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Dominican students’ intentions to pursue a mathematics-related career : an exploratory study of gender… Zapata Valerio, Joel 1995

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DOMINICAN STUDENTS' INTENTIONS TO PURSUE A MATHEMATICS-RELATED CAREER: A N EXPLORATORY STUDY OF GENDER A N D AFFECTIVE ISSUES by JOEL ZAPATA VALERIO B. Ed. Pontificia Universidad Catolica Madre y Maestra, 1987. A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE F A C U L T Y OF G R A D U A T E STUDIES ( DEPARTMENT OF C U R R I C U L U M STUDIES) ( Faculty of Education) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A July, 1995 © Joel Zapata V. , 1995 v In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis 'for scholarly purposes may be i'granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of di/f f <e</ /u *^ ^FrK/gJfeS The University of British Columbia Vancouver, Canada Date J u l ^ X t , 111$-' DE-6 (2/88) 11 Abstract The main goal of the present study was to investigate, using survey data and at the Grade 12 level in the Dominican Republic, the relationships between four affective variables known to be highly correlated to students' participation in mathematics as well as three students' characteristics -gender, school type (socio-economic condition), and intentions to pursue a mathematics-related career. The rational behind this study comes from the author's teaching experience, from observing that many students are afraid of mathematics and consequently choose careers which do not require much mathematics. However, what is of most concern to the author is that so few female students choose to elect careers in which they must take more than one or two mathematics courses. M A N O V A with follow-up A N O V A s were used to investigate differences by gender, school type, and career choice in the four affective variables related to mathematics used in this study-Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, Perception of Mathematics as a Male Domain, and Perceived Usefulness of Mathematics. Post-hoc comparisons were made using Duncan and Scheffe approaches to uncover which means were different. In addition, differences in intended participation by gender and by school type in choosing mathematics related-careers were studied using the chi-square test of association. The sample included 808 students in Grade 12 distributed over 25 schools. Four types of schools located in the second largest city of the country and in seven rural areas in the same province were sampled, Public Urban (PuU), Public Rural (PuR), Private Elite (PrE), and Private Non-elite (PrNE). The instrument consisted of 48 Likert-type items which were a subset of the Fennema-Sherman Mathematics Attitudes Scales (Fennema & Sherman, 1976) and was translated into Spanish. The questionnaire also included five background questions, I l l including the choice for the intention to pursue "high," "middle," and "low" mathematics-related careers. Students' answers to these closed-format questions were analyzed to investigate gender and school differences in terms of career choice. Conclusions of this study include the following. First, Grade 12 Dominican females did not intend to pursue a high mathematics-related career as often as did males, while middle and low mathematics-related careers attracted more females than males. Further, the greatest number of students intending to pursue high mathematics-related careers were from the public schools. Second, Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, and Perceived Usefulness of Mathematics were the most important variables differentiating between students intending/nonintending to pursue a mathematics-related career. On the other hand, Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, and Perception of Mathematics as a Male Domain were the most important variables differentiating between males and females, and among types of schools. Third, PrNE schools and PuU schools had similar mean scores in the four affective variables. Finally, the results of this study suggest that other instruments could be adapted for use not only in the Dominican Republic but in any Spanish-speaking country by following the procedures outlined in this study. iv T A B L E OF C O N T E N T S Page Abstract i i Table of contents iv List of Tables vii List of Figures x Acknowledgements xii CHAPTER 1: THE P R O B L E M 1 Background to the Problem 1 Affective Factors and Gender Differences in Career Choice 1 The Dorninican Republic 5 The Educational System of the Dominican Republic 6 Purpose and Nature of the Study 10 Research Questions 11 Significance of the Study 12 Definitions of Terms 13 CHAPTER 2: REVIEW OF THE LITERATURE 16 Overview 16 Mathematics and Gender 16 Performance in Mathematics 17 Career Choice and Participation in Mathematics 20 Confidence in Learning Mathematics 23 Attitudes Toward Mathematics 25 Mathematics as a Male Domain 27 Usefulness of Mathematics 30 Background on Education in Developing