . I t i s i n t e r e s t i n g to note though t h a t , on many of the l i t e r a c y measures (e.g., WJ-III Word Attack) as w e l l as on a l l language loaded numeracy measures (e.g., WJ-III A p p l i e d Problems), the immigrant/ESL group d i d not d i f f e r from the Canadian born p a r e n t s / E n g l i s h group. Moreover, on the S p e l l i n g t e s t i n grade 4, the performance of the immigrant/ESL group was at a su p e r i o r l e v e l compared to the Canadian born pa r e n t s / E n g l i s h group. In a previous study, a l s o conducted i n North Vancouver schools, i t was found that grade 2 immigrant/ESL c h i l d r e n performed at a higher l e v e l than n a t i v e E n g l i s h speaking c h i l d r e n on s p e l l i n g t e s t s (Lesaux, & S i e g e l , 2003). I t was suggested that p o s i t i v e e f f e c t s of b i l i n g u a l i s m c o n t r i b u t e d to the high performance of c h i l d r e n with ESL. A l a c k of s i g n i f i c a n t d i f f e r e n c e between the two groups on most of the l i t e r a c y measures suggests that many students i n our immigrant/ESL sample have become b i l i n g u a l or p r o f i c i e n t i n E n g l i s h . The f a c t s that some c h i l d r e n w i t h i n our immigrant/ESL sample were born i n Canada and that many came to Canada when they were very young and were exposed to E n g l i s h and the Canadian educational system r e l a t i v e l y e a r l y were l i k e l y to have an impact on both t h e i r E n g l i s h p r o f i c i e n c y and school achievement. The ne a r l y matching performance of the immigrant/ESL c h i l d r e n on l i t e r a c y measures with that of the Canadian born p a r e n t s / E n g l i s h group suggests that the c u l t u r a l imperatives emphasizing high academic achievement - along with the c o g n i t i v e advantages that may accrue to b i l i n g u a l c h i l d r e n -compensate f o r t h e i r r e l a t i v e inexperience with E n g l i s h . I f an ESL c h i l d becomes b i l i n g u a l or acquires good E n g l i s h p r o f i c i e n c y , then that c h i l d ' s ESL status changes from a disadvantage to an advantage. This assumption i s supported by f i n d i n g s i n a number of studie s showing that students' exposure to m u l t i p l e languages p o s i t i v e l y c o r r e l a t e s with school success (Caplan, et a l . , 1991; 1992; F u l i g n i , 1997; Kao, & Tienda, 1995, Lesaux & S i e g e l , 2003; Rodriquez, 2002; Zhang, 2001). Attitudes towards Education and Mathematics, Home Support and Numeracy Performance In grades 5 and 6, a survey was administered to c h i l d r e n and to t h e i r parents. The goal of t h i s q u estionnaire was to i n v e s t i g a t e c h i l d r e n ' s and parents' a t t i t u d e s towards mathematics, schoo l i n g and the home support c h i l d r e n r e c e ived i n mathematics, and to i n v e s t i g a t e some of the d i f f e r e n c e s between the immigrant/ESL and Canadian born p a r e n t s / E n g l i s h groups i n t h i s regard. I t was hypothesized that the immigrant/ESL parents would have higher educational a s p i r a t i o n s f o r t h e i r c h i l d r e n , would care more about t h e i r c h i l d r e n ' s grades and school achievement, and would provide more t u t o r i n g and a s s i s t a n c e with mathematics at home than Canadian born parents, and that immigrant/ESL c h i l d r e n would care more about t h e i r mathematical achievement and have higher educational a s p i r a t i o n s than c h i l d r e n with Canadian born parents. When i n t e r p r e t i n g questionnaire responses the " s o c i a l d e s i r a b i l i t y e f f e c t " was considered. At l e a s t some parents and c h i l d r e n were l i k e l y to provide answers more r e f l e c t i n g t h e i r d e s i r e to present f a v o r a b l y t h e i r home l e a r n i n g environment than to give i t s true d e s c r i p t i o n . In order to minimize the " s o c i a l d e s i r a b i l i t y e f f e c t " , the questions and statements were designed to be as n e u t r a l as p o s s i b l e , and both parents and c h i l d r e n were ensured that t h e i r answers w i l l be kept c o n f i d e n t i a l . In a d d i t i o n , i t i s l i k e l y t hat the parents answering the questionnaires were the ones most i n c l i n e d to cooperate with schools, and who valued the importance of t h e i r c h i l d r e n ' s education. These parents were more l i k e l y to provide p o s i t i v e answers regarding the importance of grades, higher education and home support i n l e a r n i n g ; however, i t i s encouraging t h a t , despite t h i s f a c t o r , the d i f f e r e n c e between the immigrant and Canadian groups s t i l l appeared. A l s o , to increase the v a l i d i t y 156 of the questionnaire responses, matching questions were given to both parents and c h i l d r e n . There appeared to be a strong p o s i t i v e c o r r e l a t i o n between a l l matching p a r e n t a l and c h i l d r e n ' s responses. This suggests that the m a j o r i t y of the questionnaires were answered with honesty. There were some notable c o n t r a s t s supporting our hypotheses i n the c h i l d r e n ' s and p a r e n t a l responses when the immigrant/ESL group was compared to the Canadian born p a r e n t s / E n g l i s h group. I t was a l s o hoped that the questionnaires might o f f e r some i n s i g h t i n t o the r e l a t i o n s h i p between c h i l d r e n ' s and parents' a t t i t u d e s towards mathematics, education and mathematical achievement. In support of the o r i g i n a l hypothesis, a r e l a t i o n s h i p was found between c h i l d r e n ' s numeracy performance i n grades 5 and 6 and questionnaire responses ( i n the case of both c h i l d r e n ' s and parents' answers). This f i n d i n g of a r e l a t i o n s h i p between p a r e n t a l a t t i t u d e s towards education, the l e a r n i n g environment at home and academic performance i s not new. I t i s w e l l accepted that p a r e n t a l a t t i t u d e s towards mathematics and education a f f e c t c h i l d r e n ' s mathematical achievement i n both elementary and middle schools (Entwisle & Alexander, 1990; 1996; G i l l & Reynolds, 1999; H a l l e , K urtz-Costes & Mahoney, 1997; Sheldon & Eps t e i n , 2005; Wang & Wildman, 1994) . 