UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Sex-related differences in mathematics achievement scores in Grade 4 and Grade 8 in Kerala, India Nair, Leila Karunakaran 1984

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A8 N33.pdf [ 4.49MB ]
Metadata
JSON: 831-1.0096209.json
JSON-LD: 831-1.0096209-ld.json
RDF/XML (Pretty): 831-1.0096209-rdf.xml
RDF/JSON: 831-1.0096209-rdf.json
Turtle: 831-1.0096209-turtle.txt
N-Triples: 831-1.0096209-rdf-ntriples.txt
Original Record: 831-1.0096209-source.json
Full Text
831-1.0096209-fulltext.txt
Citation
831-1.0096209.ris

Full Text

SEX-RELATED DIFFERENCES IN MATHEMATICS ACHIEVEMENT SCORES IN GRADE 4 AND GRADE 8 IN KERALA, INDIA By LEILA KARUNAKARAN M.A. U n i v e r s i t y of Madras,  NAIR I n d i a , 1957  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS  in THE FACULTY OF GRADUATE STUDIES (Department  of Mathematics and S c i e n c e E d u c a t i o n )  We a c c e p t t h i s to  t h e s i s as conforming  the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA June 1984 © Leila  Karunakaran N a i r , 1984  In p r e s e n t i n g requirements  this  thesis  i n partial  fulfilment of the  f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y  of  B r i t i s h Columbia, I agree that  the Library  shall  it  freely  and study.  I  available  f o rreference  agree t h a t p e r m i s s i o n for  scholarly  thesis  p u r p o s e s may be g r a n t e d by t h e h e a d o f my  understood that financial  further  f o rextensive copying o f t h i s  department o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  copying or p u b l i c a t i o n  gain  shall  of this  It i s thesis  n o t be a l l o w e d w i t h o u t my  written  permission.  D e p a r t m e n t o f f^c^Li^c^ACu,  CWc/  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall Vancouver, Canada V6T 1Y3  Columbia  Date  DE-6  (3/81)  $IASU<^B  <^cplu^<zoJ^cy^  ABSTRACT  The related a  purpose  differences  sample  from  the  findings  on  such  levels, state of  of  from  were Study  Columbia  varying  sample, urban and  and  if  and  sample,  girls  rural  from  boys  girls  Based  on t h e r e s u l t s  the  "nature-position" ability  of  Items  1981  8  existed  i n favour girls  Columbia  Study  i s the reason  Learning 4  level  level. differences  a t t h e two g r a d e location  o f t h e same  8 level.  8  in  levels of  the  sex. In the  b y 2% a t t h e G r a d e  genetic  the  conducted i n  b y 7% a t t h e G r a d e  study,  grade  in  f o r t h e Grade  b y 8% a t t h e G r a d e  of  positions  f o r the instruments  b y 3% a t t h e G r a d e  of t h i s  in  bearing  districts  the urban-rural  o u t p e r f o r m e d boys  outperformed g i r l s  mathematical  on  outperformed boys  three  sex-related  scores  sex-  existed  "nurture"  Mathematics  that  scores  i f s o , what  British  f o r the Grade  depending  outperformed  sample,  tested.  not c o n s i s t e n t l y boys  from  the  whether  1 3 7 7 s t u d e n t s a t two  of  International  showed  and  "nature" and  Mathematics  achievement  achievement  drawn  drawn  i n 1982  degrees  8,  to investigate  world;  total  were  in  results  mathematics  A  India,  the Second  The  in  the current  4 and Grade  Kerala,  testing  British  the under-developed h a d on  Grade  s t u d y was  i n mathematics  differences.  Assessment and  of t h i s  4  level  In 4  the level  level.  i t i s hypothesized that male  superiority  f o r the instances  of  in  superior  male scores i n t h i s study, show  marginally  different  locale  data at the same  superior indicate  'remedy any d e f i c i e n c i e s  female  grade  achievement  levels scores  that in a  that "nurture" of some s o r t can l i k e l y  in  mathematical  imposed by "nature".  Research S u p e r v i s o r : Dr. D. F. R o b i t a i l l e .  ability  that  may  be  iv  CONTENTS Page  LIST OF TABLES  vii  ACKNOWLEDGEMENT  vi i i  Chapter 1 . INTRODUCTION Theories  1  to E x p l a i n S e x - r e l a t e d D i f f e r e n c e s  3  The N a t u r e - P o s i t i o n  4  The N u r t u r e - P o s i t i o n  5  The P r o j e c t  6  Major Questions Posed i n the Study Reasons  7  f o r the Separate Study of  Urban and R u r a l Samples Reasons  8  f o r the Choice of K e r a l a  11  2. REVIEW OF RELATED LITERATURE B r i t i s h Columbia Learning Assessment  14 S t u d i e s ..15  A l b e r t a Assessment of School Mathematics  17  Case f o r S e x - r e l a t e d D i f f e r e n c e s i n Mathematical Reasoning A b i l i t y  18  H i s t o r i c a l Perspective  23  Are Males S u p e r i o r Visualization  in Spatial  Ability?  24  V  Is Mathematical Achievement  Dependent on  Spatial Visualization Ability?  25  Present  29  Status of Genetic-Based T h e o r i e s  L i t e r a t u r e on the N u r t u r e - P o s i t i o n Summary  33  Some S t u d i e s  i n Other C u l t u r e s  Some Recent  Studies  i n India  3. METHOD  35 37  40  Sample School  30  41 Structure in Kerala  42  S e l e c t i o n of Sample  43  Instruments of T e s t i n g  46  Test A f o r Grade 4 L e v e l  46  Test B f o r Grade 8 L e v e l  46  Procedure  47  4. RESULTS  49  D e s c r i p t i o n of Sample  49  Comparison  49  of Mean Scores  Urban Sample  50  Grade 4  50  Grade 8  50  Rural Sample Grade 4  50 50  vi  Grade 8  51  5. SUMMARY OF RESULTS and IMPLICATIONS Findings Bearing  57 57  of F i n d i n g s on  Nature-Nurture P o s i t i o n s  58  A l t e r n a t i v e Inference  59  from F i n d i n g s  L i m i t a t i o n s of the Study  59  Suggestions f o r Further Research  60  REFERENCES  ..62  APPENDIX I. Map of K e r a l a I I . S y l l a b u s i n Mathematics f o r K e r a l a Schools  74 76  Standard IV  77  Standard VIII  78  I I I . Instruments of T e s t i n g  79  Test A  80  Test B  93  IV. Tables  of R e s u l t s by Item  107  vii  LIST  OF  TABLES  TABLE  Page  1. D i s t r i b u t i o n  of  Subjects  i n Sample  52  2.  Grade  4 Level:  Urban  Scores  in Percentages  by  Domain  .53  3.  Grade  8 Level:  Urban  Scores  in Percentages  by  Domain  .54  4.  Grade  4 Level:  Rural  Scores  i n Percentages  by  Domain  .55  5.  Grade  8 Level:  Rural  Scores  in Percentages  by  Domain  .56  6.  Itemwise  p-values  on  Test  A  a t Grade  4 Level  108  7.  Itemwise  p-values  on  Test  B a t Grade  8 Level  109  vi i i ACKNOWLEDGEMENTS  I  am  most  permitting  me  Kerala  making  John  for  Mathai,  Vedamani of  Institute to  Sri.  Education,  the  Department  that  this  debt. of  I  to  heads,  teachers  who  willingly  Columbia  without  brought  to  a  whose  in  of  I  as  his  encouragement,  University 1983-84, study.  known  due  of  to  Kerala,  S r i .  and  Dr.  University  the  project  I  would  Women,  eased the  who  be  mention  of  to  vain  with  the to  the  attempt  gratitude  Evaluation  My  State  and  the  Officer,  Smt.  thanks  P.  V.  are  various  also  schools  project. at  this  the  study  offer  R o b i t a i l l e ,  a  would  students  guidance  D.  have  it  (Mathematics)  the  Dr.  Finally,  are  indebted  Mathews,  advisors  conclusion, F.  so  Research Officer.  supervisor,  not  for  Government  gave  is  only  Thomas  and  participated committee  that  Director  due  would  India  Education,  capacities  can  S r i .  Textbooks  without  thanks  of  of  the  Instruction,  project  Kerala,  Ammal,  my  to  special  Public  Meenakshi  To  and  of  Bhaskaran, Deputy  the  My  different  work,  participation  N.  Government  needed.  discharge  active  their  field  of  of  the  study,  possible.  Head  in  it  its  it  to  this  Director  who  impetus In  conduct  Manuel,  Kerala,  the  to  grateful  I  my  must  support  University  of  could  have  not  grateful remain  and  British  thanks.  ever  confidence  been To  my  indebted, this  study  beginning. like by  weight  to  thank  granting of  my  the me  Canadian  the  financial  Alice  Federation Wilson  commitment  Award to  of for this  1  Chapter 1  INTRODUCTION  There  is  outperform While  a  consensus  females  theories  on  of  school  data  came  the  with  First  achievement  tests.  s u p e r i o r i t y have not been  earliest  the  Study conducted across twelve Association  mathematics  male i n t e l l e c t u a l  l a c k i n g through h i s t o r y , research  i n e d u c a t i o n a l research that males  evidence  of  extensive  I n t e r n a t i o n a l Mathematics  countries  by  the  International  f o r the E v a l u a t i o n of E d u c a t i o n a l Achievement  (IEA),  i n 1964. A study  limited  p i l o t p r o j e c t conducted as a forerunner  i n Belgium, England,  Poland,  Scotland,  Finland,  Sweden,  Switzerland,  Y u g o s l a v i a had shown a marginal numerical  Germany,  when  the  data  Mathematics Study was analyzed, null  hypothesis  Israel,  the U n i t e d States and  d i f f e r e n c e i n favour of g i r l s i n  a b i l i t y at the 13 year o l d age l e v e l  Consequently,  the  France,  to t h i s  from  the  (Foshay,  First  1962).  International  i t was with some  surprise  that  on s e x - r e l a t e d d i f f e r e n c e s i n mathematics  achievement scores at each of  the  four  years,  and  P r e - U n i v e r s i t y ) was r e j e c t e d  13  years,  17  years  (Husen, 1967). In every country  population  s t u d i e d males  had  levels  (9  outperformed  females. Since  then,  a  large  number  of  studies  on s e x - r e l a t e d  2  differences  in  mathematics  implemented  in  many  of  achievement  these  scores  countries,  who  had  identified  mathematics  as  achievement  i n mathematics gained impetus  (Armstrong,  1981;  Levine  1982). A l l the same, d i f f e r e n c e s s t i l l above the j u n i o r high school l e v e l  &  filter  1982,  p.16).  t o promote  female  1981;  Fox,  Ornstein,  exist  1976b;  1983; Tobias,  i n favour of  males  (Kapoor, 1983; NAEP, 1980).  the United Kingdom and A u s t r a l i a , there i s some evidence  s e x - r e l a t e d d i f f e r e n c e s i n mathematics achievement scores i n  favour of g i r l s  i n the lower age group of  (Byrne,  Shelley,  the  critical  1982) and a narrowing of s e x - r e l a t e d d i f f e r e n c e s has been  observed  In  country  (Blum & Givant, 1982;  Fennema, W o l l e a t , Pedro, Becker, & DeVancy, Sells,  groups who were  (Mura,  As a r e s u l t , a s e r i e s of i n t e r v e n t i o n measures  issue i n  in their  the  p r e v e n t i n g a c c e s s t o many jobs and c a r e e r s "  of  in this  U n i t e d S t a t e s had been "spurred by p o l i t i c a l  f i g h t i n g the o c c u p a t i o n a l segregation e x i s t i n g and  been  most of a l l i n the  U n i t e d S t a t e s . By the e a r l y s e v e n t i e s , i n t e r e s t the  have  1978;  rule in  older  age  Harding, 1977; K e l l y , That  the  Western Europe "education  and  11  years  and  under  1982); but male s u p e r i o r i t y seems t o be groups  (Cornelius  &  Cockburn,  1978;  1976, 1981; Murphy, 1978; Preece, 1979).  situation  i s much the same i n the c o u n t r i e s of  i s evident equality  from of  a  statement  opportunity  of  concern  on  f o r g i r l s and women"  ( C o u n c i l of Europe, 1982, p. 1) expressed a t the 11th s e s s i o n of the  Standing Conference of European M i n i s t e r s  of  Education at  3  The  Hague  in  May,  1981 at Honefoss  represented.  1979. Consequently, a workshop was held e a r l y i n where  the  Federal  Netherlands,  Republic  Norway,  the  and  occupation  as  a  of  cited  result  mathematics and the p h y s i c a l s c i e n c e s  a  major  topic  at  the  Germany,  were  of  Fourth  Ireland,  Spain,  male  Sweden,  advantage  male  1982).  achievement  scores  I n t e r n a t i o n a l Congress on  Mathematical E d u c a t i o n h e l d at Berkeley i n 1980. As a r e s u l t the  proceedings,  Erika  an i n t e r n a t i o n a l survey was  Schildkamp-Kundiger,  International title  in  Mathematics  The  contributions  superiority  in  physical sciences  cooperation  of  undertaken by Dr. with  the  Second  Study (IEA), and p u b l i s h e d under the  "An I n t e r n a t i o n a l Review  1982.  in  s u p e r i o r i t y in  ( C o u n c i l of Europe,  S e x - r e l a t e d d i f f e r e n c e s i n mathematics was  countries  Portugal,  S w i t z e r l a n d and the United Kingdom — career  of  At the workshop, each of the c o u n t r i e s -- A u s t r i a ,  Belgium, F i n l a n d , the Italy,  thirteen  of  from  achievement  Gender  and  Mathematics"  in  almost every country c i t e d male  scores  in  mathematics  and  the  (Schildkamp-Kundiger, 1982).  T h e o r i e s To E x p l a i n S e x - r e l a t e d D i f f e r e n c e s It would appear that evidence of s e x - r e l a t e d d i f f e r e n c e s i n favour  of  males  in  mathematics  achievement  scores  in  developed world i s unequivocal at the present time. But what controversial  i s whether  these d i f f e r e n c e s are to be  as evidence of innate s u p e r i o r mathematical a b i l i t y  the is  interpreted i n the male,  4  or  as  evidence  of  the extent  of i n e q u a l i t y of o p p o r t u n i t y  r e l a t i o n to mathematical achievement that  is  built  into  in  human  soc i e t y .  The  Nature-Position Those  has  who  would favour  been c a l l e d the  biological  or  &  genetic  Broverman, D. M.,  Gray,  1972;  former i n t e r p r e t a t i o n , or what  " n a t u r e - p o s i t i o n " , support differences  female (Benbow & Stanley, Vogel,  the  1980,  1981,  Clarkson  Corah, 1965;  1972). While such a theory  between  and  1982;  the  far  Broverman,  into  superior 1908; at  the  Buffery  point  1896;  present  1963, the  superior  a t t r i b u t e d to s u p e r i o r b r a i n s i z e , then to  b r a i n weight, or even s u p e r i o r muscle s t r e n g t h  Lourbet,  K.,  history,  r a t i o n a l e f o r i t has changed p e r i o d i c a l l y . At one male i n t e l l i g e n c e was  the  I.  S t a f f o r d , 1961,  back  of  male and  Rosenkrantz, 1972;  Garron, 1970;  dates  i t on grounds  Mozans, 1913). The  most  (Ellis,  persuasive  time seems to be developed along  the  theory  following  lines: (1) Males have s u p e r i o r s p a t i a l v i s u a l i z a t i o n (2) Mathematical spatial  males  the b a s i s of  is  positively  correlated  with  visualization.  (3) Therefore That  ability  ability.  males are s u p e r i o r have  i n mathematical  superior s p a t i a l a b i l i t y  (a) d i f f e r e n c e s i n l a t e r a l b r a i n  ability.  i s explained  development,  on (b)  5  the X - l i n k e d chromosome i n h e r i t a n c e theory, or (c) the theory of d i f f e r e n t i a l hormonal infuences.  The N u r t u r e - P o s i t i o n Those  who  support  the a l t e r n a t e  interpretation  achievement scores i n females, or s u b s c r i b e called  the  "nurture-position"  psychological-cultural  to  attribute  what it  for lesser has to  been socio-  f a c t o r s such a s :  (1) Sex-role s t e r e o t y p i n g . ( 2 ) Mathematics viewed as belonging to the male domain. (3) Fear of o s t r a c i s m by male peer  group.  (4) Mathematics a n x i e t y . (5) Lack of mathematical (6)  activity  in childhood.  Lack of encouragement from parents and/or teachers  and  counsellors. (7) D i f f e r e n t i a l c o u r s e - t a k i n g . While  n e i t h e r p o s i t i o n can be "proved"  i n the s t r i c t  of the word, a b a s i c tenet of g e n e r a l i z a b i l i t y research  differentiates  hypotheses factors  between  generated. The nurture extraneous  to  the  the  credibility  theory,  individual,  which  to most of human s o c i e t y as i t e x i s t s today theory  on  the  other  experimental of  the two  i s based  generalizes  p o p u l a t i o n t o which those f a c t o r s a p p l y . That  nature  in  sense  over  on a  such f a c t o r s apply  is  incidental.  The  hand, g e n e r a l i z e s over the human  6  race. Q u a n t i t a t i v e have  been  data that have generated t h i s genetic  gathered  almost  (Lancy, 1983). E m p i r i c a l  entirely  as  a  S o v i e t Union has  determining  education  factor  (Krutetskii,  from the developed world  s t u d i e s have been  largely  in  Zealand  and  c o n s i s t e n t l y avoided c o n s i d e r i n g  sex  the North American c o n t i n e n t , Japan. The  theory  Europe, A u s t r a l i a , New  in  1976;  centred  research  studies  Menchinskaya, 1946,  in mathematics 1969).  Hence, i t would appear that a hypothesis f o r the human i s generated on the b a s i s of evidence from than  25%  of the world p o p u l a t i o n .  If any  humanity as a whole i s to be c o n s i d e r e d , cited,  should  1983). The currently  be  manifest  all  i n progress may  would  provide  to  be  a b i l i t i e s are  as  necessary of  is  s t r a t a (Lancy,  Study  of  c u l t u r a l and before  mathematical  the  IEA But  economic  theories  of  ability  or  study  therefore,  Project investigated  whether  d i f f e r e n c e s i n mathematics achievement scores a  evidence  entertained.  The  from  less  such a p r o b a b i l i t y sample.  d i f f e r e n t i a l b i o l o g i c a l embedding  This  such  of  that speaks f o r  l e v e l s and  in d i v e r s e g e o g r a p h i c a l , seem  stratum  theory  Second I n t e r n a t i o n a l Mathematics  empirical studies strata  at  a  race  different  part  of  sex-related  exist in a  sample  the world, i n a d i f f e r e n t economic  stratum, in a d i f f e r e n t c u l t u r e and h i s t o r y , v i z . the State of K e r a l a  with a d i f f e r e n t e d u c a t i o n a l  i n I n d i a . L i m i t a t i o n s of  time  7  and f u n d s districts  1  r e s t r i c t e d the study  to two  grade  levels  in  three  i n the S t a t e .  