Countries 31 V Problems in Education in the Dominican Republic 34 Research in the Dominican Republic and Latin America 36 Summary 38 CHAPTER 3: METHODOLOGY 41 Research Design 41 Subjects 41 Selection Technique 41 Selection of Schools and Subjects 42 Instrumentation 43 Translation, Validation and Reliability of the Questionnaire 44 Reliability of the Questionnaire (Scales) 47 Dimensionality of the Questionnaire (Scales) 49 Data Gathering and Procedures 62 Data Analysis 63 Limitations of the Design 63 CHAPTER 4: RESULTS 65 Description of the Data 65 Research Question l a 69 Research Question lb 70 Affective Variables 72 Statistical Assumptions 75 Research Question 2 77 Research Question 2(i) 79 Research Question 2(ii) 82 Research Question 2(iii) 84 Research Question 2(iv) 87 v i CHAPTER 5: CONCLUSIONS A N D RECOMMENDATIONS 90 Summary of the Findings 90 Conclusions 95 Implications 97 Going Beyond 100 Suggestions for Further Research 100 REFERENCES 103 APPENDIX A: School Education Structure in the Dominican Republic 113 B: Distribution of Students and Sampled Schools 114 C: School's Letter and Student Questionnaire (Originals) 115 D: School's Letter and Student Questionnaire (Translated) 120 E: Tables for Figures in Chapter 3 125 F: Reliability and Factor Analyses of the Main Data 128 G: Tables for Figures in Chapter 4 138 H : Duncan and Scheffe Post Hoc Comparisons 141 V l l LIST OF TABLES Table 3.1 Reliability of the Affect Questionnaire (SPSS Output) 48 3.2 Total Questionnaire and Scales Reliabilities, Means, Standard Deviations, and Number of Cases 49 3.3 Principal Components of the Total Questionnaire 52 3.4 Varimax Rotated Factor Loadings of the Total Questionnaire 53 3.5 Confirmatory Varimax Rotated Factor Loadings of the Total Questionnaire 54 3.6 Principal Components of the Perceived Confidence in Learning Mathematics Scale's Items 56 3.7 Principal Components of the Attitude Toward Success in Mathematics Scale's Items 57 3.8 Principal Components of the Perception of Mathematics as a Male Domain Scale's Items 59 3.9 Principal Components of the Perceived Usefulness of Mathematics Scale's Items 60 4.1 Post-High School Plans of Students by School Type and Gender 66 4.2 Males' and females' Career Choice (or Intended Field of Study) 69 4.3 School Type Students' Career Choice (or Intended Field of Study) 70 vm 4.4 Intended Career Choice by School Type and Gender 72 4.5 Descriptive Statistics for the Four Affective Variables 73 4.6 Ns, Means, and Standard Deviations for A l l Variables 74 4.7 Multivariate Analysis of Variance Testing Main and Interaction Effects 77 4.8 Follow-up Univariate Analysis 78 F l Reliability of the Affect Questionnaire (Main Data) 129 F2 Total Questionnaire and Scales Reliabilities, Means, Standard Deviations, and Number of Cases (Main Data) 129 F3 Principal Components of the Total Questionnaire (Main Data) 130 F4 Varimax Rotated Factor Loadings of the Total Questionnaire (Main Data) 131 F5 Confirmatory Varimax Rotated Factor Loadings of the Total Questionnaire (Main Data) 132 F6 Principal Components of the Perceived Confidence in Learning Mathematics Scale's Items 134 F7 Principal Components of the Attitude Toward Success in Mathematics Scale's Items 135 F8 Principal Components of the Perception of Mathematics as a Male Domain Scale's Items 136 F9 Principal Components of the Perceived Usefulness of Mathematics Scale's Items 137 IX HI Comparison of Career Choice Means on Perceived Confidence in Earning Mathematics 142 H2 Comparison of Career Choice Means on Attitude toward Success in Mathematics 142 H3 Comparison of Career Choice Means on Perception of Mathematics of as a Male Domain 143 H4 Comparison of Career Choice Means on Perceived Usefulness Mathematics 143 H5 Comparison of School Means on Perceived Confidence in Learning Mathematics 144 H6 Comparison of School Means on Attitude toward Success in Mathematics 144 H7 Comparison of School Means on Perception of Mathematics as a Male Domain 145 H8 Comparison of School Means on Perceived Usefulness of Mathematics 145 LIST OF FIGURES Figure 3.1 Screen output for pilot data produced by SPSS X FACTOR 3.2 Correlations of the Perceived Confidence in Learning Mathematics scale's items with factors 3.3 Correlations of the Attitude toward Success in Mathematics scale's items with factors 3.4 Correlations of the Perception of Mathematics as a Male Domain scale's items with factors 3.5 Correlations of the Perceived Usefulness of Mathematics scale's items with factors 4.1 Age of students by school type 4.2 Mean score of students by gender, school type and career choice on Perceived Confidence in Earning Mathematics 4.3 Mean score of students by gender, school type and career choice on Attitude toward Success in Mathematics 4.4 Mean score of students by gender, school type and career choice on Perception of Mathematics as a Male Domain 4.5 Mean score of students by gender, school type and career choice on Perceived Usefulness of Mathematics Fl Screen output for main data produced by SPSS X FACTOR F2 