157 As expected, immigrant/ESL parents rated as more important that t h e i r c h i l d r e n a t t a i n u n i v e r s i t y education and o b t a i n high grades i n mathematics than d i d Canadian born/English speaking parents. This f i n d i n g i s supported by a number of s t u d i e s . For example, i t was reported that immigrant parents are more l i k e l y to d i s c u s s c o l l e g e options with t h e i r c h i l d r e n (Kao, 2004) and there appears to be a strong emphasis on school success i n recent immigrant f a m i l i e s (e.g., Bankston, & Zhou, 1995; Caplan et a l . , 1991; 1992; Gibson, 1991; F u l i g n i , 1997; Kao & Tienda, 1995; S c h a l l e r , Rocha, & Barshinger, 2007). Immigrant parents from various c u l t u r a l backgrounds, i n c l u d i n g East Asians, F i l i p i n o s , Indians, Caribbeans and Europeans, encourage t h e i r c h i l d r e n to value education and motivate them to work hard i n school (Caplan, et a l . , 1991/ 1992; Gibson, 1991; F u l i g n i , 1997; Waters, 1994). In the present study i t was a l s o shown that foreign-born parents b e l i e v e d that t h e i r c h i l d r e n can do b e t t e r i n mathematics and want them to do b e t t e r compared to Canadian born parents. Again, t h i s f i n d i n g i s w e l l supported. For example, i t was reported that East Asian parents are much more ambitious about t h e i r c h i l d r e n ' s mathematical achievement and show l e s s s a t i s f a c t i o n with t h e i r c h i l d r e n ' s performance than North American parents (Stevenson et a l . , 1986; Stevenson et a l . , 1993) and that Mexican immigrant mothers with l i m i t e d 158 academic backgrounds e x h i b i t e d high a s p i r a t i o n s i n terms of t h e i r c h i l d r e n ' s school achievement ( S c h a l l e r , et a l . , 2007). When the o v e r a l l performance of c h i l d r e n whose parents wanted them to do b e t t e r i n mathematics and b e l i e v e d that they can do b e t t e r was compared to the performance of c h i l d r e n whose parents had the opposite b e l i e f s , i t was found that c h i l d r e n whose parents are not s a t i s f i e d with t h e i r mathematical s k i l l s have weaker performance on s e l e c t e d numeracy measures i n both grades. This f i n d i n g i s not s u r p r i s i n g . I t i s expected that i f c h i l d r e n do not do w e l l i n mathematics t h e i r parents w i l l want them to improve t h e i r s k i l l s and are l i k e l y to b e l i e v e that t h e i r c h i l d r e n are capable of improvement; however, f i n d i n g s i g n i f i c a n t d i f f e r e n c e s i n these p a r e n t a l a s p i r a t i o n s between d i f f e r e n t groups i s l i k e l y to r e f l e c t the tendency of a given group - i n our case immigrant parents - to motivate t h e i r c h i l d r e n to be d i s s a t i s f i e d with t h e i r performance and to s t r i v e f o r improvement regardless of how they compare to others. The emphasis on education and school success seems to be shared by c h i l d r e n of immigrant parents hol d i n g these a s p i r a t i o n s f o r them. I t i s w e l l documented that parents i n f l u e n c e t h e i r c h i l d r e n ' s a t t i t u d e s towards mathematics ( B a l l i , 1998) and towards school performance and behavior i n general (Fantuzzo, Davis, & Ginsburg, 1995; H i l l & C r a f t , 2003; Izzo, Weissberg, Kasprow, & Frendrich, 1999). In the present study, 159 s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n s were found between c h i l d r e n ' s and p a r e n t a l responses on qu e s t i o n n a i r e s . For example, c h i l d r e n whose parents b e l i e v e d that t h e i r c h i l d r e n can and should improve t h e i r performance i n mathematics shared the same a s p i r a t i o n s about t h e i r mathematical s k i l l s . Parents p l a y an important r o l e i n t h e i r c h i l d r e n ' s education, and i t i s understandable that t h e i r b e l i e f s and expectations are r e f l e c t e d i n t h e i r c h i l d r e n ' s perception of schooli n g and t h e i r academic performance. I t was reported that c h i l d r e n of foreign-born parents are aware that t h e i r parents want them to do w e l l i n school, to have high grades and to obta i n post-secondary education ( F u l i g n i , 1997; Gibson, 1991; Matute-Bianchi, 1991). I t has a l s o been observed that c h i l d r e n of recent immigrants are motivated to do w e l l and to t r y hard i n school (Caplan, et a l . , 1991; F u l i g n i , 1997; Waters, 1994). In the present study, c h i l d r e n with f o r e i g n born parents were more l i k e l y than students with Canadian born parents to say that they l i k e mathematics, that they want to do b e t t e r i n mathematics than they do now and that they w i l l need mathematics l a t e r i n l i f e . C h i l d r e n ' s a t t i t u d e s are a l s o an important f a c t o r i n f l u e n c i n g t h e i r mathematical achievement. For example, i t was reported that c h i l d r e n ' s b e l i e f s about mathematics were p o s i t i v e l y r e l a t e d to t h e i r mathematical achievement (Anderson, Rogers, K l i n g e r , Ungerleider, Glickman, & Anderson, 2006) and 160 