Major Questions  Posed i n the Study  The two major q u e s t i o n s posed i n the study were: (1)  Are  there  sex-related  mathematics achievement Grade 8 l e v e l s  (2)  Are  scores  differences at  Grade 4  in and  i n the urban schools tested?  there  sex-related  mathematics achievement  scores  differences at  Grade 4  in and  'Grade 8 l e v e l s i n the r u r a l schools tested?  A (1) and  secondary (2) had  positions  o b j e c t i v e was to determine i f the f i n d i n g s i n any  bearing  on  the  "nature"  and  on s e x - r e l a t e d d i f f e r e n c e s i n mathematics  "nurture" achievement  scores.  1  The P r o j e c t was p a r t l y supported by the A l i c e Wilson Award f o r 1983-84 from the Canadian F e d e r a t i o n f o r U n i v e r s i t y Women.  8  Reasons f o r the Separate The  reasons  samples  are  investigation  Study of Urban and Rural Samples  f o r the best  separate  illustrated  In  the  second  Study conducted by the IEA, them,  was  countries, Chile, developed low  in  by  of  urban  the  India  such  " S i x Subject  across  and  a l l subjects  mean  Thailand  were,  of  the  data  from  f o r the  developed  that  differences  higher  levels  of  l a r g e i n r u r a l areas,  India  area,  where  i t was found  countries  were  small  of  population;  the  population.  difference  while 1974).  the that  reported  from  exceeded  that f o r the The  between  analyses  Indian  difference  and  decreasing  but that d i f f e r e n c e s were increasing  with  higher  A sharp drop i n mathematics achievement  scores with higher grade l e v e l s from the primary been  under-  from most of the  (14 year o l d s , 17 year o l d s and P r e - U n i v e r s i t y )  i n t e r n a t i o n a l scores i n urban areas, the  levels  the  (Comber & Keeves, 1973).  p o p u l a t i o n I l e v e l remained below (Shukla,  with  from  f o r the c i t y schools at the p o p u l a t i o n I I , I I I and IV  median  showed  science  22 n a t i o n s . Three of these  m e t r o p o l i t a n and r u r a l schools were separated,  the  urban-rural  Survey",  that they were excluded  In a l a t e r a n a l y s i s  levels  another  world. But the mean scores f o r these c o u n t r i e s were so  more d e t a i l e d analyses  the  of  rural  phase of the F i r s t I n t e r n a t i o n a l  a  conducted  and  study  i n India which d i d not draw any  distinctions.  among  study  another  recent study  stage has  also  i n an under-developed  v i z . The Indigenous Mathematics P r o j e c t  in  Papua,  New  9  Guinea  (Lancy,  In  1983).  India,  any study of academic achievement  by the l a r g e i l l i t e r a c y and  economic  f i g u r e s that combine with  i s confounded caste,  class  s t a t u s to make w i t h i n - c o u n t r y d i f f e r e n c e s between  r u r a l and urban areas almost as l a r g e as the d i f f e r e n c e s between India and the developed world  (Jayaraman,  1981;  That these c o n d i t i o n s confuse f i n d i n g s from any a  conventionally  evident in  Six  i n v e s t i g a t i o n of  from some other f a c t s surrounding the Six Subject Survey  in  villages  (the  figure  or  more  of I n d i a ' s  f o r 1981  80%), 70.65% of the p o p u l a t i o n was 30%  1974).  r e p r e s e n t a t i v e sample of a reasonable s i z e i s  I n d i a . At the time of the study, 80.1%  lived  Shukla,  illiterate  l i v e d below the poverty l i n e  Subject Survey,  was  India took part  population  n e a r l y the same,  and  (Iyer,  an  estimated  1970). In the  i n s c i e n c e and reading,  and  samples were drawn from the H i n d i - s p e a k i n g S t a t e s as the l a r g e s t one-language  r e g i o n i n the c o u n t r y . There are 14 other  languages  i n India and  400  non-literate  are  languages there  1652  mother-tongues of which  (Pattanayak,  1981).  only  still  25  different  languages  counted,  i n the country, with  e d u c a t i o n a l standards v a r y i n g widely among the v a r i o u s groups  (Jayaraman,  On  the  -  language  1981).  variable  Bihar - 19.97%, Madhya Rajasthan  about  Even i f only those  that are spoken by 50 000 people or over are  are  official  of  literacy,  Pradesh  -  the r e l e v a n t  22.03%,  f i g u r e s were:  Haryana  -  26.69%,  18.79%, U t t a r Pradesh - 21.64% and D e l h i - 56.65%.  10  D e l h i alone, a m e t r o p o l i s with a p o p u l a t i o n of 4 m i l l i o n ,  raised  the l i t e r a c y  India,  29.35.  f i g u r e of the sample t o  that  f o r a l l of  The r e s t of the s t a t e s represented a t o t a l p o p u l a t i o n of  222 m i l l ion (Shukla, 1974). A r e p r e s e n t a t i v e sample in  these  states  could  not, and  by  middle  (which  and upper c l a s s c h i l d r e n  l e s s than 4% of the Indian p o p u l a t i o n English  language  even  today  schools  d i d not, i n c l u d e any of the  s c h o o l s teaching i n the medium of E n g l i s h largely  of  are  i n urban areas) as  i s acquainted  (Pattanayak,  e f f e c t i v e a d m i n i s t r a t i o n of the country  in  attended  1981).  every  with  the  Yet, the  aspect  draws  l a r g e l y from t h i s s e c t i o n of the p o p u l a t i o n (Lewandowski, 1980). As has been mentioned, the r e s u l t of the I n t e r n a t i o n a l Study was that  the  scores,  that no worthwhile That  any  proportionately  both  i n s c i e n c e and i n r e a d i n g , were so low  analyses c o u l d be made.  small  sample  stratified,  randomly cannot  selected,  450  world's  million  illiterate  1983). (2) technical  that  the  personnel  third  (Narayanan,  (Ummat, 1982).  (1)  an estimated 50% of the  largest  pool  of  scientists  and  i n I n d i a (Prasad, 1983).  industrialized  country  i n the  1982). (4) that I n d i a p r o v i d e s t e c h n o l o g i c a l  know-how to 37 other n a t i o n s , i n c l u d i n g some world  statistics:  i n I n d i a (Manorama Yearbook,  i n the world l i v e  (3) that I n d i a i s the 9th most world  people,  i l l i t e r a t e population, l i v e  if  present an accurate p i c t u r e  of the country may be evident from a few other that  even  in  the  developed  11  This  study  t h e r e f o r e , takes i n t o cognizance the  the middle c l a s s e s of I n d i a , l i v i n g total  numbers  exceed  the  Kingdom, Canada, Japan and to 1 by the (Census  a  this  sample  combined  urban  populations  France, but  who  of  of  study was  confined  separately.  urban areas and  studied  Reasons f o r the choice choice  of  Kerala in India Kerala  is  of K e r a l a was  p a r t l y one  in  India  in  from  to the  the  were  of  that  India,  for  all  1981).  i s 64.48%, the highest  rural  The  of  India,  in I n d i a . The  that  of p u b l i c in  literacy  1881, figures  f i g u r e for  36.17%  female l i t e r a c y  s i x years the s t a t e has  fact  area  the l i t e r a c y  f o l l o w s next i n rank with a female l i t e r a c y In the past  its  initiated  c o n s i s t e n t l y r e g i s t e r e d the highest  (Lewandowski, 1980). At present  Commissioner Kerala  distinctive  i s 69.17% and  was  of convenience ( i t i s  p a r t l y due  Ever s i n c e census s t u d i e s  has  areas  Kerala  i n v e s t i g a t o r ' s home s t a t e ) , and  education.  rural  to three d i s t r i c t s i n  and  state  the  s u b j e c t s , no p r o b a b i l i t y sampling  samples were drawn  the  United  on  the  merit  a s i n g l e s t a t e , K e r a l a , and  the  of the  investigation i s a limited individual project  attempted. Instead,  The  whose  own  1400  1981)  areas,  study i n t h e i r  about  India,  that  are yet outnumbered 5  l e s s p r i v i l e g e d , l i v i n g mostly in  Commissioner  r i g h t . As  in i t s  fact  (Census  figure for  s t a t e of Maharashtra f i g u r e of 35.08%.  almost  achieved  what  12  remains a t a r g e t f o r the r e s t of the country, its  6-11  year o l d s in school  100%  enrollment  of  (Government of K e r a l a , 1981). But  t h i s r a p i d advance i n p u b l i c education on an economy that i s the poorest  among  anomalies. third  all  One  lack  the  has  not  been  without  of  water,  Kerala,  educational f a c i l i t i e s  one  half  have  no  electricity  1978). These f a c t s must speak f o r what  i n the  nature  of  books,  laboratories,  gymnasiums, a r t s and c r a f t s e t c . the schools are l i k e l y The  state  spends  55%  of  its  revenue  per p u p i l per school day works out to  elementary  schools and  to  cents  for elementary  school i n B r i t i s h Columbia f o r the year $21  17  the in  25 cents i n the high s c h o o l s (Government  of K e r a l a , 1979). The average expenditure  out  to have.  on e d u c a t i o n . Yet  expenditure  secondary  its  quarter of K e r a l a ' s schools lack washrooms, one  drinking  (Government  states,  through  1980-81  works  per p u p i l per school day d e s p i t e the f a c t that the  p r o v i n c e spends no more than  15.5%  of i t s  budget  on  education  ( S t a t i s t i c s Canada, 1983). In prevail with  many  Kerala  highest  kilometer  density  the c o n t r a d i c t i o n s that  of  population,  38 863  km ),  654 persons  to the  2  (the average i n other s t a t e s i s 387). The  a l s o has the lowest death for  epitomizes  i n I n d i a . I t i s the s m a l l e s t s t a t e (area:  the  square  ways  r a t e i n I n d i a , and the lowest  state  figures  i n f a n t m o r t a l i t y , which i s a t t r i b u t e d to i t s higher l e v e l of  female  literacy  (Chattopadhyay,  1983). With Education,  Planning and Health Care together accounting  f o r three  Family  quarters  13  of  its  expenditure,  the  S t a t e has a l s o succeeded  down the p o p u l a t i o n growth r a t e to 1.80 the lowest growth r a t e i n I n d i a The to 935 been  female-male  females per associated  per thousand  (Narayanan,  is  about  per  r a t i o i n India had p r o g r e s s i v e l y  1000  males over the past century,  which  the  same  as  the  f o r the r e s t of the world,  1035  1983). cited  a  of c o n f o r m i t y with the r e s t of I n d i a . For i n s t a n c e , while  female teachers outnumber male teachers by levels  in  schools,  be  it  9%  1981,  unmistakable.  see  Table  15).  The  in  Kerala,  the  primary, upper primary or  secondary, are taught more by males than females Kerala,  has  alone,  But f o r every departure from the norm can a l s o be  highest  declined  with d i f f e r e n t i a l treatment meted out to g i r l s  females to 1000 males (Manorama Yearbook,  point  annum,  1982).  in food and n u t r i t i o n w i t h i n the f a m i l y . For K e r a l a ratio  in bringing  (Government  sex-related  of  hierarchy i s  14  Chapter 2  REVIEW OF RELATED LITERATURE  In a review mathematics  of l i t e r a t u r e  achievement  (1977) draws a  dividing  before that date  on  sex-related  shift  all,  line  around  1974.  Studies  i n trends can be seen in two  there has been a r e d u c t i o n in  mathematics achievement scores  1982;  reported  show d i f f e r e n c e s in favour of males while  Levine & O r n s t e i n , 1983;  in  in the United S t a t e s , E l i z a b e t h Fennema  r e p o r t e d a f t e r that date are more ambivalent. this  differences  The  reasons  those behind  major f a c t o r s . F i r s t  sex-related  (Blum & Givant,  Schonberger, 1976;  differences 1982;  Sells,  Dees,  1982;  of in  1982;  Tobias,  U s i s k i n , 1982). Secondly,  sexes  in  the l e s s d i s p a r a t e achievement scores between the  combination  with  the  more  sensitive  climate  c o n t r o v e r s y as a r e s u l t of the a c t i v e f e m i n i s t and equal movements  in  the  country  (Mura,  1982),  is  c a u t i o u s c o n c l u s i o n s being drawn from the data 1981) .  All  the  of  rights  l e a d i n g to more (Gray  &  Schafer,  same, i t must be mentioned that there are some  notable exceptions  to t h i s trend  (Benbow & Stanley,  1980,  1981,  1982) . Canada  and  the U n i t e d S t a t e s are not always d i f f e r e n t i a t e d  in e d u c a t i o n a l r e s e a r c h as there are, undeniably, in  common  between the two  a  great  deal  c o u n t r i e s . Yet, the d i f f e r e n c e s that  15  exist  in  educational  considerable  in  and  certain  social areas  that n e i t h e r of the f a c t o r s Canada.  Sex-related  scores were f i r s t Learning  Assessment  could  be  (Mura, 1982). I t i s evident i n  described  differences  mentioned  environments  above  in  apply  mathematics  wholly  achievement  i n Canada with the B r i t i s h  Studies of 1977  (Mura,  to  1982). Such  Columbia research  as has been r e p o r t e d s i n c e t h e n ' c i t e l a r g e r and not smaller sexrelated  differences  Sigurdson,  (Robitaille,  1981;  the f i r s t  (1977),  the  Computation the 8  Learning Assessment  test and  content  was  Study i n B r i t i s h Columbia  divided  into  Knowledge, Comprehension,  three  domains:  and A p p l i c a t i o n s . In  nine comparisons p o s s i b l e i n these domains at the grades and  boys  12  levels,  girls  were  superior  significant The elect  4,  outperformed boys i n the computation  although  other  comparisons  a l l differences  N e v e r t h e l e s s , the d i f f e r e n c e s must be  considered  were  the  small.  educationally  as the study was based on a census and not a sample.  study  also  drew a t t e n t i o n to the f a c t that g i r l s d i d  to take mathematics s u b j e c t s i n the same p r o p o r t i o n as  boys. While the male-female r a t i o was and  and  Studies  domain i n grades 8 and 12. In the seven  not  Olson  1981).  B r i t i s h Columbia Learning Assessment In  Sawada,  Grade 8  levels,  to 42 ( R o b i t a i l l e  51 to 49  i n the o p t i o n a l Algebra  & Sherrill,  1977).  at  the  Grade 4  12 group i t was  58  16  In the second Learning Assessment four  years  later,  the  test  was  Study  divided  (1981) into  conducted  five  domains: Number and Operation, Geometry, Measurement, Topics  and  level, in  Computer  Literacy.  there were s i g n i f i c a n t  Geometry  content  Algebraic  In mean s c o r e s , at the Grade 4  d i f f e r e n c e s only i n  i n favour of g i r l s and  two  domains:  i n Measurement i n favour of  boys, both d i f f e r e n c e s being s m a l l . At the Grade 8 l e v e l , were s i g n i f i c a n t Measurement  but small d i f f e r e n c e s i n three a r e a s : Geometry,  and  Computer L i t e r a c y ; a l l three were i n favour of  boys. At the Grade 12 l e v e l there were in  all  there  domains  ranging  between  significant  7% and  17%,  Study  of  differences  a l l i n favour of  ma1e s. In analysis  the was  Learning  Assessment  done by d i v i d i n g  Algebra  12, Algebra  males outperformed each  of  the  a  current  mathematics  11 or Mathematics 10. I t was  females  i n each of  domains. I t was  further  the Grade 12 p o p u l a t i o n i n t o  p o p u l a t i o n s of those whose l a s t or was  1981,  the  sub-  course  found that  sub-populations,  in  only on a s i n g l e o b j e c t i v e w i t h i n  the domain of A l g e b r a i c T o p i c s that  there  was  no  sex-related  difference. The  male-female r a t i o i n Algebra  40 i n the i n t e r v a l . The  r a t i o was  12 had  similarly  i n c r e a s e d to 60 to high  in  S c i e n c e , Geometry and Trade Mathematics ( R o b i t a i l l e , As Studies  demonstrated of  1977  and  by  scores i n the two  1981,  where  domains  Computing 1981)'.  L e a r n i n g Assessment were  classified  17  differently  but overlapped c o n s i d e r a b l y  d i f f e r e n c e s i n favour of males i n widened  in  British  Columbia.  minority  in upper l e v e l o p t i o n a l  i n content,  mathematics  Females courses  sex-related  achievement  had  a l s o continued to be a in  secondary  school  mathemat i c s .  A l b e r t a Assessment Of School Mathematics In the s p r i n g of 1978, the p r o v i n c e of A l b e r t a conducted an assessment levels The  study  in  mathematics  at the grades 3, 6, 9 and 12  (Olson, Sawada and Sigurdson, 1979; Sawada et a l ,  content  areas were: Number, A l g e b r a , Geometry,  and S t a t i s t i c s over the three Comprehension  and  number of i n s t a n c e s significantly  cognitive  Application. where  superior  the  levels  An  analysis  mean  score  Measurement  of  Knowledge,  was for  made of the one  females  area,  was  that  males  17 to 11 at Grade 3, 26 to 10 at Grade 6,  28 to 6 at Grade 9 and 43 to content  sex  to the mean score f o r the other sex. On  t h i s c r i t e r i o n , comparison by g r a d e - l e v e l i n d i c a t e d outperformed  1981).  3  at  Grade  12.  By  mathematical  i n the 20 comparisons p o s s i b l e , only i n the area  of Number at the Grade 3 l e v e l d i d females do b e t t e r . A l l  other  comparisons  males  favoured boys. By the three c o g n i t i v e l e v e l s ,  d i d b e t t e r than females 15  to  Comprehension  2  and  33  to  9  in  Knowledge,  30  to  6  in  at A p p l i c a t i o n s . At the Knowledge  l e v e l alone g i r l s were ahead at grades 3 and  6,  but  were ahead by Grade 9, and c o n s i d e r a b l y so by Grade  12.  the  boys  18  The  Alberta  consistent  study  findings  achievement  seems  of  scores  remarkable  male  by  not  superiority  grade,  by  content,  only  such  unequivocal  data.  