Correlations of the Perceived Confidence in Learning Mathematics scale's items with factors F3 Correlations of the Attitude toward Success in Mathematics scale's items with factors F4 Correlations of the Perception of Mathematics as a Male Domain scale's items with factors F5 Correlations of the Perceived Usefulness of Mathematics scale's items with factors Xll Acknowledgements I would like to thank the members of my research committee, Dr. James M . Sherrill; Dr. Ann G. Anderson; and Dr. David J. Bateson for their insightful comments, and their invaluable advice throughout the process of conceptualizing, planning, developing, and writing this thesis. It has been a pleasurable challenge to work with you in this project. I would like to thank a number of people from my native Dominican Republic for their constant support and encouragement. Particularly, I express my sincere gratitude to Dr. Eduardo Luna and to Professor Sarah Gonzalez for giving me the opportunity to study at U B C . Many thanks to my dear friend and colleague, Mr. Rafael Balbuena, for his encouragement and support and for being instrumental in helping me collect the data for both, the pilot and main studies. I would also like to thank all my friends and fellow graduate students who provided me with needed support and friendship and who contributed in one way or another to the successful completion of my graduate studies. Among them, special thanks are due to Sandra Crespo, Franc Feng, George Frempong, Hari Koirala, Rita Acton, Susan Brigden, and Gabriel Taylor. I also wish to extend my gratitude to the support staff in the Department of Curriculum Studies whose collaboration made it possible for this study to be completed successfully. Among them, thanks to Saroj Chand, Diana Colquhoun, and Bob Hapke. In addition, I would like to thank my mother, father, brother, and sisters for their patience, encouragement, and constant support. Finally, but not least, I wish to thank my wife, Rosa Elena, whose support and understanding helped me through my studies; and to my newborn baby Kevin Joel. To them this work is dedicated. 1 CHAPTER 1: THE PROBLEM Background to the Problem The present study will examine four affective factors which may result in gender and school differences in high school mathematics. In addition, the study will describe patterns of intended participation in mathematics-related careers by gender and by school type. Affective Factors and Gender Differences in Career Choice In mathematics, as in other cognitive fields, affective variables can play an important role in how students approach the learning of mathematical content and their decisions about how much mathematics they will need in the future for their everyday life or for their university education (Reyes, 1984). For instance, if a student feels positive about mathematics, it is likely that s/he will also demonstrate better achievement than does a student who feels negative about mathematics (Reyes, 1984; Reyes & Stanic, 1988a; Yong, 1993). The importance of affective variables is reflected in the Curriculum and Evaluation Standards for School Mathematics [National Council of Teachers of Mathematics (NCTM), 1989], where two of the five general goals for all students in Grades K-12 are: (1) that they learn to value mathematics, and (2) that they become confident in their ability to do mathematics (p.5). Fennema and Sherman (1976) state that affective factors influence students' selection of mathematics courses and thereby are important variables in explaining individual differences in the learning of mathematics. They indicate that an increasing number of intellectually qualified students are deciding not to study more mathematics beyond the minimal high school or university requirements, and that many more females than males make this decision. 2 According to the N C T M (1989), females and minorities study less mathematics and are seriously underrepresented in careers which use science and technology (Research Advisory Committee of the N C T M , 1989). Also, the Research Advisory Committee of the N C T M (1989) contends that mathematics has become a critical filter for employment and full participation in society. Mura (1987) asserts that, as in many other countries, females in Canada are currently seriously underrepresented in mathematics and in mathematics-related fields. For example, Hanna and Leder (1990) report that in Canada, only 12 percent of the students enrolled in engineering are females. It is reported that the ratio of males to females electing careers in engineering and science approaches 3 to 1 in the United States (Dick & Rallis, 1991; Rosenberg, 1987) and 7 to 1 in Canada (Hanna & Leder, 1990). Females may avoid mathematics because they lack confidence in their ability to learn mathematics, they underestimate their ability to solve mathematical problems, and they do not see mathematics as personally useful (Cross, 1988; Meyer & Koehler, 1990). The low participation rate of females in scientific and technical