that educational a s p i r a t i o n s of both parents and c h i l d r e n p o s i t i v e l y c o r r e l a t e d with school success (Aldous, 2006). In the present study, c h i l d r e n saying that i t i s important f o r them to get high grades i n mathematics had higher numeracy performance, i n both grades than c h i l d r e n who d i d not say so. S p e c i f i c a l l y , c h i l d r e n who answered "yes" to the question: " I s i t very important f o r you to get high grades i n mathematics?" had s i g n i f i c a n t l y higher scores on a l l three grade 5 numeracy measures and one measure i n grade 6 than c h i l d r e n who answered "no" to the same question. C h i l d r e n ' s l i k i n g of mathematics was a l s o r e l a t e d to t h e i r numeracy performance i n both grades. C h i l d r e n who s a i d that they l i k e mathematics had s i g n i f i c a n t l y higher scores on some measures i n both grades than c h i l d r e n who s a i d that they do not l i k e mathematics. S i m i l a r l y , i n grade 6, c h i l d r e n who s a i d that they would be happy i f someone c a n c e l l e d a l l c l a s s e s i n mathematics had s i g n i f i c a n t l y lower numeracy performance than c h i l d r e n who answered "no" to t h i s question. According to p a r e n t a l and c h i l d r e n ' s responses on the que s t i o n n a i r e , i t appears that f a m i l i e s with recent immigrant backgrounds, besides wanting t h e i r c h i l d r e n to do w e l l i n mathematics, a l s o provide support such as t u t o r i n g and help with mathematics to help t h e i r c h i l d r e n succeed. Immigrant/ESL c h i l d r e n i n d i c a t e d more than E n g l i s h speaking c h i l d r e n with Canadian born parents that they r e c e i v e help with mathematics 161 outside of school (mostly from f a m i l y members, but a l s o from f r i e n d s and t u t o r s ) . S i m i l a r l y , immigrant/ESL parents were more l i k e l y than Canadian born parents to i n d i c a t e that t h e i r c h i l d r e n r e c e i v e t u t o r i n g i n mathematics outside of school, that they or other f a m i l y members t u t o r t h e i r c h i l d r e n i n mathematics, and that t h e i r c h i l d r e n are exposed to other-than-school mathematical e x e r c i s e s . This f i n d i n g i s supported by a previous study conducted i n North Vancouver using the same cohort of c h i l d r e n who p a r t i c i p a t e d l o n g i t u d i n a l l y i n t h i s study from kindergarten to grade 3 (Kerr, 2004). Some parents of grade 6 c h i l d r e n who answered our questionnaire i n the present study a l s o answered a s i m i l a r q uestionnaire when t h e i r c h i l d r e n were i n grade 3. In t h i s study, f o r e i g n born parents of grade 3 c h i l d r e n were more l i k e l y to t u t o r t h e i r c h i l d r e n i n academic subjects than Canadian-born parents. I t i s w e l l documented that a supportive l e a r n i n g environment at home i s as s o c i a t e d with c h i l d r e n ' s academic success (Grolnick & Slowjaczek, 1994; Hickman, Greenwood, & M i l l e r , 1995; Peng SWright, 1993; Shaver & Walls, 1998). In the present study, r e c e i v i n g e x t r a p r a c t i c e i n mathematics at home was p o s i t i v e l y r e l a t e d to c h i l d r e n ' s performance on numeracy measures. I t was found that t u t o r i n g and exposure to other-than-school mathematical e x e r c i s e s was p o s i t i v e l y r e l a t e d to c h i l d r e n ' s math achievement. C h i l d r e n of parents who s a i d that t h e i r c h i l d r e n r e c e i v e t u t o r i n g i n 162 mathematics performed s i g n i f i c a n t l y higher on the WRAT-III A r i t h m e t i c i n grades 5 and 6 than d i d c h i l d r e n who d i d not r e c e i v e t u t o r i n g . C h i l d r e n who were exposed to any other-than-school mathematical e x e r c i s e s had s i g n i f i c a n t l y higher scores on the WRAT-III A r i t h m e t i c i n grade 6 than c h i l d r e n who were not exposed to i t . However, not a l l the a t t e n t i o n from parents was p o s i t i v e l y r e l a t e d to t h e i r c h i l d r e n ' s performance. There were some inverse r e l a t i o n s h i p s between p a r e n t a l support and c h i l d r e n ' s school achievement. In some instances, i t appears that the help with mathematics c h i l d r e n received r e f l e c t s the c h i l d r e n ' s weakness i n mathematics and the need f o r a s s i s t a n c e , r a t h e r than t h e i r s t r i v i n g f o r e x c e l l e n c e . For example, c h i l d r e n who, according to t h e i r parents, received help with homework had s i g n i f i c a n t l y lower scores on some numeracy measures i n both grades than c h i l d r e n who d i d not r e c e i v e help with homework. S i m i l a r l y , c h i l d r e n who s a i d that t h e i r parents p r a c t i c e mathematics with them had s i g n i f i c a n t l y lower performance on some numeracy measures i n both grades than c h i l d r e n who s a i d that t h e i r parents do not p r a c t i c e mathematics with them. S i m i l a r f i n d i n g s of inverse r e l a t i o n s h i p s between p a r e n t a l a t t e n t i o n and students' school performance have been reported i n other s t u d i e s . For example, the r e l a t i o n s h i p between the amount of time spent doing homework and mathematical achievement of 163 elementary school c h i l d r e n l i v i n g i n China, Japan and the United States was not s i g n i f i c a n t when achievement w i t h i n each country was considered (Chen & Stevenson, 1989). In the same study, i t was a l s o found that p a r e n t a l a s s i s t a n c e was n e g a t i v e l y c o r r e l a t e d with c h i l d r e n ' s achievement. In other s t u d i e s , i t