The  authors  school systems, modes of i n s t r u c t i o n and for  sex  bias.  mathematics  and  by c o g n i t i v e conclusions  recommend examining  choice  of  test  They suggest that as 90% of the t e s t  to  be  sex  biased  report  concludes  National  (NAEP) which have been found  ( T i t t l e , McCarthy and  p o s s i b l e that such a b i a s  pervades  this  S t e c k l e r , 1974), i t i s study  as  well.  The  with a recommendation that Canada i n v e s t i g a t e  what s o r t of s o c i o - e d u c a t i o n a l - c u l t u r a l v a r i a b l e s give male  items  items were  s e l e c t e d from s t u d i e s i n the United S t a t e s such as the Assessment f o r E d u c a t i o n a l Progress  its  in  l e v e l s , but a l s o f o r i t s extreme c a u t i o n i n drawing from  for  superiority  in  mathematics  so  that  introduced to give females a f a i r o p p o r t u n i t y  changes  rise  to  may  be  i n an area of such  significance.  Case f o r S e x - r e l a t e d D i f f e r e n c e s i n Mathematical Reasoning Ability In d i r e c t c o n t r a s t to the i n f e r e n c e s drawn from the A l b e r t a Assessment of School Mathematics (Olson et a l . , 1979; al.,  1981)  Precocious 1982).  is  that  done  Youth (SMPY) at  Between  1972  and  in Johns 1974  the  Study  Hopkins  of  Sawada  et  Mathematically  (Benbow  &  Stanley,  the SMPY i d e n t i f i e d , through a  19  talent had  search, over 2000 seventh and e i g h t h  performed  as  well  sections  S t a n l e y pursued through  of the  the  the  Mathematics  (SAT-M)  and  careers  of  these  the f o l l o w i n g f i v e y e a r s . I t was found that  to s u c c e s s i v e SAT-M and SAT-V Program  Mathematics  Achievement  Verbal  S c h o l a s t i c A p t i t u d e T e s t . Benbow and  mathematical  Placement  who  as the n a t i o n a l sample of e l e v e n t h and  t w e l f t h grade females at (SAT-V)  grade students  scores,  Examination  scores  in  students  in relation  on  the  Advance  Calculus,  and  on  the  T e s t , L e v e l s I & I I , males scored higher  than females. Therefore,  i t was  hypothesized,  superior  mathematical  ability  differing  l a t e r a l development  for  that  genetic  males  may  have  reasons of e i t h e r  of the b r a i n , or p r e n a t a l hormonal  i n f l u e n c e s (Benbow & S t a n l e y , 1982). However, the data r e v e a l e d : (1) that males took more mathematics courses  than  especially  Geometry  in  College  Algebra,  Analytic  C a l c u l u s , although a l l s u b j e c t s took the courses up t o Grade 11 l e v e l (2)  same  females and  mathematics  (p.604);  that males took the courses one semester e a r l i e r on an  average, than d i d the females  (p. 604);  (3) that the p r o p o r t i o n of females t a k i n g the optional  courses  upper  level  i n mathematics was s m a l l e r than f o r boys  (p. 608).  When females d i d take these c o u r s e s , i t was r e p o r t e d that  their  20  mean  course grades were m a r g i n a l l y higher than those  f o r males.  T h i s f a c t was e x p l a i n e d by the o b s e r v a t i o n : The mathematics course-grade d i f f e r e n c e s can probably be e x p l a i n e d by the sex d i f f e r e n c e s f a v o u r i n g g i r l s that have been found i n conduct and demeanor i n school (Baker, 1981; see E n t w i s l e & Hayduk, 1981, i n p r e s s ) . G i r l s have b e t t e r conduct and demeanor. This possibility is c o n s i s t e n t with the stronger r e l a t i o n s h i p between mathematics reasoning a b i l i t y and mathematics course grades f o r boys than g i r l s . U n f o r t u n a t e l y , we c o u l d not c o n t r o l f o r conduct or demeanor, (p.617, emphasis added) What can be i n f e r r e d from the r e p o r t e d data  i s that  females  d i d not take mathematics courses  semester a f t e r semester as d i d  the  (and l o s s e s ? ) . The "mathematics  males  but only with breaks  reasoning a b i l i t y " r e f e r r e d to i s the measure of the SAT-M score at  the  time  of  the  talent  relationship..." translates  search,  to  and  the  "stronger  the f a c t that boys' scores were  high or low i n the courses depending on whether they or  low  in  the SAT-M, but g i r l s '  The  inference  w e l l be that one needs t o e x p l a i n away the higher s c o r i n g  of g i r l s  i n mathematics c o u r s e s , as the authors  that the performance of g i r l s When  high  scores i n the courses d i d not  f o l l o w the p a t t e r n of t h e i r scores i n the SAT-M. could  were  one  considers  that  i n the SAT-M tended  to  or  t o be e r r a t i c .  that  course  grades  are  i n d i c a t e achievement i n mathematics, i t appears to  be i n c o n s i s t e n t that mathematics identified  done;  scores on the SAT-M were supposed t o  p r e d i c t a p t i t u d e f o r mathematics, and supposed  have  with  the  reasoning  prediction  ability  criterion,  but  should  be  should  be  21  summarily d i v o r c e d from mathematics achievement to make way f o r "conduct  and demeanor".  Another study  q u e s t i o n a b l e aspect of the Benbow & Stanley (1982)  i s the p e r s i s t e n t use of "mathematical  interchangably earlier,  with SAT-M s c o r e s . Apart  reasoning  ability"  from the i n s t a n c e c i t e d  to c i t e a few o t h e r s :  (1) "when for..."  mathemaical  reasoning  ability  was  controlled  (p. 611), when what was meant was that SAT-M scores  were c o n t r o l l e d f o r . (2) "the l e s s w e l l developed  reasoning a b i l i t y  (p.  authors had access to were the  618), when  what  the  of g i r l s . . . "  lower SAT-M scores of g i r l s . (3) The c o n c l u s i o n : "We conclude that sex d i f f e r e n c e s i n mathematical reasoning ability and achievement a r e widely noted i n t h i s h i g h l y a b l e group of students, they persist over s e v e r a l y e a r s , and they are b e t t e r accounted for by the sex difference in mathematical reasoning ability than by sex differences in expressed attitudes toward mathematics and mathematics course taking in j u n i o r and s e n i o r high s c h o o l " (p. 619). There appears to  indicate  that  t o be no evidence the quest  with  literature  to i d e n t i f y mathematical  a b i l i t y which began with Hadamard concluded  i n the r e s e a r c h  (1954)  and  reasoning  Poincare  the SAT-M. On the c o n t r a r y , i t appears  (1963) that the  quest goes on (Luchins & Luchins, 1980). In f a c t , the a b i l i t y of the SAT-M even to assess mathematical  reasoning a b i l i t y  has not  22  gone  unquestioned  (Aiken,  1982;  Gray  & Schafer,  1981). In a  study commissioned by the C o l l e g e Entrance Examination Board, i t was found that drilling, standard  while  SAT-M  SAT-V  scores  was  could  be  raised  d e v i a t i o n by such p r e p a r a t i o n  As a f u r t h e r c o n c l u s i o n , identification ability  impervious  of  SAT-M  to general  Benbow  scores  reasoning  to by  coaching  as  much as one  (Pike & Evans, 1972). and  from  Stanley  extend  mathematical  least  the  reasoning  a b i l i t y . To quote the a u t h o r s :  "Moreover, why boys tend to reason b e t t e r than at  and  girls  from  as e a r l y as second grade (Dougherty et a l . , Note  5) onward i s a l s o , of course, not c l e a r " (p. 620). On the b a s i s of the data presented i n the l a s t (Benbow that  &  Stanley,  achievement Sawada  et  evidence  scores. al.,  they  two  who  performance and  (2)  on that  circumstances  than Benbow & Stanley,  male  genetic  in  mathematics  male  and not  superiority  in  ability. have been d e a l t with at some length as  dramatically mathematics  that:  highly  (1)  superior  achievement t e s t s i s s t i l l  interpretations are  superiority  who have  i t i s Benbow and S t a n l e y ,  claim  studies  demonstrate  of  While  mathematical reasoning These  studies  1982; Sawada et a l , 1981), i t would appear  i t i s Sawada et a l . , r a t h e r  uncontroversial  two  of  subjective,  support to any p l a u s i b l e theory  related  male a fact,  factors  and  and may be used t o lend  for sex-related differences.  23  Historical  Perspective  No assessment  of t h e o r i e s of inherent or g e n e t i c or gender-  based male i n t e l l e c t u a l s u p e r i o r i t y can be p l a c e d  in perspective  unless i t i s c o n s i d e r e d i n i t s h i s t o r i c a l c o n t e x t . A r i s t o t l e an  oft-quoted  authority  on  the  theory,  and no doubt he had  innumerable unrecorded f o r b e a r s . The preoccupation of t r y i n g "prove" such t h e o r i e s l o g i c a l l y spurt  in  mathematical  an  Hersh,  "if-then"  thought  approach  in  the  to  Renaissance p e r i o d i n only  the  theories  s o c i o l o g i c a l problems  can  logical  backing  to  (Davis &  superiority  of  male  (Gould, 1981;  over  progressively male  lateralization  more  the  1864). But  even  if  such  (Chorover, 1979), the means have become  (Bufferey  ability &  due  Grey,  to  differential  1974; McGee, 1979; McGlone & K e r t e s z ,  functions  female, i t i s of i n t e r e s t  must to  exist  brain  1972; Harshman & Remington,  Granting that b i o l o g i c a l d i f f e r e n c e s i n the related  effective  s o p h i s t i c a t e d . The c u r r e n t theory i s one of  spatial  1976; Levy, 1972,  for  female, white over b l a c k , west over  LeBon, 1879; Vogt,  proof has proved e l u s i v e  superior  blindly-accepted  be seen i n the measuring and weighing of craniums  and grey matter to provide s c i e n t i f i c proof  and  calculus,  1981).  T h i s search to give  east  to  seem to have o r i g i n a t e d with the  Europe. With Newton and L e i b n i t z began not but  is  between  investigate  the  human  the  1973). anatomy  male and the  succeeding  two  24  steps  i n the l o g i c a l (1) that  sequence: males  are  superior  in  spatial  visualization, (2) that mathematics achievement i s dependent spatial  visualization.  Are Males Superior Up  to  in Spatial Visualization Ability?  the m i d - s e v e n t i e s ,  a b i l i t y was almost u n i f o r m a l l y 1915;  Fennema,  1976).  Since  on  superior associated  1974; Maccoby then  spatial visualization  &  inferences  with  Jacklin,  from  data  males  (Carey,  1974; Schonberger, have  become  less  conclusive. In the F a l l of 1978, the Education Commission of the States (ECS)  conducted the Women i n Mathematics P r o j e c t , a survey of 13  year o l d s and high the  same  time  school  the ECS  Assessment of E d u c a t i o n a l Mathematics  Project  seniors also  i n the U n i t e d conducted  Progress  and  Algebra,  between  neither  males  and  (NAEP).  Problem  i n the NAEP  domains of Computation, Algebra and  the second  the Women i n  study females  Solving  and S p a t i a l  i t was d i v i d e d i n t o the three  and A p p l i c a t i o n s . In Computation  showed  any  significant  difference  a t the 13 year l e v e l . 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 problem-solving was  In  National  the t e s t content was d i v i d e d i n t o the four  domains of Computation, Algebra, Visualization  S t a t e s . At about  a s i g n i f i c a n t d i f f e r e n c e i n favour  domain, but  there  of males i n A p p l i c a t i o n s  25  and a s i m i l a r  significant difference  spatial visualization It  can  be  (Armstrong,  concluded  visualization ability  in  favour  1981; NAEP,  that  evidence  i s ambivalent  of  females  in  1980). of s u p e r i o r  spatial  between the sexes.  Is Mathematics Achievement Dependent On S p a t i a l  Visualization  Ability? In a study sponsored by the N a t i o n a l Science Foundation the  United  States,  a  probability  sample of 1330 students i n  grades 6-8 i n four school areas were s t u d i e d 1977).  There  achievement  were in  significant  favour  same  study  in  (Fennema & Sherman,  sex-related  differences  in  of males i n one of the areas but i t was  not accompanied by any d i f f e r e n c e i n s p a t i a l the  in  grades  visualization.  In  9-12 (N=1233), two of four schools  showed s i g n i f i c a n t d i f f e r e n c e s i n favour of males i n mathematics achievement spatial A  but only one of them  a  male  causal  ability"  relationship  between  s p a t i a l v i s u a l i z a t i o n and  has been q u e s t i o n e d by Werdelin  between  the  ability  to  visualize  despite  and  geometric  (Werdelin, 1971). L o g i c a l as such a connection appears  to be, e m p i r i c a l r e s e a r c h has f a i l e d to e s t a b l i s h  1949;  in  a p p a r a n t l y i s a "strong pedagogical reason t o b e l i e v e i n a  connection  (Aiken  advantage  visualization.  mathematics achievement what  showed  1973; Radatz,  Fruchter, 1979; Smith,  1954;  Lean  1964; Very,  & Clements,  i t s existence 1981; Murray,  1967; Werdelin,  1971).  26  On the c o g n i t i v e l e v e l , Twyman (1972) d i s t i n g u i s h e s between "memory images" and " a b s t r a c t images" and the "use" of The  irrelevant details in visual  the A  imagery.  images, he s a i d , c o u l d d i s t r a c t  " o r i g i n a l s t i m u l u s " from making the necessary a b s t r a c t i o n s . similar  distinction  Menchinskaya  (1946)  categorizes geometric  in  problem and  cognitive  and  abilities  Krutetskii  solvers  into  was  found  visualization  in and  reviewing  the  literature  mathematics  shift  geometric  that mathematics educators may need  done  clarify  the  implications  of  related  achievement  statement to  analytic,  to be more r e s t r i c t i v e than the a n a l y t i c mode.  Lean and Clements (1981) spatial  types:  However,  by  Krutetskii  i n the l a s t category  between the other two modes with ease. mode  (1976).  three  harmonic, where those  i s made  further  make  to the  research  information-processing  t h e o r i e s . They quote the experience of e d u c a t i o n a l p s y c h o l o g i s t s who had conducted "auditory"  and  r e s e a r c h f o r decades on "visual"  separate  (DeBoth & Dominowski, 1978; Jensen, and  existence  of  Mathematics Regression  was  ambiguous  1971).  Clements (1981) i n t h e i r study of 116 foundation  year e n g i n e e r i n g students at Papua, New Guinea, battery  that  l e a r n e r s c o u l d be i d e n t i f i e d , only to  f i n d that evidence of t h e i r  Lean  the assumption  five and  a  analysis  spatial test of  ability  in Applied data  a b i l i t y t e s t s together accounted  tests,  administered a  test  Mathematics.  in  a  Pure  Multiple  r e v e a l e d that a l l of the s p a t i a l f o r 10% of the v a r i a n c e i n Pure  27  Mathematics, partialled  and a f t e r out,  Mathematics. tendency students  i t accounted  One i n f e r e n c e drawn from the a n a l y s i s was that "the  who  abstract  preferred  a  and  on  by  a  mode  therefore  study  on  avoid  the  1981, p.  The g r e a t e r s i g n i f i c a n c e of a n a l y t i c a l  in  formation  s k i l l s over  was  spatial  i n another study done i n New D e l h i ,  India  1963-67 (Sharma, 1973a, 1973b). Students from standards 8-11,  to  19+ age group  s c h o o l , i n the  (N=2628), were the s u b j e c t s i n a combined  s i x areas:  verbal,  numerical,  mechanical  a b i l i t i e s , deductive reasoning, and c l e r i c a l The students were d i v i d e d of  of  1981, 1982).  c r o s s - s e c t i o n a l and l o n g i t u d i n a l study on achievement the  to  grade students i n  where standard 11 was the f i n a l year of secondary 12+  by  of p r o c e s s i n g  296). T h i s  seventh  V i c t o r i a , A u s t r a l i a , by Suwarsono (Clements,  s k i l l s was the f i n d i n g  tests  be due to a developed a b i l i t y  images" (Lean & Clements,  supported  mathematics  verbal-logical  i n f o r m a t i o n might  readily,  unnecessary  been  f o r 2% of the v a r i a n c e i n A p p l i e d  towards s u p e r i o r performance  mathematical  further  the e f f e c t s of Pure Mathematics had  their  mean  into five a b i l i t y  comprehension  scores  on  The  growth  curves  levels  i n each  showed  that:  a b i l i t i e s were very high f o r the upper  and  in  spatial  speed and a c c u r a c y . l e v e l s on the  basis  the t e s t s and growth  curves were t r a c e d f o r each domain by c l a s s , each c l a s s and by a b i l i t y  scores  by  modal  age i n  class. (1) v e r b a l and reasoning  levels  i n standard 8, but  that those at lower l e v e l s grew at a f a s t e r r a t e so that the gap  28  was  narrowed by standard  ability,  clerical  11;  (2) Numerical  ability,  speed and accuracy grew at p a r a l l e l  that whatever d i f f e r e n c e s there had  been  levels  through  In  at standard 8 was  spatial ability  higher l e v e l  maintained  between  Stanley  the  various  i n standard 8, but progressed at a f a s t e r  more  or  less  (1982) f i n d i n g that males who  the SAT-V scores in the by  11;  the  Talent  end  of  rate  conform with the Benbow and were lower  Search  almost  than  females  on  out  the  wiped  h i g h s c h o o l , while growth i n SAT-M  with the data. Benbow and S t a n l e y concluded rate  plateauing reached  than  females.  i n v e r b a l and  high  levels  so  11.  scores were only s l i g h t l y higher f o r males. But c o n f o r m i t y  faster  (3)  alone, the a b l e r groups not only s t a r t e d at a  results  difference  r a t e s so  to standard  that the gap widened c o n s i d e r a b l y by standard These  mechanical  Sharma  that males grew at a  inferred  reasoning a b i l i t i e s  earlier  grew  at  ends  that there was  so that  a  those  who  a slower pace. No  sex-  r e l a t e d d i f f e r e n c e s were s t u d i e d although the sample was  a mixed  one. Another i n t e r e s t i n g r e s u l t when  the  six  a b i l i t i e s were rank ordered  l e v e l s i n each c l a s s , the  last  10 and  from the Sharma study  f o r the top l e v e l ,  11. V e r b a l , Numerical  spatial ability  outranked  spatial  exception  of  ability  verbal  and  that  f o r each of the  i n standard 8, 4th i n standard 9, and  standard  was  five  ranked  5th i n standard  Reasoning  abilities  i n each of the c l a s s e s with a s i n g l e  ability  following  spatial  ability  in  29  standard  9.  