fields is hypothesized to be due to the traditional avoidance of mathematics by females (Armstrong & Price, 1982; Dick & Rallis, 1991; Fennema & Hart, 1994; Hart, 1989; Leder, 1985). Unfortunately, there is some evidence that even very young males and females differ in their desire to take mathematics (Pedersen, Bleyer, & Elmore, 1985). Affective variables such as confidence in learning mathematics, attitudes toward success in mathematics, and perceptions of the usefulness of mathematics are seen as significant factors affecting differences between the sexes either in mathematics achievement or in the selection of mathematics courses (Armstrong & Price, 1982; Fennema & Sherman, 1977, 1978; Haladyna, Shaughnessy, & Shaughnessy, 1983; Meyer & Koehler, 1990; Mura, 1987; Pedro, Wolleat, Fennema, & Becker, 1981; Rosenberg, 1987). In addition, beliefs about mathematics, stereotypes of mathematics, and social and cultural sex role expectations are factors related to gender differences in mathematics achievement, students' selection of mathematics courses, and participation of students in 3 mathematics-related careers (Eccles, 1985; Hyde, Fennema, Ryan, Frost, & Hopp, 1990; Leder, 1985, 1992; Schoenfeld, 1989; Sherman & Fennema, 1977). For example, many female students feel that many of their peers, teachers, and relatives hold negative stereotypes about females learning mathematics. Negative statements, such as "Men become better engineers than women, but women can be good nurses or secretaries." sometimes made in class (by both teachers and peers) or at home (by parents, siblings, and others) influence negatively female students' attitudes toward mathematics (Becker, 1981; Fennema, 1980; Leder, 1985). During the author's seven years of teaching high school and university students, he, like Fennema and Sherman (1976; 1978), has noticed that many students are afraid of mathematics, and many of them have chosen careers for which they do not need to take much mathematics. However, what is of most concern is that so few female students choose to elect careers in which they must take more than one or two mathematics courses. Therefore, a study that provides information about this problem is deemed worthwhile. A review by Stromquist (1989), which reported studies in developing countries, discussed factors that contribute to gender inequalities in education and that affect females' achievement and participation. Stromquist (1989) found that in Latin America and the Caribbean there have been improvements at all levels of education. However, the enrollment of most females is still in traditionally feminine fields which offer limited potential leadership and economic reward. The limited enrollment of female students in mathematics-related careers has an impact on their opportunities for future work. Stromquist (1989) concluded that social and cultural norms significantly affect females' career choices. However, little research has been done to address the issues of affective factors in mathematics and career choices in the Dominican Republic, thus there is a need to study these problems. 4 Marret and Gates (1983), and Reyes and Stanic (1988a) point out that most of the research on gender differences and participation in mathematics has focused on white students without examining the possibility of different patterns of mathematics achievement between black and white students of various socio-economic (SES) levels. In addition, Marret and Gates (1983), and Reyes and Stanic (1988a) assert that there is very little research in mathematics education that documents differences in course enrollment by SES. Nebres (1988) claims that most mathematics studies focus on cognitive factors. He argues that if culture, values, and/or beliefs affect mathematics in an important way, then non-cognitive factors such as affective factors or the cultural environment must be understood as well. Fennema and Hart (1994) assert that gender differences in mathematics still exist in career choices that involve mathematics and that these differences vary by ethnicity, socio-economic status, school, and teacher. Consequently, it is also important to examine factors such as gender and school type in exploring the relationship between career choice and affective variables. Further, most of the studies regarding gender differences have taken place in countries such as the United States, Australia, England, and Canada (Leder, 1985). Marrett and Gates (1983) argue that one cannot assume that the findings from a developed context apply to a less developed context, or that patterns found in one system prevail elsewhere. Therefore, it is important to extend such research by investigating mathematics learning in other contexts, such as developing countries. This is one of the main reasons for deciding to conduct the present study in the Dominican Republic. The present study concentrated on Grade 12 students because it is at this level that students' choices immediately affect their futures and reflect their past