was found that p a r e n t a l a s s i s t a n c e with mathematics homework was n e g a t i v e l y r e l a t e d to mathematics scores (Anderson, et a l . , 2006) and that p a r e n t a l help with mathematics was a negative f a c t o r i n c h i l d r e n ' s achievement (Aldous, 2006). This may be because c h i l d r e n who st r u g g l e i n mathematics are l i k e l y to need more help from parents than students who f i n d mathematics easy. Canadian born parents i n d i c a t e d more than f o r e i g n born parents that they p l a y mathematics - r e l a t e d games with t h e i r c h i l d r e n , such as Monopoly. P l a y i n g mathematics - r e l a t e d games was not r e f l e c t e d i n c h i l d r e n ' s numeracy performance i n grades 5 and 6. There was no s i g n i f i c a n t d i f f e r e n c e i n the numeracy performance of c h i l d r e n who were p l a y i n g mathematics-related games with t h e i r f a m i l i e s . I t may be that immigrant/ESL parents focus on more e x p l i c i t f a c t o r s c o n t r i b u t i n g to t h e i r c h i l d r e n ' s mathematical performance such as p r a c t i c e , t u t o r i n g and s t r e s s i n g high education. Canadian born parents are l e s s concerned with these i s s u e s . The f a c t that they p l a y f a m i l y mathematics - r e l a t e d games with t h e i r c h i l d r e n more than immigrant parents may be r e l a t e d to the p o p u l a r i t y of these games i n Canadian c u l t u r e , r a t h e r than to the goal of improving the mathematical s k i l l s of t h e i r c h i l d r e n . Students with Canadian born parents b e l i e v e d more that they l e a r n u s e f u l things i n mathematics compared to immigrant/ESL students. I t could be t h a t , when l e a r n i n g mathematics, c h i l d r e n with Canadian born parents focus more on the p r a c t i c a l use of mathematics compared to c h i l d r e n with recent immigrant backgrounds who enjoy mathematics, who see t h e i r f u t u r e educational attainment, and focus on improving t h e i r mathematical s k i l l s i n order to succeed; however, t h i s assumption i s l i k e l y to be relev a n t only to a small sample of c h i l d r e n h o l d i n g these b e l i e f s about the usefulness of mathematics. Considering the f a c t t h a t , d e s pite t h i s s i g n i f i c a n t d i f f e r e n c e between groups, the m a j o r i t y of c h i l d r e n i n both groups (92% of immigrant/ESL c h i l d r e n and a l l c h i l d r e n with Canadian born parents) b e l i e v e d i n the usefulness of mathematics, the s i g n i f i c a n t d i f f e r e n c e between the two groups i s not l i k e l y to have p r a c t i c a l importance. There were some s i g n i f i c a n t d i f f e r e n c e s between groups when the answers of c h i l d r e n and parents of three immigrant groups (East Asian, Middle Eastern and F i l i p i n o ) were compared. East Asian and Middle Eastern c h i l d r e n s a i d that they l i k e mathematics more than F i l i p i n o c h i l d r e n . In a d d i t i o n , East Asian c h i l d r e n were most l i k e l y to b e l i e v e that they do b e t t e r i n 165 mathematics than other c h i l d r e n and F i l i p i n o c h i l d r e n were most l i k e l y to say that they do not do as w e l l . These answers correspond with c h i l d r e n ' s numeracy performance: o v e r a l l , East Asian students had the highest scores and F i l i p i n o students the lowest. The s u p e r i o r performance of East Asian students i n mathematics has been w e l l demonstrated i n a number of st u d i e s as described above. The f a c t that East Asian students do w e l l i s r e l a t e d to various f a c t o r s such as the high q u a l i t y of mathematical education i n East Asian c o u n t r i e s , the importance these c u l t u r e s a t t a c h to l e a r n i n g mathematics and education i n general and the m o t i v a t i o n of these students to work hard and to succeed. The f a c t that more East Asian parents than F i l i p i n o and Middle Eastern parents s a i d that t h e i r c h i l d r e n r e c e i v e t u t o r i n g outside of school a l s o r e f l e c t s the importance of l e a r n i n g mathematics f o r East Asian f a m i l i e s . From a l l three groups, Middle Eastern parents s t r e s s e d the importance of t h e i r c h i l d r e n g e t t i n g u n i v e r s i t y education the most. When d e s c r i b i n g the performance of immigrant students as a whole, one has to be c a r e f u l not g e n e r a l i z e the r e s u l t s and to acknowledge d i v e r s i t y w i t h i n t h i s group. Practical Implications Educators o f t e n f e e l overwhelmed by d i v e r s i t y i n t h e i r classrooms, and by the l i m i t e d language s k i l l s of many of the students. Research may provide s p e c i f i c i n s i g h t s i n t o how best to accommodate students with recent immigrant backgrounds. I t i s p o s s i b l e that s p e c i f i c i n t e r v e n t i o n by parents of immigrant backgrounds i s having the d e s i r e d e f f e c t of compensating f o r some very r e a l disadvantages faced by c h i l d r e n of immigrant/ESL backgrounds i n t h e i r e a r l y education. E x p l o r i n g the parenting f a c t o r s promoting school success may help i n generating parent t r a i n i n g i n t e r v e n t i o n s f o r c e r t a i n populations whose c h i l d r e n s t r u g g l e i n school, and i n understanding the impact of moti v a t i o n on c h i l d r e n ' s achievement. In a s o c i e t y as d i v e r s e as Canada, i t i s important to understand the s p e c i f i c features of c e r t a i n populations and the r e l a t i o n s h i p of t h e i r s o c i e t a l f a c t o r s to t h e i r c h i l d r e n ' s school performance. The