The q u e s t i o n a r i s e s as to how  in achievement scores f o r accounted  for  numerical on  the  by  the  high  spatial ability  scorers  would  have  and reasoning a b i l i t i e s had been p a r t i a l l e d out. basis  of  rank  ordering,  In an e a r l i e r  the  results  "favoured and  (1981).  study of the SMPY (Benbow & S t a n l e y , 1980) i t  the h y p o t h e s i s that sex d i f f e r e n c e s i n achievement i n toward  ability,  which may  spatial  tasks."  mathematics  are  result  from  superior  (Benbow  &  S t a n l e y , 1980, p.1264) But as y e t , that high l e v e l s  of  evidence  there  has  that i t i s the s u p e r i o r s p a t i a l a b i l i t y  that  c o n t r i b u t e s to the s u p e r i o r there or  i s evidence  without  Sherman, Gray,  spatial  found among h i g h a c h i e v e r s i n mathematics, and low  a c h i e v e r s i n mathematics are low i n s p a t i a l a b i l i t y , no  male  i n t u r n be r e l a t e d to g r e a t e r male a b i l i t y i n  while there has been f a i r evidence  been  far  high s c o r i n g females i n SAT-M. The authors t h e r e f o r e  attitude  ability  Even  seem to be i n  r e p o r t e d that between 1972 and 1979, high s c o r i n g males  outnumbered  been  a f t e r the e f f e c t s of v e r b a l ,  c o n f o r m i t y with that of Lean and Clements  was  much of the v a r i a n c e  achievement.  In  fact  t h a t mathematics achievement can be h i g h with  superior s p a t i a l 1977;  mathematics  Lean  1974; S a t t e r l y ,  visualization  ability  (Fennema  &  & Clements, 1981; Roach,,1979; Robinson & 1968,  1976)  Present S t a t u s Of Genetic-based If the genetic-based  Theories  theories for  sex-related differences  30  in  mathematics  spatial  achievement  visualization  findings  ability,  Differential  do  not  account  Considering  discredit  other  f o r the  appear  from  brain  the  that  d e s c r i b e d on  theories  discriminating in  short span  size  recent  per se.  or any of the other f a c t o r s ,  differential  the r e l a t i v e l y  not be considered 1982)  i t would  brain l a t e r a l i z a t i o n ,  c o u l d b r i n g to l i g h t some  shifted  are based on s u p e r i o r male  d i s r u p t the sequence of l o g i c a l deduction  page 4, though they  could  scores  in  ability  which  achievement which  scores.  theories  have  to b r a i n s i d e , such a d i s c o v e r y  could  u n l i k e l y . If Benbow and Stanley  (1980,  are r e p r e s e n t a t i v e of the school of thought that  1981,  supports  g e n e t i c , s e x - r e l a t e d d i f f e r e n c e s i n mathematical a b i l i t y , a  point  of  note  that  generated a hypothesis  i t was  of  male  data  from the same study that  superiority  based  on  ability  i n 1980, and one based on b r a i n l a t e r a l i z a t i o n  In  interval  the  controversial  spatial  as  a  ability  had  discriminating  i t is  become factor,  comprehensive c r i t e r i o n of b r a i n l a t e r a l i z a t i o n  spatial i n 1982.  increasingly and  the more  was needed.  L i t e r a t u r e on the N u r t u r e - P o s i t i o n While accident  neither victims  i n j u r i e s provided lateralization opportunity  nature, and  war  some data  (McGlone  &  nor  nurture,  veterans  who  f o r experimental Kertesz,  can had  be  contrived,  sustained  studies  on  brain brain  1973). Even though no such  e x i s t s f o r the study of induced  changes i n  nurture,  31  experimental demonstrate scores  and  1964; K e l l y ,  1977), Preston,  Maccoby lack  mathematics  domain  1982),  activities  of  single  exogenous  between  1982).  This (Husen,  the  Mullis,  most  and  female  first,  Columbia  L e a r n i n g Assessment  Robitaille,  NAEP  from  1982),  exogenous 1971,  and  factors  1973,  evidence  1975;  i n support of  range  of  overlap  i n mathematics  Kelly,  1981;  & Stanley, studies  and  Tobias,  Mathematics 1980,  1982)  (Kapoor,  and second  (Robitaille  1 9 8 1 ) a n d i n t h e Women  parents  1982).  i n the f i r s t  Studies  Luchins &  1969; H o r n e r ,  International  (Benbow  third  1975, 1980),  (Fink,  scores  1977;  i n the F i r s t  and  1976),  considerable  achievement  i n t h e SMPY  second  1975; NAEP,  the  1978; T o b i a s ,  other  research  Katkovsky 1964;  Ormerod,  (Fennema,  evident  1967),  1971;  1977;  1978; K a g a n ,  1974; T o b i a s ,  1982; S p e n d e r ,  i s  sciences was  and  significant  theory  male  physical  these  1978; S e l l s ,  Fennema,  encouragement  (Osen,  1976a;  perception  ( F o x , 1976b;  of success  to  achievement  1981),  1976;  & Keeling,  fear  McMahon,  designed  1982; F o x ,  & Collings,  1975; E r n e s t ,  lack  of  (Casserly,  (Ernest,  1973; S e p p i e  1974),  been  of c o n f i d e n c e ( C r a n d a l l ,  mathematical  1958;  The  1977;  female  1962; C r o s s w h i t e ,  1980; O s e n ,  Schonberger,  in  of  and lack  combinations  (Carey,  Study  have  teachers and c o u n s e l l o r s  various  the  anxiety  Humphreys,  and/or  theory  stereotyping  as a male  of c h i l d h o o d  1968;  the  1981; S m i t h e r s  & Jacklin,  Luchins,  the  sex-role  mathematics  Fox,  in  the s e n s i t i v i t y  to:  Kagan, of  studies  &  i n Mathematics  1983;  British  Sherrill, Project  32  (Armstrong,  1981).  proportion  of  proportion this '0'  of  level  males.  for  as  fact,  scores  a  achievement  student  of  as  investigations,  high  as,  for in  their  England  as  well,  than  large a  large  (1980)  cite  investigation  of  GCE  for  The  and  higher  a  Meighan  a  more  Sharma  significant scores  physics  or  and  differences.  finding  mathematics  these  Sharma  reason  sex-related  in  of  scored  In  mathematics  resulted  a  each  females  observation  reason  was  In  the  consistent  & Meighan  correlation  whether  rather  or  than  not  between  the  the  study  subject  sex  of  the  subject. In  the  First  International  national  differences  national  differences.  year-old and  level  England.  outperformed including that  population both  in But  made,  the  the  the  instance,  sex  in  States.  highest  Israeli as  had  the  The  well in  as  the  the results  mean  girls  boys  score scored  sex-related  advantage on  in  differences  of  Another  40  sex-related  cross-  sex-related  girls  computational 42  Study,  Netherlands,  "low-achieving"  United  had  exceeded  "high-achieving"  overall,  boys  this  But  and  summarizing with  greatest  the  verbal  For  were  the  Israel  far  Mathematics  for higher  these other  result  of  the  them.  Japan  countries countries was  13  year  old  Israeli  boys  (Husen, that  Benjamin  differences  1967). were Bloom,  concluded  statement: We had o r i g i n a l l y attempted d i f f e r e n c e s in mathematics as  13-  study  comparisons of  the  the  than  subtests  at  Belgium,  of  many  within-  to understand these functions of the  33  differential r o l e s of males and females in the different countries. However, we find so few exceptions to the r u l e of male s u p e r i o r i t y i n mathematics that we are l e d to believe that variation i n the roles of the sexes in these c o u n t r i e s w i l l not be helpful in understanding mathematics achievement d i f f e r e n c e s between the sexes (Husen, 1967, p.259, emphasis added). In the although  two  decades that  there  are  have  Ornstein,  1983),  accounted  for  essential  sex-related  and  other  t o be  countries  narrowed  studies  since  (Brush,  in d i f f e r i n g  differences  to  the  d i f f e r e n c e s and  over i t s i m p l i c a t i o n s s t i l l in  elapsed  i n d i c a t i o n s that s e x - r e l a t e d  some of the c o u n t r i e s  the  have  that  d i f f e r e n c e s in  1980;  Levine  sex-roles  the attendant  of  some,  controversy  p e r s i s t in these c o u n t r i e s . the  &  partially  conviction  f o r an added dimension on  study,  Studies  issues appear  necessary.  Summary Research evidence t h e r e f o r e 1.  Sex-related  scores 1983;  exist  age  and  grade &  in  NAEP, 1975,  level  1980;  achievement  (Husen, 1967;  Kapoor,  R o b i t a i l l e , 1981).  i n favour of males, widens with  (Kapoor,  Sherrill,  that:  mathematics  i n the developed world  d i f f e r e n c e in scores  Robitaille al,  differences  K e l l y , 1981;  2. The  appears to i n d i c a t e  1977;  1983;  NAEP,  1975,  R o b i t a i l l e , 1981;  1980;  Sawada et  1981).  3. In the past  decade  these  differences  have  tended  to  34  decrease i n the United S t a t e s , but they s t i l l &  Stanley,  1980;  Blum & Givant,  1983; S e l l s , 1982; Tobias, The  rationale  achievement is  scores  mainly d i v i d e d  deductions  dependent  1982).  for  male  superiority  still  evident r e g a r d l e s s of observed trends  that  ( i ) mathematics  1974; Maccoby & J a c k l i n , studies,  superiority  in  (Armstrong,  1981;  spatial  increasingly 1954;  make  Fennema  &  Sherman,  should e x i s t ,  dependent  dubious (Aiken,  on  Clements,  Gray,  little  males  are  of  male  ability  ' questionable  1977).  Even  i f such  achievement  ability  has  1982;  in  become  Fruchter,  1949; Radatz, 1979; Smith,  That  spatial  visualization  to s u p e r i o r mathematics  1981; Menchinskaya,  1974; S a t t e r l y ,  are  assumption  Clements,  was the c o n c l u s i o n i n many such s t u d i e s &  sequence  scores  and ( i i )  whether  spatial  1973;  1964; Very, 1967; Werdelin, 1971). contributes  the  (Carey, 1915; Fennema,  the  visualization  Lean & Clements, 1981; Murray,  ability  on  1974).  however,  superior s p a t i a l a b i l i t y is  mathematics  achievement  superior i n s p a t i a l v i s u a l i z a t i o n a b i l i t y  mathematics  in  i n t o two s c h o o l s :  on s p a t i a l v i s u a l i z a t i o n a b i l i t y ,  Recent  (Benbow  1982; Levine & O r n s t e i n ,  I. The Nature-Theory, which i s based p r i m a r i l y of  exist  (Krutetskii,  1946; Roach,  achievement 1976;  Lean  1979; Robinson &  1976; Sharma, 1973a, 1973b).  I I . The Nurture-Theory, a t t r i b u t e s  sex-related  differences  in  35  mathematics and  achievement  environmental  done  in  this  differences b e c a u s e of  in  been  shown  Fox,  Newton,  investigation,  f a c t o r s has  to  be  sensitive  1977;  Humphreys,  scores  been  sex-related  exist  solely  scores  of  females  socio-psychological 1975;  1982;  Ernest,  Luchins  1976;  have and  Fennema,  &  Luchins,  1980;  on  West I n d i a n  1981).  Recent  studies  in  children in Britain  randomly chosen  on  mathematics  It  was  found  positive  among g i r l s  and  have p r o d u c e d  studies  up  males,  but  Roach  results  with the than  a l s o found  t o now also  have  at variance  (1979) t e s t e d 206  mathematics  that  higher  was  I n d i e s and  achievement, conceptual that  significantly  Cultures  b o y s and  from G r a d e 6 c l a s s e s i n 5 J a m a i c a n  correlations  intelligence  In O t h e r  t h e West  many t h a t have been c i t e d . girls  to  f a c t o r s (Crosswhite,  that  has  demonstrated.  achievement  Some S t u d i e s  Asian  t o be  psychological  research  evidence  achievement yet  mathematics  environmental 1977;  of  mathematics  such  to s o c i o l o g i c a l ,  f a c t o r s . While c o n s i d e r a b l e area  However,  scores  achievement  analytical mean that  t o be  recorded  a higher  style  f o r boys  variance  had  for  only  that  212  schools  significant style girls  (p<.0l).  l a r g e r than  with  intelligence.  conceptual  scores  not  and  and  The  and were  variance  f o r b o y s . Most  higher  among m a l e s . No  scores  for  significant  36  s e x - r e l a t e d d i f f e r e n c e s had earlier  the  age  of  and  multiracial  science,  West Indian g i r l s ,  dropped  out  of  higher  West Indian g i r l s  and  6  science  schools  in  English  Britain.  the ranking among the  boys,  West  level  Indian  mathematics courses  done c o n t r o l l i n g  still  their  kept  their  others  boys  and  f o r course  than  others  background.  last  weeks of school)  2,  7  (in  their  first  three sex-  d i f f e r e n c e in block c o n s t r u c t i o n in favour of males samples. There was  group i n mental r o t a t i o n or p a t t e r n  either  assembling. of  c u l t u r a l change on mathematical thought by studying  samples  of  and  12/13  northwest primary  (1979)  in  effects  Asian  Trown  no d i f f e r e n c e  was  the  immigrant  and  4  three weeks of school) with a p a r a l l e l  in s p a t i a l p e r c e p t i o n t a s k s . A s i g n i f i c a n t  the same i n the two  The  rank.  group i n S c o t l a n d i n grades 3, 5 and  Tanner  In  (no d i f f e r e n c e s  (1979) compared 72 Ghanian c h i l d r e n i n grades  (in  related  mathematics,  in that order. As l a r g e r numbers of E n g l i s h g i r l s  f u r t h e r a n a l y s i s was  Jahoda  1974).  Asian boys and g i r l s  are mentioned) d i d best of a l l , and  English g i r l s ,  two  2300 West Indian, Asian and E n g l i s h sudents of  group from 5  mathematics  was,  Isaacs,  (1980) s t u d i e d achievement in  English 16+  in Jamican schools in  s t u d i e s as w e l l (Vernon, 1961;  Driver and  been found  investigated  school c h i l d r e n i n two  age  groups, 10/11  years, from 22 schools i n 11 towns in of  England.  education  i n the  Among  children  country,  Asian  who  the  years  industrial  had had a l l t h e i r  girls  were  markedly  37  superior to their male counterparts  at age 10/11, and marginally  so at 12/13. Some Recent Studies in India Sex-related  differences  in mathematics achievement  have not been an issue in educational research in India preoccupation illiteracy  scores as  the  in the country i s s t i l l mainly with the problem of  (Sunder,  1982).  However, a few studies that have a  tangential bearing on this investigation are c i t e d below. Sinha (1980) compared the competence of students typical  from  four  schools, a government boys' school, a government g i r l s '  school, a private boys' school and a private g i r l s ' school, with a t o t a l of 5200 students. to  cover  components  confidence,  positive  reinforcement,  Competence was  such  as  self  moderate  acquisition  concept,  and/or  operationally  ranked  first  on  high  leadership  skills,  internal  control  The private  qualities,  That the result does  to  by  girls  is  indicated  other  studies  personality of women across India (Gaur, which  found  that  while  women  of  of  1980;  the  upper  girls'  intelligence,  extroversion and self concept. all  self  level of achievement and  positive leadership q u a l i t i e s among others. school  of  defined  not  extend  of status and Sharma,  1979),  classes  themselves responsible for their success, the middle  held  and lower  classes held God or Fate responsible. Upper class g i r l s in India are  to  be  found  almost  entirely  in  private g i r l s '  schools  38  (Jayaraman,1981). Chauhan and Singh  (1982) i n an i n v e s t i g a t i o n  h a b i t s of 500 10-12 year o l d s i n the sex-related  differences  in  Simla  e i t h e r urban  i n t o the study  district  found  or r u r a l p o p u l a t i o n s ,  but the mean s c o r e s , a c c o r d i n g t o the manual of the Study Inventory used, were average rural  areas.  The e f f e c t  scores  by  Habits  i n urban areas and below normal  in  of p a r e n t a l p r o f e s s i o n on study h a b i t s  was a l s o found to be s i g n i f i c a n t mean  no  parental  at the .05 l e v e l . The order profession  were:  of  Teaching-171,  Government Services-163, Defence Services-161, Business-160, and Agriculture-156. Another the  study i n v e s t i g a t e d the d i f f e r e n c e s i n the  secondary  school  teacher  1971). The data r e v e a l e d t h a t : were  generally  better  role  i n urban and r u r a l areas (1) heads of  qualified  urban  than  of  (Shah,  institutions  heads  of  rural  institutions;  (2) heads of i n s t i t u t i o n s , t e a c h e r s and parents i n  urban  set  areas  priority  while  subject-training  in  rural  as  the  objective  areas the p r i o r i t y was on c h a r a c t e r -  b u i l d i n g , g o o d - c i t i z e n s h i p and s u b j e c t - t r a i n i n g , Bhargava deprivation covered food,  (1982) on  of top  studied  the  effects  i n that o r d e r . of  academic achievement. The independent  15 m a t e r i a l , s o c i a l and  emotional  dimensions  prolonged variables such  as  c l o t h i n g , housing, m o t i v a t i o n a l experiences and c h i l d h o o d  experiences.  