experiences. Furthermore, at this level gender differences in career choice is most prominent (Dick & Rallis, 1991; Gaskell, McLaren, Oberg, & Eyre, 1993). In addition, high school mathematics seems to be the source of both low achievement and much boredom (Dossey, Mullis, Lindquist, & Chambers, 1988). The following sections provide some insight into 5 the Dominican Republic and its educational system to familiarize the reader with the context in which the present study was implemented. The Dominican Republic The Dominican Republic occupies the eastern two thirds of the island of Hispaniola, which it shares with the Republic of Haiti. The island is located in the Caribbean Sea, with Cuba and Jamaica to the west, and Puerto Rico to the east. The country has an area of about 49 000 km^ divided in 26 provinces and one national district which includes the capital city of Santo Domingo. In 1988, the population was approximately seven million people with an average annual rate of population increase of 2.92%. At the beginning of the 1980s, the proportions of rural population and urban population were about equal, but the trend toward migration to urban areas has resulted in the present rate of 40 percent rural and 60 percent urban. Another characteristic of the country is that the population is relatively young: approximately 75 percent of the population is under 25 years of age (Fernandez, 1990; Haverstock, 1988; Troxell, 1987). The Dominican Republic's economy is typical of most developing countries. About 25 percent of its gross national product comes from agriculture, livestock, and mining, with the main products being coffee, cocoa, tobacco, sugar, tropical fruit (citrus fruit, avocados, bananas, and mangoes), cattle, poultry, fish, gold, silver, bauxite, and iron-nickel. The manufacturing industry which encourages foreign investment is another important part of the economy. In recent years, tourism has become an important and increasing source of wealth. The main problem currently facing the country is an energy shortage. The energy supply has been declining for the past five or six years, making the country almost totally dependent on foreign oil for transportation and electricity. In fact, the lack of fuel and electricity has almost brought the country to a halt several times in the past three years. Another problem is the economic differences among population groups in the country. The higher strata (approximately 14 percent) receives 50 percent of the total 6 income, while the lower strata (29 percent) receives only 6 percent of the total. The rate of unemployment is over 20 percent of the economically active population and underemployment is an even worse problem (Aleman, 1988; Fernandez, 1990). The form of government is a representative democracy with characteristics typical of developing countries, namely a history of a dependent economy and dictatorship. The Dominican democracy has the customary division of powers among the executive, legislature, and judiciary. The executive branch is headed by the president. The legislative branch consists of a bicameral house of a 27-member chamber of senators and a 91-member chamber of deputies. The judicial branch is headed by a supreme court of nine justices. The government has been controlled alternately by two political parties for the past 24 years, with strong opposition from a third party, making unified planning and implementation of what could otherwise be productive governmental policies very difficult at best (Aleman, 1988; Haverstock, 1988). The Educational System of the Dominican Republic Preschool, Primary and Secondary Education The Consejo Nacional de Education, CNE (National Council for Education) is the main regulatory body of the Dominican Republic's educational system. Public and private education at the preschool, primary, and secondary levels in the Dominican Republic operate under the jurisdiction of the Secretaria de Estado de Education, Bellas Artes y Cultos, SEEBAC, (Secretariat of Education, Fine Arts and Culture). The SEEBAC, also sets curriculum for all three levels of education for both private and public educational institutions, and approves the textbooks used for teaching. Education up to the sixth grade is mandatory and free, although this is more in theory than in practice, because drop-outs, overage (older than is normal for one's grade), and repetition are a cause for concern (Crespo, 1990; Fernandez, 1990; Troxell, 1987). Around 10 percent of the national budget is spent on education, but it is still insufficient to fulfill the growing demand. Nearly 7 three-quarters of Dominicans can read and write, and public pressure on the government to boost that figure has been increasing in the last few years (Haverstock, 1988). Two educational programs are currently in effect. The Traditional program includes six years of primary education, two years of intermediate school, and four years of secondary education. It is academic in orientation and designed to prepare students for