task of t h i s study was to t e s t whether the performance of c h i l d r e n from f a m i l i e s with recent immigrant backgrounds d i f f e r s from that of c h i l d r e n with Canadian born parents. In a d d i t i o n , the a t t i t u d e s towards mathematics and the home environment of both c h i l d r e n and t h e i r parents i n these two groups were i n v e s t i g a t e d . The performance of c h i l d r e n of f o r e i g n born parents was as good or b e t t e r on a l l the numeracy measures when compared to the performance of c h i l d r e n with Canadian born parents. The p a r e n t a l involvement (e.g., t u t o r i n g , educational a s p i r a t i o n s ) of immigrant parents was higher than that of Canadian parents, and t h i s p a r e n t a l behavior was r e f l e c t e d i n t h e i r c h i l d r e n ' s a t t i t u d e s towards mathematics and t h e i r numeracy performance. 167 I d e n t i f i c a t i o n of these f a c t o r s and r e l a t i o n s h i p s helps to understand the complex i n t e r p l a y between the immigrant s t a t u s , home environment, c u l t u r a l values and school achievement of elementary school students. Concluding Remarks Moving one's f a m i l y to a new country i n v o l v e s enormous e f f o r t , r i s k , and s a c r i f i c e . People leave behind t h e i r homes, t h e i r extended f a m i l y , t h e i r f r i e n d s , secure, o f t e n p r e s t i g i o u s careers, and the c u l t u r a l and l i n g u i s t i c environment they have known t h e i r e n t i r e l i v e s . They come to a place about which they may know next to nothing, where t h e i r p r o f e s s i o n a l c r e d e n t i a l s may never be recognized, where they face having to s t r u g g l e to f i n d even menial work, where they do not know the language or c u l t u r e , and where they may la c k a l l the support of f a m i l y and f r i e n d s that they enjoyed i n t h e i r country of o r i g i n . In the present study, there was no s i g n i f i c a n t d i f f e r e n c e i n the educational l e v e l s of immigrant parents and Canadian parents; however, about h a l f of immigrant parents had lower status work i n Canada than i n t h e i r home country. In some cases, the change was q u i t e dramatic: f o r example, i n one fa m i l y , both parents are working at a gas s t a t i o n i n Canada, while i n t h e i r home country, the f a t h e r was an accountant and the mother was s t a y i n g home r a i s i n g t h e i r c h i l d r e n . In another f a m i l y , both parents were working as medical l a b t e c h n i c i a n s i n t h e i r home country, and i n 168 Canada, the mother works as a c a s h i e r and the f a t h e r as a ro o f e r . Contrary to what many b e l i e v e , coming to Canada means a much harder l i f e f o r many immigrants than what they enjoyed i n t h e i r homeland. The challenges faced by immigrant parents i n e s t a b l i s h i n g themselves i n a new country can make the choice to come seem incomprehensible, not l e a s t to the immigrants themselves; yet even among those who seem to have s a c r i f i c e d the most, the p o s s i b i l i t y of a b e t t e r f u t u r e f o r t h e i r c h i l d r e n can be enough to f o s t e r a deep c o n v i c t i o n that t h e i r choice was the r i g h t one. I f an immigrant f a m i l y has l e f t a r e l a t i v e l y comfortable, middle c l a s s existence i n t h e i r homeland f o r a l i f e i n Canada where parents might have to work m u l t i p l e , low-status, low^paing jobs, i t i s not s u r p r i s i n g that they would look to t h e i r c h i l d r e n ' s futures as the r a t i o n a l e f o r a l l t h e i r s a c r i f i c e . Many f a m i l i e s are f u l l y aware of the r i s k s and challenges they face as immigrants w e l l before they migrate. While Canada does welcome lar g e numbers of refugees, the bulk of immigrants are not f l e e i n g poverty or war. They are, however, oft e n l e a v i n g places where t h e i r existences ^ comfortable though they may be -are under the shadow of f a c t o r s which could threaten the q u a l i t y of l i f e , the l i b e r t y , and even the p h y s i c a l s a f e t y of t h e i r c h i l d r e n . Many I r a n i a n f a m i l i e s , f o r example, leave s o l i d l y 169 middle=class l i v e s because they are deeply t r o u b l e d by the a u t h o r i t a r i a n , t h e o c r a t i c regime under which they l i v e . P r i o r to 1979, under the l e a d e r s h i p of the Shah, Iran's regime may have been j u s t as a u t o c r a t i c , but i t was s e c u l a r and cosmopolitan, and d i d not a t t r a c t the animosity of i t s neighbours and the West. Since the r e v o l u t i o n i n 1979, o l d e r Iranians have witnessed a war with neighbouring I r a q that cost n e a r l y a m i l l i o n l i v e s , and the emergence of a theocracy decidedly h o s t i l e to the educated, urban middle c l a s s from which most Ir a n i a n immigrants to Canada come. They come to Canada not because of what they lacked i n Iran, but because of what they fear might await t h e i r c h i l d r e n there. Every parent wants t h e i r c h i l d r e n to have a secure, happy f u t u r e ; but few need that outcome i n the way that immigrant parents do. Immigrant parents' wishes f o r t h e i r c h i l d r e n ' s f u t u r e happiness and s e c u r i t y are expressed through the emphasis they place on educational achievement. Their very newness i n the country means that immigrant parents w i l l have fewer p r o f e s s i o n a l and s o c i a l preoccupations than many Canadian born parents, f u r t h e r sharpening t h e i r focus on the w e l l being and achievement of t h e i r c h i l d r e n . They w i l l consequently pay more a t t e n t i o n and devote more e f f o r t to t h e i r c h i l d r e n ' s school achievement. C h i l d r e n of immigrants are encouraged to have high a s p i r a t i o n s , to value education, and to work hard at school. They are made to understand that t h e i r school achievement i s of great importance to t h e i r parents, and that t h e i r parents' expectations are high. The n a t u r a l d e s i r e of c h i l d r e n to please t h e i r parents t r a n s l a t e s i n t o an added i n c e n t i v e f o r immigrant c h i l d r e n to do w e l l i n school. 