13  significant,  8  of of  these  dimensions  were  found  them a t the .01 l e v e l . A c r u c i a l  to  be  r e s u l t was  39  that these and  f a c t o r s a f f e c t e d the p o t e n t i a l high  female,  achievers,  f a r more t h a n t h e l o w a c h i e v e r s . However,  was made a s t o w h e t h e r t h e e f f e c t s v a r i e d i n e x t e n t  no  male study  with sex.  40  Chapter  3  METHOD  In I n d i a , have  yet  standardized  t o be  used  p a p e r s of p u b l i c school  program  do  as w e l l ,  just  comment  on  designed favour was  in educational  or b e t t e r  India  has been  textual  that  had  developed  world  i t e m s were t h e r e f o r e S t u d y of  been  selected 1981  (Robitaille,  educational  (Shukla,  1974;  mathematics  Inkeles,  girls  in  general external largely  more l i k e l y in this  known  i f test in  than i n d i g e n o u s ones. Columbia  1981),  and  to  study i t  samples  from the B r i t i s h  the The  Learning  the  Second  Columbia  in  1982). disparity  direct Columbia 1979;  high  found to  the q u e s t i o n s are  on  sufficiency,  and B r i t i s h  been  Study conducted i n B r i t i s h  a  the  be more d e f i n i t i v e  rather  large  objectives,  between K e r a l a  used  O'Shea, & D i r k s ,  economic  of  (Robitaille,  the  have  and t h e r e f o r e  would  chosen  I n t e r n a t i o n a l Mathematics  development,  mathematics  In t h e  ( H a t e , 1969). Hence,  the r e s u l t s  were  that  knowledge  already  Considering  in  ( H a t e , 1969). But a  performance  females than males  items that  1982  t h a n boys  superior  to test  Assessment  studies.  throughout the c o u n t r y , g i r l s  in  considered  tests  e x a m i n a t i o n s c o n d u c t e d a t t h e end of  the  examinations  achievement  in  standard comparison would  Niles,  technological of  living  of  mean  be n e i t h e r 1981a,  and scores  justifiable  1981b),  nor  41  profitable.  But  differences basis  it  was  i n a s e c t i o n of  of  tests  used  Columbia,  would  extend  investigations procedure  hoped  have  employed  in  t h a t an  the  a n a l y s i s of s e x - r e l a t e d  population  a  developed  the  frontiers  of  region  study  on  such  British  within  been made. A d e s c r i p t i o n  i n the  India,  i s presented  as  the  which  of  such  t h e method  in this  and  chapter.  Sample A total  of  1377  districts  of K e r a l a  students  from  students  were  standard  from s t a n d a r d  The sample  students  total were:  population  i n standard  5905  students.  5 (1124  three d i s t r i c t s  location  and  Ernakulam ( s e e map  central  i n Appendix  different Cochin  and  system  up  (384  boys  9 (300  boys and  in these 9  boys and  and 296  grades (1789 983  to  1956.  history,  the  areas  were,  an  i n the  female  they  0.66%  literacy for  781  and  596  schools  in  the  2009 g i r l s )  for  Trivandrum at  of  was:  girls)  a  Cannanore a t the  index  in 3  girls).  boys and  e a c h of w h i c h had  the  schools  i n K e r a l a were s e l e c t e d on  K e r a l a and  As  397  girls),  I). Historically,  Travancore,  18  distribution  s e c t i o n s of B r i t i s h M a l a b a r and  educational three  The  educational history:  in  c l a s s e s from  tested.  3798 i n s t a n d a r d  2107  The  5  i n 37  total  the  the  Princely  a different  tip  three  States  of  educational  the d i f f e r e n c e s i n figures  end,  southern  represent  the  of  b a s i s of  northern  the  and  for  B r i t i s h Malabar,  their  1891  for  3.76%  for  42  Cochin all  o f I n d i a was  merged to has  S t a t e and 2.69% f o r T r a v a n c o r e  been u n i f o r m  present,  Kerala:  with  a  which  a r e two d i f f e r e n t  Secondary  Schools  o f Government  s t u d i e s do n o t  10 and s t a n d a r d  most  American  from t h e s e  get  system'  schools  government  and  private  10 s t a n d a r d s ; section,  upper p r i m a r y constitute allow  is  the  run through  high  and school  by  the  11  schools, standards; stage  Graduates  t o a degree program Leaving  the  large  standards  standards,  in  Certificate majority  of  last  three  of courses,  constitute  the  5-7, c o n s t i t u t e t h e  s e c t i o n . The l a s t  f o r some s e l e c t i o n  to place,  i n t h e S t a t e . The s c h o o l s r u n  four  three  schools  the s e n i o r secondary  directly  schools  Central  These  i n t h e A r t s and S c i e n c e s .  the f i r s t  section,  the  from p l a c e  interrupted.  followed  the next  by  I n d i a . These  (2) The S e c o n d a r y S c h o o l  (SSLC) s t r u c t u r e t h a t  structures in  s e r v a n t s and members o f o t h e r  11 c o v e r i n g  schools are admitted  universities;  school  run  s e r v i c e s who a r e s u b j e c t t o t r a n s f e r  standard  primary  Malayalam,  education  school  system a l l over  a r e a l l l o c a t e d i n urban a r e a s ,  through  the  were  the State.  uniform  f o r the c h i l d r e n  so t h a t t h e i r  the  there  (1) The H i g h e r  Goverment  of  throughout  regions  common l a n g u a g e  then,  for  Structure in Kerala  At  public  1980). The t h r e e  i n 1956, on t h e b a s i s o f t h e i r  form t h e s t a t e o f K e r a l a . S i n c e  School  are  1% (Lewandowski,  S t a t e when t h e f i g u r e  standards, two y e a r s  8-10, of h i g h  but mathematics  isa  43  compulsory  s u b j e c t . G r a d u a t e s of  years  of  pre-university  degree  program.  Selection As  of  the  system  ,over  examination  of  section  of  schools  i n the  number  studies before  of  of  000  --  the  school three  districts at  5 ) , were 350 1,  envisaged  i n the  study  and  the  list  of  Insitute  the  various  standard  10.  the  drawn up  number  of  such  s e l e c t e d were 3565, and  the  total  The  two  the  mainly  on  schools  (Govt. the  The  Kerala,  limited  wide  of  was  the  of  in  mode  As  sample standards  instruction,  class,  of p o p u l a t i o n ,  attempted.  the  study  1981).  size  disparity  in quality  Instead,  in  no a  educational the  State  l o c a t e d at Trivandrum. This  list  b a s i s of  schools  Of  under  E v a l u a t i o n Department  Kerala,  in  for  levels  educational history  the  the  total  grade  represented by  appeared  latter  this  000  schools  that  of E d u c a t i o n ,  drawn  follow  to a  from  a representative basis  was  was  admitted  SSLC  with  s t a t u s and  schools  standards  this  various  economic on  are  two  the  the  Chapter  sampling  undergo  s a m p l e s were drawn e n t i r e l y  in  caste,  system  they  Kerala  candidates  mentioned  between  in  population.  students 9 and  schools  500  1983  the  (standards  school  Sample majority  --  this  SSLC i n the  of  t h e p e r c e n t a g e of p a s s e s examination  at  sample were t h e n  the  end  from of  s e l e c t e d from  list. In  the  rural  areas,  there  was  one  coeducational  high  school  44  per  village.  could  T h e r e were no  t h e r e f o r e be  rural  schools.  Boys'  school,  one  selected  from  selected  on  be  but  the  families  with  as  the  followed always girls,  by  teacher,  or  and  Girls'  of  in Standard  taught  by  numbers  in a class,  be  the  various i n the  standing.  8.  fed  i t might  be  standard  levels  were  sample. No  system  of  taught  primary  (a  Boys'  i t would i s more  i n Burnaby the  8 for g i r l s  that  classes.  explanation  one  i n the  pairs. by was  almost case  The  of  same  mathematics  a l l schools. in r u r a l  t o be of  the  chosen  the  was  In t e r m s of  areas  l a r g e s t number e n c o u n t e r e d  a l l - f e m a l e c l a s s e s tended  same  mathematics to a l l the  levels,  i n almost  by  example  c l a s s e s were d i v i d e d  In g e n e r a l ,  given  an  were  streaming  f o l l o w i n g paragraph.  Standard  was  said  i n the  c l a s s teacher  school  by  o f names; e x c e p t  the  one  which  school  of  least  schools,  order  t h e more numerous; t h e  An  cite  for G i r l s  is  list  were s e l e c t e d i n matched  teachers,  At  at  Collegiate  (a G i r l s '  Or,  selection  schools  To  Boys'  which  s c h o o l s . The  a t most two  classes  to  the  order)  schools  i s discussed  the  single-sex  House S c h o o l  school.  alphabetical  which  of  that  coeducational  s e l e c t e d from t h e  Boys'  i n any  parity  Crofton  schools  made so  The  The  comprehensive  i f S t . Thomas More  the  of  the  one  Marian High School  c l a s s e s at  heads  from  and  district.  same r e l i g i o u s  Boys' s c h o o l s The  school  b a s i s of  with  schools.  s e l e c t i o n was  Girls'  Columbia,  p a i r e d not  by  urban  i n B u r n a b y ) was  "elite", run  made randomly  each  the  from B r i t i s h school  The  single-sex  tended was  62.  l a r g e r than  all-male  headmasters  for  the  45  disparity  in  discipline  in a large class  The  class-size  selection  was  of  time two  of  urban  schools,  student  in  classroom,  i f not  than  in  and  of  school  effect,  rural  boys.  study,  schools  the  was  the  distinction  had  in Kerala,  choice  of  E n g l i s h or  But  this  instruction. areas.  In t h e  like  functioned  The levels months  mean  were:  exception  every  sex  high  school  environment this  in  de  the  facto  c o u l d have i t s i m p l i c a t i o n s f o r the  s i n g l e - s e x and  the  i n other  native  is  purposes  of  coeducational  a  p a r t s of  language as  operative  sample, a l l r u r a l large  number  the  almost  schools  India,  medium of  entirely  functioned  (80%)  have  of  the  in  in the  urban  in English.  ages  of  13 y e a r s ,  for standard  between t h e  those  choice  medium of M a l a y a l a m , and schools  between  the  at  d i v i d e d i t s students  s c h o o l . Although  schools  But,  collapsed.  Schools  urban  schools.  that with  almost  single  i n the  maintain  i n t e n t i o n of d i s t i n g u i s h i n g  discovered  a  easier to  single-sex  high  in  always  the  was  s e x - r e l a t e d d i f f e r e n c e s in achievement,  this  age  girls  every  is  status  of  i t was  So  Kerala  single-sex for  sex.  it  schools  testing,  i n t o c l a s s e s by  that  made w i t h  between c o e d u c a t i o n a l the  was  the  students  at  the d i f f e r e n t  6 months f o r s t a n d a r d  5. T h e r e were no  u r b a n and  rural  9;  and  significant  samples.  9  standard years,  5  differences in  46  Instruments of T e s t i n g  Test  A f o r Grade  4 Level  Form 4C o f t h e B r i t i s h (Robitaille, items, item  was c h o s e n  46  time,  in  item  measure, in  1981),  with  for  Number  Columbia  ten items d e l e t e d  this  and  Computer  level.  The  Operations,  34 i n Measurement  items  Learning  Assessment t o make t o t a l  items  item  of temperature,  deleted  changed t o s u i t  o f 36 were:  18 i n Measurement o f item  31 i n m o n e t a r y  19, 44 and 45 i n P r o b a b i l i t y a n d i t e m s 5 Literacy.  Study  and  Where p o s s i b l e , names a n d c o n t e x t s  the l o c a l  lifestyle  (see Appendix  III).  24  were  Testing  t i m e was 35 m i n u t e s .  Test  B f o r Grade 8 L e v e l A  Rotated British  selection Forms  of  Columbia  domains  Arithmetic, Testing No  items  i n t h e Second of  Names a n d c o n t e x t s The  38  of  from t h e C o r e T e s t  I n t e r n a t i o n a l Mathematics  1982  (Robitaille  were  Study  of  e t a l . , 1982) was made.  were c h a n g e d where p o s s i b l e , a s testing  and t h e f o u r  Algebra,  f o r Test  A.  Geometry, Measurement,  R a t i o and P r o b a b i l i t y & S t a t i s t i c s  (Appendix I I I ) .  t i m e was 35 m i n u t e s . attempt  with  the Kerala  the  primary  was made t o match t h e i t e m s on T e s t s y l l a b u s i n the subject  objective  A or Test  B  (see Appendix  I I ) , as  was n o t a l e a r n i n g a s s e s s m e n t  of K e r a l a  47  s c h o o l s , b u t an i n v e s t i g a t a t i o n o f s e x - r e l a t e d d i f f e r e n c e s boys  and  questions, The the  girls familiar  tests  Textbook  They  from  were  or  Kerala  were  faced  with  when  mathematical  otherwise.  were t r a n s l a t e d i n t o M a l a y a l a m w i t h  the  Department  of Education.  then  of  translated  the State back  v e r s i o n s of the t e s t s a r e given  Institute  into  English.  help  The  of  English  i n Appendix I I I .  Procedure Schools and to  a half  i n Kerala  reopened a f t e r  months on J u n e  a l l i n the t h i r d  16, 1983.  schools  took  classes enter  charge  1  of  one  taking  the t e s t s .  the classroom  teachers.  were  before  of  administered  and' t h e  e a c h . E a c h of t h e  by t h e member c o n c e r n e d and and t h e t e a c h e r s  I t was d e c i d e d or during were  Education  district  t h e head o f t h e s c h o o l  r e m a i n e d n o r m a l . The t e s t s class  Institute  i n t h e sample was v i s i t e d  meeting h e l d with  The t e s t s  o f two  week o f c l a s s e s , J u l y 4-8.  Two members o f t h e S t a t e investigator  1  t h e summer v a c a t i o n  that  testing,  given,  The i n v e s t i g a t o r s c o r e d  and  no member  so t h a t  a  of the should  conditions  collected  by  the  a l l the t e s t s .  Schools o r d i n a r i l y r e o p e n a f t e r t h e summer b r e a k on June 1. The d e l a y e d monsoon and t h e a t t e n d a n t d r o u g h t c a u s e d t h e d a t e t o be postponed. As i t happened, t h e S.W.Monsoon which normally r e a c h e s t h e K e r a l a c o a s t a r o u n d June 1, d i d f i n a l l y a r r i v e — on June 16.  48  Poor p r i n t i n g and  unclear.  and  35 o f T e s t  the  samples,  to  i n c r e a s e almost  in  scores  chapter  1  had c a u s e d  As  1  a  some o f t h e d i a g r a m s t o be smudged  result,  B were o m i t t e d .  with  uniformly The  29  The mean  the omissions,  unaffected.  are with  item  A, and i t e m s  percentage  scores  by sex and l o c a t i o n ,  by a b o u t data  of T e s t  for found  1% l e a v i n g t h e d i f f e r e n c e  presented  t h e above m e n t i o n e d  were  13  items  in  the  following  deleted.  Due t o a combination of s t r i k e s i n v a r i o u s s e c t i o n s of i n d u s t r y and a s t a t e w i d e c u t on industrial u s e of power during the drought, the three major p r i n t i n g p r e s s e s i n t h e c a p i t a l were closed indefinitely. As a result a lesser-known and less e f f i c i e n t p r i v a t e p r e s s had t o be p a t r o n i z e d .  49  Chapter  4  RESULTS  The  scores  on  T e s t A and T e s t  B were r e c o r d e d  by sex and  location,  and t h e p e r c e n t a g e o f s u b j e c t s who s c o r e d c o r r e c t l y  each  (p-values)  item  values  on i t e m s o b t a i n e d  scores and  were c a l c u l a t e d  f o r e a c h g r o u p . From t h e p-  f o r each l o c a t i o n ,  i n e a c h o f t h e domains o f t e s t i n g  compared.  The  results  on  obtained  the percentage  were c a l c u l a t e d  are  presented  mean by sex  in  this  chapter.  Description The samples  distribution at the  presented  two  i n Table  o f s u b j e c t s by sex i n t h e u r b a n and r u r a l  grade  levels,  and  rural  Tables each Tables  Grade  Grade  i n t h e v a r i o u s domains o f t e s t i n g  samples  at  the  i n t h e two t e s t s  6 & 7.  and  8,  are  o f Mean S c o r e s  two  grade  levels  2-5. The p e r c e n t a g e o f s u b j e c t s who item  4  1.  Comparison Mean s c o r e s  of Sample  (p-values)  are presented i n  scored  are given  f o r the urban  correctly  on  i n Appendix  IV,  50  Urban  Sample  Grade 4 At  t h e Grade  domain in  of  testing  Measurement,  and  4 level, (Table  followed  Operations,  and  outperformed g i r l s  boys  outperformed  2 ) . The l a r g e s t  by 8% i n A l g e b r a  i n Geometry.  girls  difference  in  o f 15% was  and 5% e a c h i n  In o v e r a l l  every  Number  mean s c o r e s ,  boys  by 7%.  Grade 8 At  t h e Grade  domains: (Table  boys: and  level,  in Probability  3).  Geometry.  8  performance  In the  remaining  four  domains,  mean  in  two  scores,  were on a p a r i n  girls  4% i n Measurement,  In o v e r a l l  girls  by 4%, and i n R a t i o by 1%  o f b o y s and g i r l s  11% i n F r a c t i o n s ,  2% i n A l g e b r a .  outperformed  and S t a t i s t i c s  The  by  boys  outperformed  4% i n A r i t h m e t i c  girls  outperformed  b o y s by 3%.  Rural  Sample  Grade 4 At  t h e Grade  Measurement outperformed Operations, scores g i r l s  (Table boys.  4 level, 4 ) . In The  boys a n d g i r l s the  remaining  difference  and i n Geometry,  was  p e r f o r m e d on a p a r i n three  girls  3% e a c h i n Number and  and 2% i n A l g e b r a .  o u t p e r f o r m e d boys by 2%.  domains  In o v e r a l l  mean  51  Grade 8 At the Grade 8 l e v e l , both boys and g i r l s performed e q u a l l y poorly  (28%)  in  Arithmetic,  and  in  Ratio  (Table 5). In the  remaining f i v e domains boys were ahead of the g i r l s : by Algebra, and  15% i n F r a c t i o n s , 10% i n Measurement,  Statistics,  16%  in  6% i n P r o b a b i l i t y  and 2% i n Geometry. In o v e r a l l mean scores, boys  outperformed g i r l s by 8%.  52  Table 1 Distribution  Grade L e v e l  of S u b j e c t s  i n Sample  Urban  Rural  Total  Boys  Girls  Boys  Girls  4  149  161  151  135  596  Grade 8  205  191  179  206  781  Total  354  352  330  341  1377  Grade  Table G r a d e 4 L e v e l : Urban S c o r e s  Domain  Boys  2 in Percentages  Girls  by  Difference Col.2  No.  & Op.  Algebra Geometry  (17)  (4)  Numbers the  59  - Col.3  5  37  29  8  49  44  5  54  39  15  56  49  7  in parentheses  i n column  (7)  Measurement  Weighted  64  1  Domain  (7)  Mean  number o f  items  i n each  1 indicate  domain.  54  Table 3 Grade 8 L e v e l : Urban  Domain  Scores  Boys  i n Percentages  Girls  by Domain  Difference Col.2  Algebra ( 9 )  - Col.3  55  57  -2  Geometry (10)  44  44  0  Fractions  44  55  -1 1  49  . 53  -4  46  50  -4  50  46  4  46  45  1  48  51  -3  Numbers i n p a r e n t h e s e s  i n column  1  (5)  Measurement Arithmetic  (4) (3)  Probability & Statistics Ratio  (2)  Weighted  the  (3)  Mean  number o f i t e m s  i n each  1 indicate  domain.  55  Table 4 Grade 4 L e v e l : R u r a l S c o r e s  Domain  Boys  i n Percentages  Girls  by Domain  Di f ference Col.2  No. & Op. ( 1 7 ) Algebra  60  63  -3  43  45  -2  45  48  -3  53  53  0  54  56  -2  i n parentheses  i n column  1  (4)  Geometry (7) Measurement  Weighted  1  Numbers  - Col.3  (7)  Mean  t h e number o f i t e m s  i n each  1 indicate  domain.  56  Table 5 Grade 8 L e v e l :  Rural Scores  Domain  Boys  i n Percentages  Girls  by Domain  Di f f e r e n c e Col.2 - Col.3  Algebra ( 9 )  46  30  16  Geometry (10)  34  32  2  Fractions  41  26  1 5  41  31  10  28  28  0  36  30  6  28  28  0  38  30  8  i n parentheses  i n column  (5)  Measurement Arithmetic Probability Statistics Ratio  Numbers the  (4) (3) & (3)  (2)  Weighted  1  1  Mean  number o f i t e m s  i n each  1 indicate  domain.  57  Chapter 5  SUMMARY o f RESULTS and IMPLICATIONS  A  summary  of the r e s u l t s of the s t u d y ,  " n a t u r e " and " n u t u r e " p o s i t i o n s mathematics drawn this  achievement  from a p o s t  on  sex-related  scores,  hoc a n a l y s i s  i t s bearing  and  differences  an a l t e r n a t i v e  of the f i n d i n g s  on t h e in  inference  are presented  in  chapter.  Findings The study  findings  i n response to the s t a t e d  objectives  were: (1)  In  the  differences levels  At  was  (2)  the  differences levels  studied.  difference  was  At  of the grade 4  Grade  level  the  o f t h e b o y s by 7 % ;  the d i f f e r e n c e  was  in  by 3 % .  rural  existed  sex-related  each  i n favour  of the g i r l s  In  at the  t h e Grade 8 l e v e l  favour  sample,  existed  studied.  difference at  urban  at  sample,  sex-related  each  the  the  i n favour  of  grade  Grade 4 l e v e l the  of the g i r l s  by 2%;  of  this  58  at  the  favour  Bearing  of  At  of  the  Findings  the  appreciable  Grade 8 l e v e l  Grade  on  the  boys by  the  difference  (9 y e a r - o l d s ) ,  advantage over  girls  in  the  urban  d i s p l a y a marginal advantage  i n the  former  is  a  superiority setting  At  the  appreciable display the  Grade 8 l e v e l  that  As the  basis  in  not  girls  in-  girls  under  some  counteract  the  of  male  i n the  rural  advantages,  the  r e s u l t s of  i n the  rural  some  recorded  evidence  scores  beyond b e i n g  rural  boys areas  from  the  their  no  is  holds,  i n the  r e m e d i e d by  due  can  be  to  age  factors that  considered  must  i n urban to  rural  inferiority.  arrived  g r o u p of  girls  genetic  relative  differences  an  s e t t i n g . If  then g i r l s  genetic  samples  sex-related  urban  socio-psychological  that  t o have  s e t t i n g , and  i n the  advantages,  more t h a n c o u n t e r a c t study  boys a p p e a r  mathematical a b i l i t y ,  under  "nature" p o s i t i o n for achievement  then  year-olds),  unequivocal conclusion  of  that  advantage over  male  function  this  only  (13  advantage over  superiority  function  while  s e t t i n g . If theory  an  inferiority.  superiority  a r e a s must  to  t o have  setting  rural  genetic  ability,  i n urban a r e a s ,  a marginal  male  girls,  assumed  to g i r l s  genetic  support  mathematical  must be  relative their  in  to  Positions  boys a p p e a r  girls  considered  in  8%.  "Nature-Nurture"  4 level  was  in 9-13  variables, at  on  is:  the  If  the  mathematics years,  constitute  i t is the  59  "nurture"  position.  Alternative An itself  Inference  alternative  study. for  boys  Tables  2 & 4).  and  the  level  (1)  is  2%,  while  that  the f i n d i n g  that  by  suggests sex  are  mean s c o r e s  girls  for  is  7%  i s 21% ( s e e T a b l e s achieve  a t each grade  girls  girls  difference in (see  the urban-rural d i f f e r e n c e  for girls  that  u r b a n b o y s and r u r a l  apparently  findings  the urban-rural  At t h e Grade 8 l e v e l ,  lowest  the  s u c h an a n a l y s i s was n o t a s t a t e d o b j e c t i v e of  boys i s 10%, w h i l e  Together with  of  d i f f e r e n c e s i n mean s c o r e s  At t h e Grade 4 l e v e l ,  scores  for  Findings  interpretation  when u r b a n - r u r a l  examined a l t h o u g h the  from  share  both  level  3 & 5).  the  highest  ( a t t h e Grade 4  the highest  s t a n d i n g ) , an  l e g i t i m a t e i n f e r e n c e c o u l d be:  that g i r l s  a r e not i n f e r i o r  t o boys  i n mathematical  ability,  to inhibit,  depress,  but (2)  that  s u c h exogenous f a c t o r s a s t e n d  mathematics achievement differences,  Limitations This sex-related area  where  s c o r e s , as i s evident  have a g r e a t e r  effect  on g i r l s  or  i n the urban-rural  than  boys.  o f t h e Study study  was d e s i g n e d  largely  a s an e x p l o r a t o r y  d i f f e r e n c e s i n mathematics achievement no s u c h s t u d y  study i n  scores  in  an  had been u n d e r t a k e n . The e x i s t e n c e o f  60  sex-related  d i f f e r e n c e s i n favour  favour  girls  level, on be  of  differing  only  another,  considered,  and may  other  pattern scores the  parts of  scores  for  exogeneous  t o shed  data  v a r i a b l e s need t o  light  on t h e i s s u e .  Research  o f I n d i a may  sex-related  i n other  serve  districts  i n mathematics  it  achievement hand,  may . i n d i c a t e  d i f f e r e n c e s i n mathematics  a r e t o be f o u n d , n o t i n g e n e t i c  and  consistent  l o c a t i o n s . I f , on t h e o t h e r  study a r e repeated,  sex-related  of K e r a l a ,  t o e s t a b l i s h a more  differences  between u r b a n a n d r u r a l  reasons  in  o f t h e same age and g r a d e  and i n s t r u c t i o n a l  of the study  r e s u l t s of t h i s  i n one sample, and  i n d i c a t e that  be e x p e c t e d  f o r Further  Replication  both  by l o c a l e ,  socio-economic, c u l t u r a l  Suggestions  in  in  o f boys  differences  that  achievement in  ability,  but i n : (1)  Differences  teacher  in  educational  qualifications,  children  or  medium  v a r i a b l e s such as c l a s s - s i z e ,  educational  o b j e c t i v e s , study h a b i t s  of i n s t r u c t i o n , and t h e i r  of  i n t e r a c t i o n with  sex. (2) D i f f e r e n c e s rural  areas  mobility relation  such  as  in girls, to g i r l s  (3) D i f f e r e n c e s in  in socio-psychological  relation  motivation,  eroding  i n urban  f a c t o r s between u r b a n and  desire  of t r a d i t i o n a l  for  upward  social  values/inhibitions in  areas.  i n socio-economic  t o urban a n d r u r a l  status  and  parental  a r e a s and t h e i r  literacy  i n t e r a c t i o n with  61  sex. S t u d i e s i n t h e s e a r e a s i n u r b a n and explain  some  of  these  mathematics achievement  issues scores.  on  rural  Kerala  sex-related  may  further  differences in  62  REFERENCES A i k e n , L . R. A b i l i t y and C r e a t i v i t y i n Mathematics. E d u c a t i o n a l R e s e a r c h , 1973, 43, pp. 405-432. Aiken, 865  L.  R. Q u e s t i o n s  of A b i l i t y .  Science,  Review o f  1982, 216, pp 863-  A r m s t r o n g , J . M. A c h i e v e m e n t and P a r t i c i p a t i o n o f Women i n Mathematics: Results o f Two N a t i o n a l Surveys. Journal f o r R e a s e a r c h i n M a t h e m a t i c s E d u c a t i o n , 1981, 12, 5, p p . 356-372. B a k e r , D. P. P e r s o n a l c o m m u n i c a t i o n S t a n l e y ] , September, 1981. Benbow, C. P. And S t a n l e y , A b i l i t y : Fact or A r t i f a c t ? Benbow, C. P. Factor? Science,  [ t o C. P.  Benbow  &  J . C.  J . C. Sex D i f f e r e n c e s i n M a t h e m a t i c a l S c i e n c e , 1980, 210, pp 1262-1264.  & S t a n l e y , J . C. M a t h e m a t i c a l A b i l i t y : 1981, 212, pp 118-121.  I s Sex a  Benbow, C. P. & S t a n l e y , J . C. C o n s e q u e n c e s i n H i g h S c h o o l and College o f Sex D i f f e r e n c e s i n M a t h e m a t i c a l R e a s o n i n g A b i l i t y : A L o n g i t u d i n a l P e r s p e c t i v e . American E d u c a t i o n a l Research J o u r n a l , W i n t e r 1982. V o l . 19, No.4, pp 598-622. B h a r g a v a , M. A c a d e m i c P e r f o r m a n c e a s a F u n c t i o n of Prolonged D e p r i v a t i o n . I n d i a n E d u c a t i o n a l Review, J u l y 1982. Pp.128-134. Blum, L . & G i v a n t , S. I n c r e a s i n g t h e P a r t i c i p a t i o n o f C o l l e g e Women i n M a t h e m a t i c s - R e l a t e d F i e l d s . I n S. M. Humphreys (Ed.), Women and M i n o r i t i e s i n S c i e n c e . Washington, D. C : W e s t v i e w , 1982. Broverman, I . K., V o g e l , S. R., B r o v e r m a n , D. M., Clarkson, F. E. & Rosenkrantz, P. S. S e x - r o l e Stereotypes: A Current A p p r a i s a l . J o u r n a l o f S o c i a l I s s u e s , 1972, 2, 59-78. B r u s h , L . P. E n c o u r a g i n g G i r l s i n M a t h e m a t i c s : The P r o b l e m and t h e S o l u t i o n . C a m b r i d g e , Mass.: A b t Books, 1980. Buffery, A. W. H. & G r a y , J . A. Sex D i f f e r e n c e s i n the D e v e l o p m e n t o f S p a t i a l and L i n g u i s t i c S k i l l s . I n C. O u n s t e d & D. C. Taylor (Eds.), Gender D i f f e r e n c e s : T h e i r O n t o g e n y and S i g n i f i c a n c e • B a l t i m o r e : W i l l i a m s a n d W i l k i n s , 1972. B y r n e , E . Women a n d E d u c a t i o n .  L o n d o n : T a v i s t o c k , 1978.  C a r e y , G. L . Sex D i f f e r e n c e s i n P r o b l e m - S o l v i n g  Performance as a  63  Function of A t t i t u d e D i f f e r e n c e . P s y c h o l o g y , 1958, 56, 256-260.  Journal  of  Abnormal and  Social  C a r e y , N. F a c t o r s in the Mental Process of Schoolchildren: I.Visual and Auditory Imagery. B r i t i s h J o u r n a l of P s y c h o l o g y , 1915, 7, pp.453-490. Casserly, P. L. An A s s e s s m e n t of F a c t o r s A f f e c t i n g Female P a r t i c i p a t i o n i n A d v a n c e d P l a c e m e n t Programs i n M a t h e m a t i c s , P h y s i c s and C h e m i s t r y . W a s h i n g t o n , D. C : W e s t v i e w , 1982. Census Commissioner of I n d i a , O f f i c e of the R e g i s t r a r General. C e n s u s of I n d i a , 1981. New D e l h i : Government of India Press, 1981 . Chattopadhyay, K. I n d i a n Women's B a t t l e Abhinav P u b l i c a t i o n s , 1983. Chauhan, S. Habits of Profession.  f o r Freedom. New  Delhi:  S., & S i n g h , H. An Investigation into the Study C h i l d r e n , 10-12 years, with Regard to T h e i r P a r e n t a l I n d i a n E d u c a t i o n a l Review, 1982, 17, 2, pp. 118-122.  C h o r o v e r , S. L. Press: 1979.  From G e n e s i s t o G e n o c i d e .  Cambridge,  MA:  MIT  Clements, K. V i s u a l Imagery and S c h o o l M a t h e m a t i c s - I . F o r L e a r n i n g of M a t h e m a t i c s , Nov. 1981, 2, 1, pp.2-9.  the  C l e m e n t s , K. V i s u a l Imagery and S c h o o l M a t h e m a t i c s - I I . F o r L e a r n i n g of M a t h e m a t i c s , Mar. 1982, 2, 3, pp. 33-39.  the  Comber, L. Countries.  C, & Keeves, J. Stockholm: Almguist  Corah, Journal  L. D i f f e r e n t i a t i o n in Children P e r s o n a l i t y , 1965, 33, 300-308.  N. of  P. Science & Wiksell,  Cornelius, M. L., & Cockburn, Performance. Educational Research,  D. 1978,  Education 1973. and  in Nineteen  Their  Influences 21, 1, pp.  Parents.  on Pupil 48-53.  Council of E u r o p e . Sex S t e r e o t y p i n g i n S c h o o l s , A R e p o r t E d u c a t i o n a l R e s e a r c h Workshop h e l d i n H o n e f o s s , 5-8 May, L i s s e : Swets & Z e i t l i n g e r , 1982.  of t h e 1981.  C r a n d a l l , V. J . , K a t k o v s k y , W. & P r e s t o n , A. Motivational and Ability Determinants of Young Children's Intellectual A c h i e v e m e n t B e h a v i o u r s . C h i l d D e v e l o p m e n t , 1962, 33, pp. 643661 . Crosswhite,  F.  J.  Correlates  of  Attitudes  Toward  Mathematics,  64  NLSMA R e p o r t No.20. A b s t r a c t e d by L . R. A i k e n , M a t h e m a t i c s E d u c a t i o n , 1975, 8, 3, p p . 38-40. D a v i s , P. J . , & H e r s h , R. B i r k h a u s e r , 1981.  The M a t h e m a t i c a l  Investigations in  Experience.  Boston:  DeBoth, C. J . , & D o m i n o w s k i , R. L . I n d i v i d u a l D i f f e r e n c e s i n Learning: Visual versus Auditory Presentation. J o u r n a l of E d u c a t i o n a l P s y c h o l o g y , 1978, 70, p p . 498-503. Dees, R. L . Sex D i f f e r e n c e s i n Geometry A c h i e v e m e n t . Paper presented a t the annual meeting of the American Educational R e s e a r c h A s s o c i a t i o n h e l d a t New York on M a r c h 23, 1982. Dougherty, K., H e r b e r t , M., E d e n h a r t - P e p e , M., & S m a l l . A. Sexrelated Differences i n Mathematics, Grades 2-5. U n p u b l i s h e d m a n u s c r i p t , 1980. Driver, Girls). Ellis,  G. How West I n d i a n s do B e t t e r a t S c h o o l ( E s p e c i a l l y t h e New S o c i e t y , 1980, 51, 902, p p . 111-114. H. Man and Woman  (4th ed.).  New Y o r k : S c r i b n e r , 1908.  E n t w i s l e , D. R., & Hayduk, L . A. S c h o o l i n g o f Young C h i l d r e n . B a l t i m o r e , Md.: J o h n s H o p k i n s U n i v e r s i t y P r e s s , i n p r e s s . Ernest, J . M a t h e m a t i c s a n d Sex. 1976, 83, p p . 595-614.  American Mathematical  Monthly,  E r n e s t , J . Sex, Sexism and A n x i e t y i n Mathematics i n J . E. J a c o b s ( E d . ) , P e r s p e c t i v e s on Women a n d M a t h e m a t i c s . ERIC/SMEAC, Columbus, O h i o . 1978. Fennema, E. Mathematics Learning and t h e Sexes: A Review. J o u r n a l f o r R e s e a r c h i n M a t h e m a i c s E d u c a t i o n , 1974, 5, p p . 126139. Fennema, E. Influences of S e l e c t e d C o g n i t i v e , A f f e c t i v e , and E d u c a t i o n a l V a r i a b l e s on S e x - R e l a t e d D i f f e r e n c e s i n M a t h e m a t i c s Learning and Studying, i n Women and M a t h e m a t i c s : R e s e a r c h P e r s p e c t i v e s f o r Change, The N a t i o n a l Institute of Education, W a s h i n g t o n , D. C. 1977. Fennema, E . & Sherman, J . A. S e x - r e l a t e d Differences in Mathematics Achievement, Spatial Visualization and A f f e c t i v e F a c t o r s . A m e r i c a n E d u c a t i o n a l R e s e a r c h J o u r n a l , 1977, 47, 1. Fennema, E . , W o l l e a t P. L . , P e d r o , J . D., B e c k e r , A. & DeVancy. I n c r e a s i n g Women's P a r t i c i p a t i o n i n M a t h e m a t i c s : An I n t e r v e n t i o n Study. J o u r n a l f o r Research i n Mathemaics E d u c a t i o n , 1981, 12,  65  1,  pp.  3-14.  Fink, M. B. Self Concept as i t Relates to Underachievement. C a l i f o r n i a J o u r n a l of E d u c a t i o n a l 1969, 13, pp.57-61.  Academic Research,  Foshay, A. W. ( E d . ) . E d u c a t i o n a l A c h i e v e m e n t of 13 y e a r o l d s i n T w e l v e C p u n t r i e s . Hamburg: UNESCO I n s t i t u t e f o r E d u c a t i o n , 1962. Fox, L. H. G i f t e d G i r l s : S c i e n t i s t s and Mathematicians of the Future. Paper presented at the 1976 annual m e e t i n g of the N a t i o n a l A s s o c i a t i o n f o r G i f t e d C h i l d r e n , Kansas C i t y , M i s s o u r i , O c t o b e r , 1976a. Fox, L. H. The V a l u e s of G i f t e d Y o u t h . In D. P. K e e t i n g . (Ed.), I n t e l l e c t u a l T a l e n t : R e s e a r c h and D e v e l o p m e n t . Baltimore, M a r y l a n d : The J o h n s H o p k i n s U n i v e r s i t y P r e s s , 1976b. Fox, L. H. The E f f e c t s of Sex R o l e S o c i a l i z a t i o n on Mathematics Participation and Achievement, in Women and M a t h e m a t i c s : R e s e a r c h P e r s p e c t i v e s f o r Change, The National Institute of E d u c a t i o n , W a s h i n g t o n , D. C. 1977. Fruchter, B. Measurement B a c k g r o u n d . E d u c a t i o n a l and pp. 387-395.  of Spatial Abilities: History P s y c h o l o g i c a l Measurement, 1954,  G a r r o n , D. C. S e x - l i n k e d , R e c e s s i v e I n h e r i t a n c e of Numerical Abilities, and Turner's Syndrome. Review, 1970, 77, pp. 145-152.  and 14,  Spatial and Psychological  G a u r , R. S. Personality C h a r a c t e r i s t i c s of Urban and Rural Adolescent Students. I n d i a n E d u c a t i o n a l Review, J a n . 1980, 15, 1, pp. 1 1 1 -114. G o u l d , S. J . The Inc. 1981.  M i s m e a s u r e of Man.  New  Y o r k ; W.  W.  Norton  &  Co.  Government of British Columbia. F i n a n c i a l S t a t e m e n t of E d u c a t i o n . C a t . 8 1 , 208: S c h o o l b o a r d E x p e n d i t u r e f o r 1980-81. September, 1983. Government Government  of Press,  Government of Government P r e s s ,  Kerala. 1978. Kerala. 1979.  Urban Department Administrative  Government of • Kerala. T r i v a n d r u m : Government P r e s s ,  Education 1981.  Survey.  Report.  Calicut: Trivandrum:  Department G u i d e  Book.  66  G r a y , M. W., & S c h a f e r , A. T. Sex 1981, 211, J a n . 1 6 , 1981, p . 230.  and  Mathematics.  Hadamard, J . S. An E s s a y on t h e P s y c h o l o g y M a t h e m a t i c a l F i e l d . New Y o r k : D o v e r , 1954.  Science,  of Invention  H a r d i n g , J . Sex D i f f e r e n c e s i n E x a m i n a t i o n P e r f o r m a n c e Physics Education, 1977, 4, 5, pp. 280-288.  i n the  at  16+.  Harshman, R. A., & R e m i n g t o n , R. Sex, Language a n d t h e B r a i n : P a r t I . A Review o f t h e L i t e r a t u r e on A d u l t Sex D i f f e r e n c e s i n Laterization. UCLA W o r k i n g P a p e r s on P h o n e t i c s , 1976, 31, p p . 