171 References Aldous, J . (2007) . Family, e t h n i c i t y , and immigrant youths' educational achievements. Journal of Family Issues, 27, 1633-1667. A l l e n , J . P. (2005). How s u c c e s s f u l are recent immigrants to the United States and t h e i r c h i l d r e n ? Presidential Address delivered to the Association of Pacific Coast Geographers, 68th annual meeting, Phoenix, Arizona. A r i a s , B. (1986). The context of education f o r Hispanic students: An overview. American Journal of Education, 95, 26-57. Aroian, K. J . (2006). C h i l d r e n of foreign^born parents. Journal of Psychosocial Nursing, 44, 15-18. B a l l i , S. J . , Demo, D. H., & Wedman, J. F. (1998).Family involvement with c h i l d r e n ' s homework: An i n t e r v e n t i o n i n the middle grades. Family Relations, 41, 14 9-157. Beery, K. & Buktenica, N. (1989). Beery-Buktenica Developmental Test of Visual Motor Integration (VMI) . Parsippany, NJ: Modern Curriculum Press. Boyod, M. (2002). Educational attainments of immigrant o f f s p r i n g : Success or segmented a s s i m i l a t i o n ? International Migration Review, 36, 1037-1060. 172 Bradby, D. (1992). Language characteristics and Academic Achievement: A look at Asian and Hispanic Eight Grades in NELS:88. Washington, DC: U.S. Department of Education. Caplan, N., Choy, M. H., & Whitmore, J. K. (1991). Children of the Boat People: A Study of Educational Success. Ann Arbor: U n i v e r s i t y Press. Caplan, N., Choy, M. H., & Whitmore, J. K. (1992). Indochinese refugee f a m i l i e s and academic achievement. Scientific /American, 266, 36-42. Chen, C , & Stevenson, H. W. (1989). Homework: A c r o s s - c u l t u r a l examination. Child Development, 60, 551-561. Chen, C , & Stevenson, H. W. (1995). M o t i v a t i o n and mathematics achievement: A comparative study of Asian-American, Caucasian-American, and East Asian high school students. Child Development, 66, 1215-1234. Crosswhite, F. J . , Dossey, J . A., Swafford, J . 0., McKnight, C. C , & Cooney, T. J . (1985). Second International Mathematics Study Summary Report for the United States. Champaign, IL: S t i p e s . Derwing, T. M., DeCorby, E., Ichikawa, J . , & Jamieson, K. (1999). Some f a c t o r s that a f f e c t the success of ESL high school students. Canadian Modern Language Review, 55, 532-547 . Duran, B. J . , & Weffer, R. E. (1992). Immigrant's a s p i r a t i o n s , high school process, and academic outcomes. American Educational Research Journal, 29, 163-181. E n t w i s l e , D., & Alexander, K. (1996). Family type and c h i l d r e n ' s growth i n reading and math over the primary grades. Journal of Marriage and Family, 58, 341-355. E n t w i s l e , D., & Alexander, K. (1990). Beginning school math competence: M i n o r i t y and m a j o r i t y comparisons. Child Development, 61, 454-471. Fantuzzo, J . W., Davis, G. Y., & Ginsburg, M. D. (1995). E f f e c t of parent involvement i n i s o l a t i o n or i n combination with peer t u t o r i n g on student self-concept and mathematical achievement. Journal of Educational Psychology, 87, 272-281. F u l i g n i , A. J . (1997). The academic achievement of adolescents from immigrant f a m i l i e s : the r o l e s of f a m i l y background, a t t i t u d e s , and behavior. Child Development, 68, 351-363. Fuson, K. C , S t i g l e r , J. W., & Barsch, K. (1988). Grade placement of a d d i t i o n and s u b t r a c t i o n t o p i c s i n Japan, Mainland China, the Soviet Union, Taiwan, and the United States. Journal for Research in Mathematics Education, 19, 449-456. 174 Geary, D. C. (1996). I n t e r n a t i o n a l d i f f e r e n c e s i n mathematical achievement: Their nature, causes, and consequences. Current Directions in Psychological Science, 5, 133-137. Gibson, M. A. (1991). E t h n i c i t y , gender, and s o c i a l c l a s s : The school adaptation patterns of West Indian youths. In M. A. Gibson & J. U. Ogbu (Eds.), Minority Status and Schooling: A Comparative Study of Immigrant and Involuntary Minorities (pp. 169-203). New York: Garland. Gibson, M. A., & Bhachu, P. K. (1991). The dynamics of educational d e c i s i o n making: A comparative study of Sikhs i n B r i t a i n and the United States. In M. A. Gibson & J. U. Ogbu (Eds.), Minority Status and Schooling: A Comparative Study of Immigrant and Involuntary Minorities (pp. 63-96). New York: Garland. G i l l , S., & Reynolds, A. J . (1999). Educational expectations and school achievement of urban A f r i c a n American c h i l d r e n . Journal of School Psychology, 37, 403-424. Ginsburg, H. P., & R u s s e l l , R. L. (1981). S o c i a l c l a s s and r a c i a l i n f l u e n c e s on e a r l y mathematical t h i n k i n g . Monographs of the Society 'for research in Child Development, 46, 1-72. Ginsburg, H. P., Rosner, J . K., & R u s s e l l , R. L. (1981). The development of knowledge concerning w r i t t e n a r i t h m e t i c : A c r o s s - c u l t u r a l study. International Journal of Psychology, 16, 13-34. G r o l n i c k , W. S., & Slowiaczek, M. L. (1994). Parents' involvement i n c h i l d r e n ' s s c h o o l i n g : A multidimensional c o n c e p t u a l i z a t i o n and m o t i v a t i o n a l model. Child Development, 65, 237-252. H a l l e , T. G., Kurtz-Costes, B., & Mahoney, J. L. (1997). Family i n f l u e n c e s on school achievement i n low-income, A f r i c a n -American c h i l d r e n . Journal of Educational Psychology, 89, 527-537. Haung, G. G. (2000). Mathematics achievement by immigrant c h i l d r e n : A comparison of f i v e English-speaking c o u n t r i e s . Educational Policy Analysis Archives, 8, 1-14. Hess, R. D., Chih-Mei, C , & McDevitt, T. M. (1987). C u l t u r a l v a r i a t i o n s i n f a m i l y b e l i e f s about c h i l d r e n ' s performance i n mathematics: Comparisons among People's Republic of China, Chinese-American, and Caucasian-American f a m i l i e s . Journal of Educational Psychology, 19, 179-188. Hickman, C. W., Greenwood, G., & M i l l e r , M. D. (1995). High school parent involvement. Journal of Research & Development in Education, 28, 125-134. H i l l , N. E, & C r a f t , S. A. (2003). Parent-school involvement and school performance: Mediated pathways among socioeconomically comparable A f r i c a n American and Euro-American f a m i l i e s . Journal of Educational Psychology, 95, 74-83. Husen, T. (1967). International Study of Achievement in Mathematics: A Comparison of Twelve Countries. New York: Wiley. Izzo, C. V., Weissberg, R. P., Kasprow, W. J . Frendrich, M. (1999). A l o n g i t u d i n a l assessment of teacher perception of parent involvement i n c h i l d r e n ' s education and school performance. American Journal of Community Psychology, 27, 817-839. Johnson, M. L. (1984). Black i n mathematics: A stat u s r e p o r t . Journal for Research in Mathematics Education, 15, 145-153. Jones, L. V., Burton, N. W., & Davenport, JR., E. C. (1984). Monitoring the mathematics achievement of black students. Journal for Research in Mathematics Education, 15, 154-164. Kao, G. (2004). Parental i n f l u e n c e s on the educational outcomes of immigrant youth. International Migration Review, 38, 427-449. Kao, G., & Tienda, M. (1995). Optimism and achievement: The educational performance of immigrant youth. Social Science Quarterly, 76, 1-19. Kerr, Z. (2004). A r i t h m e t i c s k i l l s i n c h i l d r e n who speak E n g l i s h as a second language. Unpublished master's t h e s i s , 177 U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia, Canada. Kim-Cohen, J . , M o f f i t , T. E., Caspi, A., & Taylor, A. L. (2004). Genetics and environmental processes i n young c h i l d r e n ' s r e s i l i e n c e and v u l n e r a b i l i t y to socio-economic d e p r i v a t i o n . Child Development, 75, 651-669. Karlsen, B., & Gardner, E. (1994). Stanford Diagnostic Reading Test. San Francisco: Harcourt Brace. Lesaux, N. K., & S i e g e l , L. S. (2003). The development of reading i n c h i l d r e n who speak E n g l i s h as a second language. Developmental Psychology, 39, 1005-1019. Leung, F. K. S. (2001). In search an East Asian i d e n t i t y i n mathematics education. Educational Studies in Mathematics, 47, 35-51. Leung, F. K. S. (2002). Behind the high achievement of East Asian students. Educational Research & Evaluation, 8, 087-109. Mather, N., & J a f f e , L. E. (2002). Woodcock-Johnson III: Report, Recommendations, and Strategies. New York: John Wiley & Sons, Inc. Matthews, W., Carpenter, T. P., L i n d q u i s t , M. M., & S i l v e r , E. A. (1984). The t h i r d n a t i o n a l assessment: M i n o r i t i e s and mathematics. Journal for Research in Mathematics Education, 15, 165-171. Matute-Bianchi, M. E. (1986). Ethnic i d e n t i t i e s and patterns of school success and f a i l u r e among Mexican-descent and Japanese-American students i n a C a l i f o r n i a high school: An ethnographic a n a l y s i s . American Journal of Education, 95, 233-255. Matute-Bianchi, M. E. (1991). S i t u a t i o n a l e t h n i c i t y and patterns of school performance among immigrant and nonimmigrant Mexican-descent students. In M. A. Gibson & J. U. Ogbu (Eds.), Minority Status and Schooling: A Comparative Study of Immigrant and Involuntary Minorities (pp. 205-247). New York: Garland. Muter, V., Hulme, C , & Snowling, M. (1998). Segmentation, not rhyming, p r e d i c t s e a r l y progress i n l e a r n i n g to read. Journal of Experimental Child Psychology, 71, 3-27. Peng, S. S. (1993, January). Learning Programs at Home: An Explanation of the High Academic Achievement of Asian American Students. Paper presented at the American S t a t i s t i c a l A s s o c i a t i o n Winter Conference, Ft. Lauderdale, F l o r i d a . Posner, J . K. (1982). The development of mathematical knowledge i n two West A f r i c a n s o c i e t i e s , Child Development, 53, 200-208. Randel, B., Stevenson, H. W., Witruk, E. (2000). A t t i t u d e s , b e l i e f s , and mathematics achievement of German and Japanese high school students. International Journal of Behavioral Development, 24, 190-199. R o b i t a i l l e , D. F., & Taylor, A. R. (2001). T h i r d i n t e r n a t i o n a l mathematics and science study: Canada rep o r t . Education Quarterly Review, 7, 37-41. R o b i t a i l l e , D. F., & Garden, R. A. (1989). The IEA Study of Mathematics II. Context and Outcomes of School Mathematics Pergamon Press, Oxford. Rodriguez, T. D. (2002). O p p o s i t i o n a l c u l t u r e and academic performance among c h i l d r e n of immigrants i n the USA. Race Ethnicity and Education, 5, 200-215. Rumbaut, R. G. (1996). The new C a l i f o r n i a n s : Assessing the educational progress of c h i l d r e n of immigrants. C a l i f o r n i a U n i v e r s i t y , Berkeley. C a l i f o r n i a P o l i c y Seminar. In R. G. Rumbaut & W. A. Cor n e l i u s (Eds.), California's Immigrant Children: Theory, Research, and Implications for Educational Policy. San Diego: Center f o r U.S.