86-103. H a t e , C. A. C h a n g i n g S t a t u s o f Women i n P o s t - I n d e p e n d e n c e Bombay: A l l i e d P u b l i s h e r s , 1969.  India.  Horner, M. S. Sex D i f f e r e n c e s i n A c h i e v e m e n t M o t i v a t i o n a n d Performance i n Competetive and Noncompetetive S i t u a t i o n s . D o c t o r a l d i s s e r t a t i o n , U n i v e r s i t y o f M i c h i g a n , 1968. Humphreys, S. M. (Ed.). Women a n d M i n o r i t i e s i n S c i e n c e . W a s h i n g t o n , D. C : W e s t v i e w , 1982. Husen, T. (Ed.). Mathematics: A Comparison Y o r k : W i l e y , 1967.  I n t e r n a t i o n a l Study o f Achievement i n o f T w e l v e C o u n t r i e s . V o l s . I & I I . New  Inkeles, A. N a t i o n a l Differences i n S c h o l a s t i c Performance. C o m p a r a t i v e E d u c a t i o n Review, 1979, 23, 3,, p p . 386-407. Isaacs, I . Some Factors Related to the Performance in Mathematics of T h i r d Year Students i n Jamaican Post-Primary S c h o o l s . U n p u b l i s h e d M.A. T h e s i s , University o f West Indies, J a m a i c a , 1974. Iyer, L . A. K. S o c i a l H i s t o r y P u b l i c a t i o n s , 1970.  o f K e r a l a . M a d r a s : Book C e n t r e  J a h o d a , G. On The N a t u r e o f D i f f i c u l t i e s in Tasks: Ethnic and Sex Differrences. P s y c h o l o g y , 1979, 70, 3, 351-363.  Spatial-Perceptual B r i t i s h J o u r n a l of  J a y a r a m a n , R. C a s t e a n d C l a s s , D y n a m i c s o f I n e q u a l i t y i n I n d i a n Soc i e t y . H i n d u s t a n p u b l i s h i n g c o r p o r a t i o n ( I n d i a ) , D e l h i , 1981. Jenson, A. R. Individual Differences i n V i s u a l and A u d i t o r y Memory. J o u r n a l o f E d u c a t i o n a l P s y c h o l o g y , 1971, 62, pp. 123131.  67  Kagan, J . A q u i s i t i o n a n d S i g n i f i c a n c e o f Sex T y p i n g and Sex R o l e Identity. In M. L . Hoffman & L . Hoffman ( E d s . ) , Review o f C h i l d D e v e l o p m e n t R e s e a r c h . New Y o r k : R u s s e l Sage F o u n d a t i o n , 1964. K a p o o r , D. V. E d i t o r ' s Desk, N o t e s f r o m NCTM News B u l l e t i n , May, 1983. S a s k a t c h e w a n M a t h e m a t i c s T e a c h e r s ' S o c i e t y J o u r n a l . 1983, 20, 2, p . 4 . Kelly, A. Women i n Science: A B i b l i o g r a p h i c Review. Durham R e s e a r c h Review, 1976, 7, pp. 1092-1108. K e l l y , A. ( E d . ) . The M i s s i n g H a l f : G i r l s and S c i e n c e M a n c h e s t e r : M a n c h e s t e r U n i v e r s i t y P r e s s , 1981.  Education.  Krutetskii, V. A. The P s y c h o l o g y o f M a t h e m a t i c a l A b i l i t i e s i n School-children. J . Kilpatrick & I W i r s z u p (Eds.). Chicago: U n i v e r s i t y o f C h i c a g o P r e s s , 1976. Lancy, D. F. Cross-Cultural Studies M a t h e m a t i c s . New Y o r k : Academic P r e s s , 1983.  i n C o g n i t i o n and  L e a n , G. & C l e m e n t s , M. A. S p a t i a l A b i l i t y , V i s u a l Imagery and Mathematics Performance. E d u c a t i o n a l Studies i n Mathematics, 1981, 12, pp.267-299. LeBon, G. R e c h e r c h e s A n a t o m i q u e s e t M a t h e m a t i q u e s s u r l e s l o i s des V a r i a t i o n s du Volume du C e r v e a u e t s u r l e u r s R e l a t i o n s a v e c 1 ' I n t e l l i g e n c e . Revue d ' A n t h r o p o l o g i e . 1879, 2, pp.27-104. C i t e d i n S. J . G o u l d , The M i s m e a s u r e o f Man, New Y o r k : 1981. L e v i n e , D. U. & O r n s t e i n , A. C. Sex D i f f e r e n c e s i n A b i l i t y and Achievement. J o u r n a l o f R e s e a r c h a n d Development i n E d u c a t i o n , 1983, 16, 2, pp.65-73. L e v y , J . L a t e r a l S p e c i a l i z a t i o n o f t h e Human B r a i n : Behavioural Manifestations and P o s s i b l e Evolutionary Basis. In I n J . A. K i g e r ( E d . ) , The B i o l o g y o f B e h a v i o u r . C o r v a l l i s , O r e g o n : Oregon U n i v e r s i t y P r e s s , 1972. Levy, J . P s y c h o b i o l o g i c a l I m p l i c a t i o n s of B i l a t e r a l Assymetry. In S. Dimond & J . G. Beaumont ( E d s . ) , H e m i s p h e r e F u n c t i o n i n t h e Human B r a i n . London: P a u l E l e k , 1974. Lewandowski, S. M i g r a t i o n and E t h n i c i t y i n Urban I n d i a , K e r a l a M i g r a n t s i n t h e C i t y o f M a d r a s , 1870-1970. New Delhi: Manohar P u b l i c a t i o n s , 1980. L o u r b e t , J . L a Femme d e v a n t l a S c i e n c e . P a r i s , 1896. C i t e d J . Mozans, Women i n S c i e n c e . 1913. MIT P r e s s , 1974.  i n H.  68  Luchins, E . H. & Luchins, A. S. Female Mathematicians: A C o n t e m p o r a r y A p p r a i s a l . I n L . H. F o x , L . Brody a n d D i a n n e Tobin (Eds.), Women and t h e M a t h e m a t i c a l M y s t i q u e . Baltimore and L o n d o n : J o h n s H o p k i n s U n i v e r s i t y P r e s s , 1980. Maccoby, E . E . & J a c k l i n , C. N. Sex D i f f e r e n c e s i n I n t e l l e c t u a l F u n c t i o n i n g . Assessment i n a P l u r a l i s t i c S o c i e t y : P r o c e e d i n g s of t h e 1972 I n v i t a t i o n a l C o n f e r e n c e on T e s t i n g P r o b l e m s . P r i n c e t o n , New J e r s e y : E d u c a t i o n a l T e s t i n g S e r v i c e , 1973. Maccoby, E. E. & Jacklin, C. N. The P s y c h o l o g y D i f f e r e n c e s . S t a n f o r d U n i v e r s i t y P r e s s , 1974. Manorama Y e a r b o o k , 1983. P u b l i c a t i o n s , 1983.  Kottayam,  Kerala:  McGee, M. G. Human S p a t i a l A b i l i t i e s : P s y c h o m e t r i c E n v i r o n m e n t a l , G e n e t i c , Hormonal, and N e u r o l o g i c a l P s y c h o l o g i c a l B u l l e t i n , 1979, 86, p p . 889-918. McGlone, J . & K e r t e s z , A. Sex D i f f e r e n c e s i n C e r e b r a l of V i s u o s p a t i a l T a s k s . C o r t e x , 1973, 9, p p . 313-320.  o f Sex  Manorama S t u d i e s and Influences. Processing  McMahon, I . D. Sex D i f f e r e n c e s i n C a u s a l A t t r i b u t i o n s F o l l o w i n g Success and Failure. Paper presented at the Eastern P s y c h o l o g i c a l A s s o c i a t i o n a n n u a l C o n v e n t i o n , New Y o r k , 1971. Menchinskaya, N. A. I n t e l l e c t u a l A c t i v i t y i n S o l v i n g A r i t h m e t i c P r o b l e m s . P r o c e e d i n g s o f t h e Academy o f P e d a g o g i c a l S c i e n c e s of the RSFR, 1946, 3, p p . 99-134. ( Translated by D a v i d A. Henderson) Menchinskaya, N. A. F i f t y Years of Soviet Instructional Psychology. In J . K i l p a t r i c k and I . Wirzup (Eds.), Soviet s t u d i e s i n t h e Psychology of L e a r n i n g and T e a c h i n g Mathematics. V o l . 1 , C a l i f o r n i a , S t a n f o r d U n i v e r s i t y (SMSG), 1969. Mozans, H. J . Women i n S c i e n c e . M u l l i s , I . V. S. E d u c a t i o n a l NAEP, 1975.  1913.  MIT P r e s s  Achievement  e d i t i o n , 1974.  a n d Sex D i s c r i m i n a t i o n .  Mura, R. Women a n d M a t h e m a t i c s . Summary o f a s e s s i o n presented at the annual summer meeting of t h e Canadian Mathematical S o c i e t y , O t t a w a . June 1, 1982. Murphy, R. J . L . Sex D i f f e r e n c e s i n E x a m i n a t i o n P e r f o r m a n c e : Do These Reflect D i f f e r e n c e s i n A b i l i t y o r Sex R o l e Stereotyping? E d u c a t i o n a l Review, 1978, 30, 3, p p . 259-263.  69  M u r r a y , J . E. An Analysis of Geometric E d u c a t i o n a l P s y c h o l o g y , 1949, 40, 113-124. Narayanan, K. R. Global D e v e l o p m e n t . I n d i a n and F o r e i g n 26.  Ability.  Interdependence Review, 1982, 19,  Journal  and 16,  of  National pp.9-13,  National A s s e s s m e n t of E d u c a t i o n a l P r o g r e s s . The F i r s t N a t i o n a l A s s e s s m e n t of M a t h e m a t i c s : An O v e r v i e w ( R e p o r t ~ N o . 04-MA-40). D e n v e r : E d u c a t i o n Commission of the S t a t e s , 1975. National Assessment of Educational Progress. Handbook: 1977-78 M a t h e m a t i c s A s s e s s m e n t ( R e p o r t No. D e n v e r : E d u c a t i o n Commission of the S t a t e s , 1980.  Procedural 09-MA-40).  Newton, P. Who S a y s G i r l s C a n ' t Be E n g i n e e r s ? In A. K e l l y the M i s s i n g H a l f . Manchester U n i v e r s i t y P r e s s , 1981.  (Ed.),  Niles, F. S. Social Class and A c a d e m i c A c h i e v e m e n t : A T h i r d World R e i n t e r p r e t a t i o n . C o m a p a r a t i v e E d u c a t i o n Review, 25, 3, O c t . 1981a. Niles, F. S. N o n - i n t e l l e c t u a l F a c t o r s A s s o c i a t e d Achievement in Sri Lanka. J o u r n a l of S o c i a l L a n k a ) , J u l y , 1981b.  w i t h Academic Sciences ( S r i  O l s o n , A. T., Sawada, D. & S i g u r d s o n , S. E. E x e c u t i v e Summary o f a Report on A l b e r t a A s s e s s m e n t of S c h o o l M a t h e m a t i c s . A S t u d y conducted for the Minister's Advisory Committee on Student Achievement. A l b e r t a , 1979. Ormerod, M. B. Science. B r i t i s h pp. 335-338.  The Social Implications Factor in Attitude J o u r n a l of E d u c a t i o n a l P s y c h o l o g y , 1971, 41,  to 3,  Ormerod, M. B. Science. Science  Social and Subject Factors in Attitude Review, 1973, 54, J u n e , pp. 645-660.  to  Ormerod, M. B. S u b j e c t P r e f e r e n c e and C h o i c e i n C o - e d u c a t i o n a l and S i n g l e Sex S e c o n d a r y S c h o o l s . B r i t i s h J o u r n a l of E d u c a t i o n a l P s y c h o l o g y , 1975, 45, 3, pp. 257-267. Osen, L. Women i n M a t h e m a t i c s . C a m b r i d g e : MIT P a t t a n a y a k , D. P. M u l t i l i n g u a l i s m and D e l h i : Oxford U n i v e r s i t y Press, 1981.  Press,  Mother-Tongue  1974. Education.  Pike, L. And Evans, F. R. E f f e c t s of S p e c i a l I n s t r u c t i o n f o r T h r e e K i n d s of M a t h e m a t i c s A p t i t u d e I t e m s . Research Report I. C o l l e g e e n t r a n c e E x a m i n a t i o n B o a r d , New Y o r k : 1972.  70  Poincare, H. D o v e r , 1963.  M a t h e m a t i c s and S c i e n c e : L a s t  Prasad, S. Science and 1983, 20, 19, pp. 19-22.  Industry.  Indian  Essays.  New  and F o r e i g n  Preece, M. Mathematics: The Unpredictability M a t h e m a t i c s T e a c h i n g , 1979, 87, pp.27-29. R a d a t z , H. E r r o r A n a l y s i s i n M a t h e m a t i c s E d u c a t i o n . R e s e a r c h i n M a t h e m a i c s E d u c a t i o n , 1979, 10, 3.  of  York: Review, Girls.  Journal for  Roach, D. A. The E f f e c t s o f C o n c e p t u a l S t y l e P r e f e r e n c e , R e l a t e d Cognitive Variables and Sex on A c h i e v e m e n t i n Mathematics. B r i t i s h J o u r n a l of E d u c a t i o n a l P s y c h o l o g y , 1979, 49, p p . 79-82. R o b i n s o n , J . E . And G r a y , J . L . C o g n i t i v e S t y l e a s a V a r i a b l e i n School L e a r n i n g . . J o u r n a l of E d u c a t i o n a l P s y c h o l o g y , 1974, 66, pp. 793-799. Robitaille, D. . F . And S h e r r i l l , J . M. B r i t i s h Columbia M a t h e m a t i c s A s s e s s m e n t , 1977: Summary R e p o r t . A R e p o r t t o t h e M i n i s t r y of Education, Province of B r i t i s h Columbia. R o b i t a i l l e , D. F. B r i t i s h C o l u m b i a M a t h e m a t i c s A s s e s s m e n t , 1981: Summary R e p o r t . A R e p o r t t o t h e M i n i s t r y o f E d u c a t i o n , Province of B r i t i s h C o l u m b i a . Robitaille, D. F., O'Shea, T. J . , and D i r k s , M. K. The Second I n t e r n a t i o n a l M a t h e m a t i c s S t u d y : The T e a c h i n g and L e a r n i n g o f M a t h e m a t i c s i n B r i t i s h C o l u m b i a M a t h e m a t i c s 8 and A l g e b r a 12, 1982. A R e p o r t t o t h e M i n i s t r y o f E d u c a t i o n , P r o v i n c e o f B r i t i s h Columbia. Satterly, D. Perceptual Representation Characteristics of Primary School C h i l d r e n . E d u c a t i o n a l P s y c h o l o g y , 1968, 38, p p . 78-82.  and Conceptual B r i t i s h J o u r n a l of  Satterly, D. Cognitive Styles, Spatial Ability and School Achievement. Journal of E d u c a t i o n a l Psychology, 1976, 68, pp. 38-42. Sawada, D., O l s o n , A. T. & S i g u r d s o n , S. E . Sex D i f f e r e n c e s i n Mathematics Learning i n a Canadian S e t t i n g . Canadian J o u r n a l of E d u c a t i o n , 1981, 6, pp. 5-19. S c h i l d k a m p - K u n d i g a r , E . ( E d . ) , An I n t e r n a t i o n a l Review on Gender and M a t h e m a t i c s . Columbus, O h i o : ERIC C l e a r i n g h o u s e , 1982. S c h o n b e r g e r , A. K. The I n t e r r e l a t i o n s h i p o f Sex, V i s u a l  Spatial  71  Abilities and M a t h e m a t i c a l Problem Solving Seven. Dissertation Abstracts International, ( U n i v e r s i t y M i c r o f i l m s No. 76-17, 9 4 3 ) .  A b i l i t y i n Grade 1976, 37, 962B  Schonberger, A. K. A r e M a t h e m a t i c s P r o b l e m s a P r o b l e m f o r Women and G i r l s ? In J . E . J a c o b s (Ed.), P e r s p e c t i v e s on Women a n d M a t h e m a t i c s . ERIC/SMEAC 1978. Sells, L . W. L e v e r a g e f o r E q u a l O p p o r t u n i t y t h r o u g h M a s t e r y o f M a t h e m a t i c s . I n S. M. Humphreys (Ed.), Women and M i n o r i t i e s i n Sc i e n c e . W a s h i n g t o n , D. C : W e s t v i e w , 1982. Seppie, A. C. & K e e l i n g , B. The R e l a t i o n s h i p Between T y p e s o f Anxiety and Underachievement in Mathematics. Journal of E d u c a t i o n a l R e s e a r c h , 1978, 72, p . 1 8 Shah, B. V. The R o l e o f S e c o n d a r y T e a c h e r a s D e f i n e d by R o l e D e f i n e r s . I n S a l a m a t u l l a h and R u h e l a , S. P. ( E d s . ) , S o c i o l o q i c a l D i m e n s i o n s o f I n d i a n E d u c a t i o n . New D e l h i : R a a j P r a k a s h a n , 1971. Sharma, A. S t a b i l i z a t i o n o f A b i l i t i e s D u r i n g Adolescence I n d i a n E d u c a t i o n a l Review, 1973a, 8, 1, p p . 116-180.  -  Sharma, A. S t a b i l i z a t i o n o f A b i l i t i e s D u r i n g A d o l e s c e n c e I n d i a n E d u c a t i o n a l Review. 1973b, 8, 2, p p . 97-163.  - II.  Sharma, S. Women S t u d e n t s i n I n d i a - S t a t u s C o n c e p t P u b l i s h i n g Company, New D e l h i , 1979.  I.  and P e r s o n a l i t y .  Sharma, S. & M e i g h a n , R. S c h o o l i n g a n d Sex R o l e s : The Case o f t h e GCE '0' L e v e l Mathematics. B r i t i s h Journal of Sociology of E d u c a t i o n , 1980, 1, 2, p p . 192-205. Shelley, N. Gender and Mathematics in Australia. In E . S c h i l d k a m p - K u n d i g e r ( E d . ) , An I n t e r n a t i o n a l Review on Gender and M a t h e m a t i c s . Columbus, O h i o : ERIC C l e a r i n g h o u s e , 1982. S h u k l a , S. A c h i e v e m e n t of Indian Children i n Mother Tongue (Hindi) a n d S c i e n c e . C o m p a r a t i v e E d u c a t i o n R e v i e w , 1974, J u n e , pp. 234-248. S i n h a , S. R. E f f e c t of School System on t h e Competence o f S e c o n d a r y S c h o o l S t u d e n t s . I n d i a n E d u c a t i o n a l Review, J a n . 1980, 15, 1, pp. 62-77. Smith,  I . M. S p a t i a l  Ability.  San D i e g o : Knapp, 1964.  Smithers, A. & C o l l i n g s , J . G i r l s S t u d y i n g S c i e n c e i n t h e S i x t h Form. In A. K e l l y ( E d . ) , The M i s s i n g H a l f . M a n c h e s t e r U n i v e r s i t y P r e s s , 1981.  72  S p e n d e r , D. The R o l e of T e a c h e r s : What C h o i c e s Do They Have? Secretariat of t h e C o u n c i l of E u r o p e ( E d . ) , Sex S t e r e o t y p i n g S c h o o l s . L i s s e : Swets & Z e i t l i n g e r , 1982. S t a f f o r d , R. E. Sex Differences in Spatial E v i d e n c e of S e x - l i n k e d I n h e r i t a n c e . P e r c e p t u a l 1961, 13, p.428.  In in  Visualization as and Motor S k i l l s ,  S t a f f o r d , R. E . An I n v e s t i g a t i o n of S i m i l a r i t i e s i n P a r e n t - C h i l d Test Scores for Evidence of Heredity Components. Doctoral D i s s e r t a t i o n , P r i n c e t o n U n i v e r s i t y , 1963. S t a f f o r d , R. E. Hereditary and Environmental Components of Quantitative Reasoning. Review of E d u c a t i o n a l R e s e a r c h , 1972, 42, pp. 183-201 . Statistics 208: S c h o o l 1983.  Canada. F i n a n c i a l S t a t i s t i c s of E d u c a t i o n . C a t . 8 1 , B o a r d E x p e n d i t u r e f o r 1980-81. Ottawa: September,  S u n d e r , V. Gender and M a t h e m a t i c s i n I n d i a . In E. SchildkampKundiger (Ed.), An I n t e r n a t i o n a l Review on Gender and M a t h e m a t i c s . Columbus, O h i o : ERIC C l e a r i n g h o u s e , 1982. Tanner, R. And Thought. B r i t i s h pp. 239-248.  Trown, A. Cultural J o u r n a l of E d u c a t i o n a l  Tittle, C. K., McCarthy, K. Educational Testing. Princeton, Service, 1974. Tobias,  S.  Tobias, 14-17.  Math A n x i e t y .  S.  Ms.  Sexist Equations.  Twyman, A. Imagery and Mathematics Education, London, 1972.  & New  Change and Psychology,  Mathemtical 1979, 49, 3,  Steckler, J. F. Women and Jersey: Educational Testing  September,  1976.  P s y c h o l o g y Today,  1982,  Mathematical A c t i v i t y . The London: Chelsea College,  Ummat, R. C. I n d i a and t h e D e v e l o p i n g Review, A p r i l , 1982. Pp. 12-15.  World.  16,  1,  pp.  P s y c h o l o g y of U n i v e r s i t y of  Indian  and  Foreign  Usiskin, Z. Sex Differences in Geometry A c h i e v e m e n t . Paper presented at the Annual Meeting of the American Educational R e s e a r c h A s s o c i a t i o n h e l d a t New Y o r k , M a r c h 1982. Vernon, Kingston,  P. E. S e l e c t i o n f o r Secondary Education J a m a i c a : Government P r i n t e r , 1961.  in Jamaica.  