-Mexican Studies at the U n i v e r s i t y of C a l i f o r n i a . Satz, P., & F l e t c h e r , J . (1982). Florida Kindergarten Screening Battery. Odessa, FL: P s y c h o l o g i c a l Assessment Resources. S c h a l l e r , A, Rocha, L. 0., & Barshinger, D. (2007). Maternal a t t i t u d e s and parent education: How immigrant mothers support t h e i r c h i l d ' s education despite t h e i r own low 180 l e v e l s of education. Early Childhood Education Journal, 34, 351-356. Secada, W. G. (1992). Race, e t h n i c i t y , s o c i a l c l a s s , language, and achievement i n mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.623-660). New York: Macmillan. Shaver, A. V., & Walls, R. T. (1998). E f f e c t of t i t l e 1 parent .involvement on student reading and mathematics achievement. Journal of Research and Development in Education, 31, 90-97. Sheldon, S. B., & Eps t e i n , J. L. (2005). Involvement counts: Family and community p a r t n e r s h i p and mathematics achievement. Journal of Educational Research, 98, 196-206. S i e g e l , L. (1973). The r o l e of s p a t i a l arrangement and heterogeneity i n the development of concepts of numerical equivalence. Canadian Journal of Psychology, 27, 351-355. S i e g e l , L., & Ryan, E. B. (1989). The development of working memory i n normally a c h i e v i n g and subtypes of l e a r n i n g d i s a b l e d c h i l d r e n . Child Development, 60, 973-980. Stevenson, H. W. (1998). A study of three c u l t u r e s . Phi Delta Kappan, 7, 524-530. Stevenson, H. W., Lee, S., & S t i g l e r , J. (1993). The mathematics achievement of Chinese, Japanese, and American C h i l d r e n : ten year l a t e r . Science, 259, 53-58. Stevenson, H. W. , Lee, S., Chen, C , Lummis, M. , S t i g l e r , J. , Fan, L., & Ge, F. (1990). Mathematics achievement of c h i l d r e n i n China the United States. Child Development, 61, 1053-1066. Stevenson, H. W., Lee, S., & S t i g l e r , J. (1986). The mathematics achievement of Chinese, Japanese, and American C h i l d r e n . Science, 58, 693-699. S t i g l e r , J . W., Lee, S., Lucker, G. W. & Stevenson, H. W. (1982). Curriculum and achievement i n mathematics: A study of elementary school c h i l d r e n i n Japan, Taiwan, and the United States. Journal of Educational Psychology, 74, 315-122. S t i g l e r , J. W., Lee, S., & Stevenson, H. W. (1987). Mathematics classrooms i n Japan, Taiwan, and the United States. Child Development, 58, 1272-1285. Suarez-Orozco, M. M. (1991). Immigrant adaptation to scho o l i n g : A Hispanic case. In M. A. Gibson & J. U. Ogbu (Eds.), Minority Status and Schooling: A Comparative Study of Immigrant and Involuntary Minorities (pp. 37-61). New York: Garland. Sue, S., & Okazaki, S. (1990). Asian-American educational achievements: A phenomenon search of an e x c e p t i o n a l . American P s y c h o l o g i s t , 45, 913-920. Tate, W. F. (1997). R a c e - E t h n i c i t y , SES, gender, and language p r o f i c i e n c y trends i n mathematics achievement: An update. Journal for Research in Mathematics Education, 28, 652-679. Van Doornick, W. J . , C a l d w e l l , B. M. , Wright, C , & Frankenberg, W. K. (1981). The r e l a t i o n s h i p between twelve-month home s t i m u l a t i o n and school achievement. Child Development, 52, 1080-1083. Wang, J . (1999). Opportunity to l e a r n , language p r o f i c i e n c y , and immigrant status e f f e c t s on mathematics achievement. Journal of Educational Research, 2, 101-121. Wang, J . , & Wildman, L. (1994). The e f f e c t of f a m i l y commitment i n education on student achievement i n seventh grade mathematics. Education, 115, 317-322. Waters, M. C. (1994). Ethnic and r a c i a l i d e n t i t i e s of second generation black immigrants i n New York C i t y . International Migration Review, 28, 795-820. Watt, D., & Roessingh, H. (1994a). Some you win, most you l o s e : Tracking ESL dropout i n high school (1988-1993). English Quarterly, 26, 5-7. Watt, D., & Roessingh, H. (1994b). ESL dropout: The myth of educational equity. Alberta Journal of Educational Research, 40, 283-296. Watt, D., & Roessingh, H. (1996). Success and f a i l u r e : S t o r i e s of ESL students' educational and c u l t u r a l adjustments to high school. Urban Education, 31, 199-221. Watt, D., & Roessingh, H. (2001). The dynamics of ESL drop-out. The Canadian Modern Language Review, 58, 203-222. Wechsler, D. (1991). Wechsler Intelligence Scale for Children -III. New York: P s y c h o l o g i c a l Corporation. Whang, P.A., & Hancock. G. R. (1994). M o t i v a t i o n and mathematical achievement: Comparisons between A s i a n -American and non-Asian students. Contemporary Educational Psychology, 19, 302-322. Wilkinson, G. S. (1993). The Wide Range Achievement Test -3. Wilmington, DE: J a s t a l A s s o c i a t e s . Wong, M. G. (1980). Model students? Teachers' perception and expectations of t h e i r Asian and White students. Sociology of Education, 53, 236-246. Wong, N. Y. (1998). In search of the "CHC" l e a r n e r : Smarter, works harder or something more? Plenary l e c t u r e , i n H. S. Park, Y. H. Choe, H. Shin and S.H. Kim (Eds.). Proceeding of the ICMI-East Asia Regional Conference on mathematical education, 1, 85-98. Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson II Tests of Achievement. I t a s c a , IL: The R i v e r s i d e P u b l i s h i n g Company. 184 Young, C. (1983). Education, employment, and the Tu r k i s h community i n A u s t r a l i a . International Journal of Turkish Studies, 2, 33-57. Zhang, Y. (2001). Immigrant g e n e r a t i o n a l d i f f e r e n c e s i n academic achievement and i t s growth: The case of Asian American high school students. Paper presented at the annual meeting of the American Educational Research Association, Chicago. 

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