73  Very, P. S. Differential Factor Structure in Mathematical A b i l i t y . G e n e t i c P s y c h o l o g y Monographs, 1967, 75, pp.169-207. Vogt, C. L e c t u r e s on Man. R o b e r t s , 1864.  London:  Werdelin, I. Geometric A b i l i t y G i r l s . Lund, Sweden: U n i v e r s i t y  Longman,  G r e e n , Longman &  and t h e Space F a c t o r of Lund, 1971.  i n Boys and  74  APPENDIX I Map of  Kerala  75  76  APPENDIX I I Syllabus  i n Mathematics  for Kerala  Schools  77  Standard  IV  No. 1. D i a g n o s t i c  testing  2.  to those  Numbers up  and  remedial  having  nine  Of  periods.  teaching.  55  digits.  15  3. M u l t i p l i c a t i o n .  35  4.  Division.  35  5.  Problems  i n v o l v i n g the  four  fundamental o p e r a t i o n s .  20  6.  Number-line.  10  7.  Fractions.  25  8.  Decimal  45  9.  Measurement  Fractions.  10.  Pictorial  11.  Recognition  Diagrams.  s h a p e s and 12.  of Time.  Discovering  of  15 10  Geometrical  figures. Patterns.  10 5  Total...280  Standard  VIII  No. Of S e t s , Venn d i a g r a m s , Real  operations.  A p p r o x i m a t e Numbers, and  Always-true  20 10  Numbers.  precision  hours.  their  accuracy.  1 5 20  sentences.  sentences  i n one  variable.  22  Open s e n t e n c e s  i n two  vriables.  22  Open  Basics  concepts  Triangles Triangles  and  i n Geometry.  Perpendiculars.  (continued).  Discerning  Patterns.  26 1 5 1 5  10  T o t a l . . . 175  APPENDIX I I I I n s t r u m e n t s of  Testing  80 TEST A (Grade  4  level)  1. S u b t r a c t : 86-  64  n  22  68  n  54  n  118.  n  I  d o n ' t know  .. n  2. A d d : 678+ 9+ 34  I  3.  I f you connected  shape  would  these  901.  n  991  n  621  n  721  n  d o n ' t know  three dots  n  with  straight  you get?  •  •  Square  n  Rectangle  n  Triangle  n  Circle  n  know  n  • I  don't  lines  what  81 4. W h i c h  1/4  shows  shaded?  I don't  6.  If  children  one  child  needs  two  know  books,  n  how  .many b o o k s do  need? 3 .  n  three  82 6  n  8  n  9  n  I d o n ' t know  7.  n  10 t e n s "= One mi 1 1 i o n . . . n t h o u s a n d . . .n ten . .. n I don't  8. A b o x c o n t a i n s could closed  not decide  2 blue whether  pens,  more l i k e l y  4 r e d pens and 1 b l a c k  he w a n t e d  h i s eyes and p i c k e d  know..n  pen.  a r e d pen o r a b l u e  one f r o m  Vinod  pen.  the box. Which c o l o u r  i s he  to pick? blue  or black  .....n  red  n  blue  n  blac k I d o n ' t know  9. W h i c h u n i t  should  be u s e d  n n  t o measure t h e l e n g t h of a  millimetres  n  cent imetres  n  He  house?  83 metres kilometres I  10.  Jane  finished  don't  n '  n  know  n  h e r homework a t 7 1 4 5 . W h i c h  clock  shows  this  t ime?  I  11.  What  don't  i s the remainder  know....n  i n the f o l l o w i n g d i v  28  9  . .n  27  3  . .n  1  . .n  1 I  12. How  Eight many  cars  cars  problem?  28 . . n  9 3)  sion  are parked  a r e new?  don't  on a r o a d .  know  1/4  of the cars  a r e new.  1...n  2.  . .n  3 . ..n 4  I  d o n ' t know  13. C o u n t i n g b y  10s, t h e n e x t t h r e e  780,  n,  7 0 0 , n, n,  14. R o u n d  1368  to the nearest  '. . n  numbers a r e :  791,  I  . . .n  792,  793....n  720 , 730 , 740  n  800,  8 1 0 , 820  n  800,  801 , 8 0 2 . . . .n  don't  know........ n  hundred: 1300...n 1400...n 3 000...n 4000...n I d o n ' t know  15.  It  was  thermometre,  a  cold  i t showed:  rainy  day.  When  John  n  looked  8523 C.. . n 3 4" C . . . n 3*' C. . .n 1 6° C . . . n  I d o n ' t know  16. W h i c h  number s a y s f o u r  n  t h o u s a n d two h u n d r e d s i x t y  five?  42065...n 5624...n 4 0 2 6 5 . . .n 4265...n I d o n ' t know  17.  A hippopotamus  a buffalo to  weighs  the nearest  weighs  n  1153 k g . , a n e l e p h a n t  1196 k g , a n d  a g i r a f f e weighs  100 k g , w h i c h w e i g h s c l o s e s t  weighs  1183 kg.  t o 1100 k g ?  hippo...n elephant...n buf  falo...n  gi raf fe...n I  18.  In which f i g u r e  are a l l angles  d o n ' t know  t h e same s i z e ?  n  1127 k g , Rounding  86 12  I d o n ' t know  19.  Chandran  stamps  took  at 8 paise  25 p a i s e  twelve  rupees  to  much d i d he s p e n d o n Rs.  I  number  number o r n u m b e r s c a n go  stamps? 1 0 . 0 3 . . .n 0 . 55 . ..n  Rs.  1 .97 . . .n 1 3 . 9 7 . . .n  d o n ' t know  into  6  each and 5 stamps a t  Rs.  Rs.  20. Which  b u y s t a m p s . He b o u g h t  e a c h , 8 stamps a t 3 p a i s e  e a c h . How  n  n  the blank  t o - make  this  s e n t e n c e TRUE?  5 + (  ) <12 7 . . .n a n y number any  number  less  greater  than  7...n  than  7...n  no n u m b e r . . . . . n I  21.  Which  digits  i s the smallest  4, 3 , 9 ,  number  d o n ' t know  that  n  c a n be made u s i n g  1 ? 1934. . .n  a l l the  1 4 3 9 . . .n 1 3 4 9 . . .n 1943...n I  22.  Which  b o x i s -1/5 ( o n e - f i f t h )  d o n ' t know  n  shaded?  I d o n ' t know  23.  How  many  lines  of symmetry  does  this  n  shape  have?  1...n 2. ..n 3. ..n ,4 . . .n I  d o n ' t know  n  88 24.  156 r o u n d e d  to the nearest  10  i s : 1 6 0 . . .n 1 7 0 . . .n 1 5 0 . . .n 1 4 0 . . .n  I don't  25.  John  put a wire  garden  i s  fencing  d i d he  fence  10 m e t r e s  round  his  know  n  rectangular  long and 6 metres  w i d e . How  garden.  The  many m e t r e s o f  use? 16...n 3 2 . . . n36...n 60... n I  2 6 . How  many  centimetres  don't  are there  know  i n one  n  metre? 1... n 10 . . .n 1 0 0 . . .n 1 0 0 0 . . .n  I don't  27.  Figures  that are the  same  size  and  know....n  shape  are  congruent  figures.  Which  of the f o l l o w i n g  are  congruent?  A  C  LJ  A  a n d B...n  A  a n d D...n  C a n d D...n  B a n d C...n I  28.  About  how  long  i s this  don't  know...n  pencil?  1  centimetre....n  5  centimetres...n 1  metre...n  .10 m e t r e s . . . n I  29.  What  i s the area  of t h i s  shape  don't  in  know...n  square.centimetres  31.  A  bottle  of  milk  is likely  to  hold: 1 mi 1 1 i 1 i t r e . . . n  10  mi 1 1 i 1 i t r e s . . . n 1 l i t r e . . .n 100  l i t r e s . . .•  ' I don't  know . . . n  91 32.  One  cube  face  is  shaded  on t h i s  cube.  faces  does  the  i s true?  35 = 30 + 5  n  35 > 30 + 5  n  35 > 5 + 30  n  30 + 5 < 35  n  I  Santhosh  given The  many  have?  33. W h i c h  34.  How  below,  plane  correct  was  testing  guessed  stayed  don't  h i s model a s t o how  know....n  plane. long  u p f o r 17 m i n u t e s .  Who  Four  i t would guessed  of stay  his  i n thea i r .  closest  time? Suresh Girija  Prakash Ravi.  i  •j /  31!  - j  i Time ( i n minutes)  friends  i  to  the  92 Suresh...n Prakash...n Gi r i j a . . . n Ravi . .. n I  35. 6  M a d h u h a s 51 bottles.  there  soda  I f Madhu  be l e f t  bottles fills  don't  know . . . n  a n d 8 wooden b o x e s .  a l l the boxes,  how  Each  many  box  holds  bottles  will  over? 6 . .. n 8 . .. n 3. ..n 1 4 ... n  I  36.  Madhu d i s t r i b u t e d  collected collected  back  30  the rest.  51 of  How  don t 1  know...n '  soda-filled  bottles  the  bottles.  His  d i d Leela  collect?  many  empty bottles  to  the  18. . .n 14... n 2 1 ... n 44 ... n I  don't  know....n  shops.  sister  He  Leela  93 TEST (Grade  1.  Which  of  in  which  they  (a)  {0,  '(d)  {-1  the  1/2, ,  0,  following  occur  left  (b)  1/2};  8  level)  sequences  from  -1};  B  {0, (e)  to  of  numbers  right  - 1 ,  1/2  {-1/2,  on  };  -1 ,  the  is  in  the  number  (c)  {-1,  order  line?  -1/2,  0}  0}  Ans  2.  What  (a)  7;  (d)  17;  is  the  value  (b)  of  *s'?  13;  (e)  (c)  None  of  15  these. Ans  3.  Suma  3.1  kilometres  back  1.7  original many the  walked  from  away.  kilometres direction  kilometres railway  her  station?  to  her  walk  During to  until had  house  find she  Suma  it,  reached  walked  the  railway  she and the  lost  :  station her  then  watch,  continued  railway  altogether  which  when  went in  station. she  is  arrived  the How at  9^ (a)  1.4;  ( b ) 4.8;  ( d ) 8.2;  ( c ) 6.5  ( e ) None o f  these. Ans  4.  (-2) x  (a)  (-3)  -6;  ( d ) 5;  :  i s equal t o :  (b) - 5 ;  (c)  - 1 ;  (e) 6  Ans  5. I n w h i c h d i a g r a m first  figure  under  below  i s the second  a reflection in a  figure  the  line?  L  W  t h e image o f  CP)  (?) Ans :  6.  The  triangles  shown  a b o v e a r e c o n g r u e n t . The m e a s u r e s o f  some  95 sides  a n d a n g l e s a r e s h o w n . What  (a)  52;  ( b ) 55;  (d)  73;  (e) 75.  i s x?  ( c ) 65;  Ans  7. T h e  following  highway  in a  On has  Mon.  of Trees  the diagram been  indicate  shows  t h e number  80  below  drawn.  Tues.  Wed,  50  60  the graph  60  on  i  y/////A il  i  20  planted  along a  '///////,.  f\ W  p  A  Vn  C  r  A %&  D -  /ft  A  /////&  v  //////A ////////, Mon Tue  Wed  Thurs  Fri  F r i .  75  two d a y s '  completed,  Thursday?  9  '///////  90  was  100  U  Thurs.  f o r the f i r s t  I f the graph  the top of the graph  4 3  of t r e e s  week.  Day  No.  table  which  planting  point  would  96  (a) A; (b) B; (c) C; (d) D; (e) E, Ans  cm  90° k 4  cm  "I 9 0 °  0 C-Tn  .  —.-to.-  •  There i s a brass p l a t e of the shape and d i e n s i o n s shown f i g u r e above. What i s i t s area i n square  in the  centimetres?  (a) 16; (b) 24; (c) 32; (d) 64; (e) 9.6. Ans : C  9.  B -  AB, CD and EF are concurrent. The measures of c e r t a i n angles are shown. What i s the value of x? (a) 54; (b)  62; (c) 64; (d) 126; (e) 128; Ans :  10. S i m p l i f y :  5x + 3y + 2x - 4y  (a) 7x + 7y; (b) 8x - 2y; (c) 6xy;  97 (d)  7x - y;  ( e ) 7x + y . Ans :  11.  What  is  dimensions  the  volume  10 cm l o n g ,  of  a  10 cm w i d e ,  (a)  27 c c ; ( b ) 70 c c ; ( c ) 140 c c ;  (d)  2 8 0 c c ; ( e ) 700 c c .  r e c t a n g u l a r box w i t h a n d 7 cm  interior  high?  A n s .:  12.  I f P=LW a n d i f P=12 a n d L = 3 , t h e n  (a)  3/4;  ( b ) 3;  ( c ) 4;  W i s equal to  ( d ) 12; ( e ) 3 6 . Ans  13.  -  -™  -  :  •  i P  Q- R  M  N  U  0  V  X' ' w  "7  The  diagram  edges which  and  shows a c a r d b o a r d flattened  two c o r n e r s  will  cube  t h a t h a s been c u t a l o n g  o u t . I f i t i s f o l d e d up a g a i n touch  ( a ) Q a n d S;  ( b ) T a n d Y;  ( d ) T a n d V;  ( e ) U a n d Y.  at corner  P?  ( c ) W a n d Y;  Ans.  :  into  some  a cube,  98 14. Which of the f o l l o w i n g i s a p a i r of equivalent  fractions?  (A) 5/8, 2/3; (b) 5/6, 2/3; (c) 4/5, 14/15; (d) 3/5, 9/15; (e) 1/2, 14/24. Ans  15. Which of these i s a TRUE  statement  about  the information  shown on the graph?  22  STUDENTS IN GRADES  1,2,3 AND 1*  20 18  tn  16  -p c v  1U  3  12  -P  CO  o o S3  1 1 1  10  8  1  //  7/, //  6  It 2 0  "  1 1  P  1  p-  1 P 2  3  Grades Boys Girls  (a) Standard 2 i s the smallest  class.  (b) Standards 2 and 4 have the same number of students. (c)  Standard3 has twice as many boys as g i r l s .  (d) Standard 4 has more g i r l s  than boys.  99 (e)  Standard  Standard  1  has  as  many  boys  as  there  R={ S=Q  1,2,  3, 4, 5, 6, 7, 8,  3, 5, 7, 9, f]  9}  1 1 , 13 }  R  are  there  (a)  16; ( b ) 1 1 ; ( c ) 7;  17. 2/5 + 3/8  ( d ) 4;  elements  ( e ) 2. :  i s equal t o  5/13; ( b ) 5/40; ( c ) 6/40; ( d ) 16/15;  18. 0.40 x 6.38  (e) 31/40.  i s equal to  (a)  .2552;  (b) 2.452;  (d)  24.52;  (e) 25.52.  ( c ) 2.552;  Ans  On  many  i n s e t S?  Ans  1.9.  in  :  T h e r e a r e 9 e l e m e n t s i n s e t Q a n d 6 i n s e t R. How  (a)  girls  4. Ans  16. Q={  are  level  g r o u n d , a boy 5 u n i t s  long.  A t t h e same t i m e ,  casts  a shadow,  tall  a nearby telephone  the length  casts pole  o f w h i c h i n t h e same  :  a shadow 45  3  units  units.is  units high  100  (a) 24; (b) 27; (c) 30;  (d) 60; (e) 75. Ans  20. If 6x  3=15  then  6x  15 - 3  (i)  and  6x  12  (ii)  and  x  12/6  (iii)  x  2  (iv)  If there i s an error i n the above reasoning, i t f i r s t  (a) ( i ) ; (b) ( i i ) ; (c) ( i i i ) ;  occurs i n  (d) ( i v ) ; (e) None of these. Ans :  21. The value of 2  3  + 3' i s 2  (a) 30; (b) 36; (c) 64; (d) 72; (e) None of these. Ans  22 .  The t o t a l area of the two t r i a n g l e s  i s , in square centimetres  (a) 6 x 8; (b) (6 x 8)/2; (c) (10 x 6)/2; (d) (16 x 12)/2; (e) (20 x 12)/2.  101 Ans  23.  A  bottle  paise,  of soda,  but  returned. brings  there  is  much  will  How  back  i n c l u d i n g the p r i c e a  refund  Gopi  of the b o t t l e ,  of b p a i s e  have  t o pay  on  for  each x  ax + by p a i s e ;  (d)  (a+x) -  ( b ) ax - by p a i s e ;  number  (a)  3  (b+y) p a i s e ;  a  school  of boys  : 8;  ( e ) None  of  o f 800 p u p i l s ,  t o t h e number  (b) 5  : 8;  The a r i t h m e t i c  2.40;  he  (c) 3  300 a r e b o y s .  of g i r l s  : 11;  mean  (average)  The  ratio  (b) 2.55;  ( c ) 3.75;  : 3;  (e) 3  1.50,  : 5.  :  2.40,  ( d ) 7.65;  3.75,  ( e ) None Ans  26.  A q u a d r i l a t e r a l MUST be a p a r a l l e l o g r a m  (a)  One  pair  of adjacent  sides  equal.  of the  is  (d) 5  of  :  is  to  (a)  i f  these.  Ans  25.  bottles  bottle  ( c ) (a - b ) x p a i s e ;  Ans  In  empty  a  y_ e m p t y b o t t l e s .  (a)  24.  costs  of  these.  :  i f i t has  equal  102  (b) One p a i r of p a r a l l e l s i d e s . (c) A diagonal as a x i s of symmetry. (d) Two adjacent-angles  equal.  (e) Two p a i r s of . p a r a l l e l s i d e s . Ans :  27.  One  of the  following  points  can be joined to the point  (-3, 4) by a l i n e segment which cuts NEITHER the x,  NOR  the y  a x i s . Which one?  (a) (-2, 3); (b) (2,-3); (c) (2, 3); (d) (-2,-3); (e) (4,-3). Ans :  28.  Which  of the f o l l o w i n g i s the most l i k e l y to be nearest to  the weight of a normal man?  (a) 8.5 kg; (b) 85 kg; (c) 185 kg; (d) 850 kg; (e) 1850kg. Ans :  29. Matchsticks are arranged  If the pattern continued, making the 10th f i g u r e ?  as f o l l o w s :  how  many  matchsticks  are  used  in  103  (a)  30;  (b)  33;  ( c ) 36;  (d)  (e) 42.  39;  Ans  30. 0  The  l e n g t h of the c i r c u m f r e n c e  of the c i r c l e  i s 2 4 , a n d t h e l e n g t h o f t h e a r c RS  angle  (a)  ROS  24;  31.  30  (a)  40;  to the nearest  (b) 30;  ( c ) 45;  i s 75% o f what  (b) 90;  What  i s the square  (a9  6.25;  33.  I n t h e number  (a)  6x1/100;  Ans  :  (b) 30;  with centre at  i s 4. What  i s the  degree?  (d) 60;  (e) 90.  Ans  :  Ans  :  number?  ( c ) 105;  32.  :  (d) 225;  root  ( c ) 87;  of  (e) 2250.  12 x  (d) 625;  847.36, t h e d i g i t  75?  (e) 900. 6  Ans : represents  (b) 6 x 1 / 1 0 ; ' ( c ) 6x1; (d) 6x10;  (e) 6x100  central  104 34.  I f t h e segment  would  divide  Which  figure?  (a)  one  PQ  were  drawn  of the  f o r each  figures  into  P  figure  two  shown  congruent  below, i t triangles.  7  (d)  Ans  35. so  On  the scale  the reading  10 0  indicated  (a)  51  and  52;  ( b ) 57  and  58;  (d)  62  and  64;  ( e ) 64  and  66.  by  ( c ) 60  the arrow  and  62;  Ans  36.  i s between  105 y 4 -  3 2.:  -3 -2  -t  !  i  !  |  1  2  3  i+  -2 -3  *  O  P  -k -  What  are the coordinates  o f P?  (a)  (-3,  4);  (b)  (-4,-3);  (d)  ( 4,-3);  (e)  (-4,  (c)  ( 3,  4);  3).  Ans  37.  The  which  table a ball  below  gives  i s dropp'ed  the  relation  (d) , and  the  between height  :  the  height  to which  i t  from bounces  (b).  d  50  80  100  150  b  25  40  50  75  Which  formula describes  this  (a)  b = d ;  (b)  b =  2d;  (d)  b = d +  25;  (e)  b = d  2  relation?  (c) b = -  d/2;  25. Ans  38. On  The top  a i r temperature of  the mountain  at the  the  foot  of  temperature  :  a mountain i s -7  i s 31  degrees.  degrees. How  much  warmer  i n degrees  (a) -38;  (b) -24;  i s the a i r at the  ( c ) 7;  (d) 24;  (e)  foot  of  the  mountain?  And  :  38.  Appendix Tables  IV  of R e s u l t s  by  Item  108  Table Itemwise p - v a l u e s I tern No.  Boys  1 . 2. 3. 4. 5. 6. 7. 8. 9. 10. 11 . 12. 13. 14. 15.. 16. 17. 18. 19. 20. 21 . 22. 23. 24. 25. 26. 27. 28. 30. 31 . 32. 33. 34. 35. 36.  96 93 79 70 37 90 77 50 55 69 94 30 84 36 44 59 48 50 56 35 64 64 26 42 25 60 63 60 30 66 61 47 16 35 53  Note. D i f f .  on T e s t  Urban K e r a l a Diff Girls 96 89 57 68 29 84 81 40 34 46 78 19 68 35 38 • 56 25 55 28 1 7 65 68 21 37 5 51 55 30 34 71 58 43 16 34 61  = p-value  0 4 22 2 8 6 -4 10 21 23 16 1 1 16 1 6 3 23 -5 28 18 -1 -4 5 5 20 9 8 30 -4 -5 3 4 0 1 -8 for  6 A a t Grade  Boys 85 66 79 72 43 73 80 64 48 57 74 52 72 29 58 42 62 60 58 29 63 52 25 37 39 62 36 50 27 58 47 41 37 40 64  4 Level.  Rural Kerala Diff. Girls 90 79 72 64 55 90 80 64 57 50 95 40 77 22 41 51 57 64 47 30 64 66 25 40 42 57 41 50 23 73 59 38 46 55 51  Boys - p - v a l u e  -5 -13 7 8 -12 -17 0 0 -9 7 -21 12 -5 7 17 . -9 5 -4 1 1 -1 -1 -14 0 -3 -3 5 -5 0 4 -15 -12 3 -9 -15 1 3 for  Girls  109  Table Itemwise p - v a l u e s on T e s t I tern No. 1 . 2. 3. 4. 5. 6. 7. 8. 9. 10. 11 . 12. 14. 15. 16. 17. 18. 19. 20. 21 . 22. 23. 24. 25. 26. 27. 28. 29. 30. 31 . 32. 33. 34. 36. 37. 38.  Boys 84 31 43 83 69 49 76 28 69 45 75 79 67 55 74 39 48 51 39 75 18 31 50 18  50 1 3 73 36 35 42 27 23 39 31 28 30  Urban K e r a l a Diff. Girls 77 39 34 83 45 47 67 22 68 64 84 83 84 47 71 51 ' 57 28 39 66 24 41 47 24 62 19 80 48 34 42 36 47 61 39 37 15  7 -8 9 0 24 2 9 6 1 -19 -9 -4 -17 8 - 3 -12 -9 23 0 9 -6 -10 3 -6 -12 -6 -7 -12 1 0 -9 -24-22 -8 -9 15  7 B a t Grade 8 L e v e l  Boys 82 29 59 63 34 55 37 44 40 35 56 38 53 38 58 19 34 39 35 21 20 32 1 5 32 35 1 7 43 32 30 40 30 39 32 30 47 20  Rural Kerala Dif f . Girls 49 27 22 33 37 34 41 25 37 21 36 35 34 33 37 19 33 26 30 27 21 22 25 16 46 22 41 34 21 30 22 24 32 36 19 25  33 2 37 30 -3 21 -4 19 3 1 4 20 3 19 5 21 0 1 1 3 5 -6 -1 1 0 -10 16 -1 1 -5 2 -2 9 10 8 15 0 -6 28 -5  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0096209/manifest

Comment

Related Items