universities. The Traditional system is predominant in both rural and urban areas. The contents of the Traditional mathematics curriculum (developed in 1950) correspond to the mathematics generally taught in the United States during the period 1950-1960, with the major emphases on arithmetic, measurement, and geometry. However, at the beginning of the 70s, topics from sets and statistics were also included (Fernandez, 1990; Luna, Gonzalez, & Wolfe, 1990; Troxell, 1987). A l l the students in the Traditional system follow the same courses through Grade 11. In Grade 12 they can choose which program to follow from four orientations: sciences and letters, philosophy and letters, physical sciences and mathematics, or physical and natural sciences. Students in the physical sciences and mathematics option get the strongest background in mathematics as they have to take more advanced courses of geometry, trigonometry, higher mathematics, and technical drawing. Students in the sciences and letters option have to take higher mathematics only. Students in the physical and natural sciences, and philosophy and letters options do not have to take more mathematics courses. They have taken mathematics (algebra, geometry, trigonometry) through Grade 11. However, it should be pointed out that within individual schools students generally cannot choose an orientation, but rather have to follow the only orientation offered in that particular school. Thus, students cannot avoid mathematics or they are compelled to go to another school. The most common orientation available to students, particularly in all private schools in the Traditional system is the "sciences and letters" option. Generally, only big public schools in the Traditional system offer the other three options simultaneously. 8 Since 1970, the government has tried to implement a new "Reformed Program" as an ambitious scheme to change the curriculum of the secondary schools. Unfortunately, this initiative has not been as successful as was expected. Only 19 of the 24 schools originally set up as pilot projects still operate as pilot projects under this system, with an approximate total enrollment of 15% of the entire population of students at the secondary level. The program consists of six years of primary education and six years of secondary school (a four-year basic cycle followed by two years of a specialization cycle). The contents of the Reformed mathematics curriculum correspond mainly to the curriculum materials developed by the School Mathematics Study Group (SMSG). The emphasis of this program is not only on algorithms, but also on their justification. The Reformed program offers several options to the students: academic, industrial, commercial, agricultural, and journalism studies (Fernandez, 1990; Luna et al., 1990; Troxell, 1987). (See Appendix A) In both the Traditional and Reform systems all students take the following basic courses: Spanish, mathematics, social studies, natural sciences, English and/or French, music and art, manual technical education, and religious studies. Of these areas, Spanish and mathematics receive the most emphasis in both systems (Troxell, 1987). Schools in the Dominican Republic can be classified according to the socio-economic status (SES) of the students they serve as well as to their status with the Ministry of Education. The types of schools in the country are: public urban schools (PuU) and public rural schools (PuR), which are totally financed by the government; and private elite schools (PrE) and private non-elite (PrNE), which are only urban and receive no financial aid from the government. The public schools are run by the state and are free of charge. The private elite schools operate autonomously and are authorized to administer their own examinations since they have already met the required standards set by the SEEBAC. The private non-elite schools operate under the supervision of the SEEBAC and are not authorized to administer examinations. Most students of low SES attend both urban and 9 rural public schools. Some students of low SES and most students of middle SES attend PrNE schools. And, students of high SES and some of middle SES attend PrE schools (Luna, Gonzalez, Robitaille, Crespo, & Wolfe, 1995). Diaz Santana (1987) claims that urban schools are known to have better qualified teachers and higher standards of both teaching and accommodation than rural schools. Higher Education Higher education has been characterized by its rapid growth. Dominicans see education as a way to a better economic and social position. In fact, education has contributed to the growth of the middle socio-economic sector. In consequence, university education is highly valued for career goals, and the demand for post secondary studies has increased greatly. It is estimated that 85% of secondary school graduates from the Traditional program (university preparatory) and 70% of graduates from the Reform program (technical-vocational) go on to higher education (SEEBAC, 1984; Troxell, 1987). Before 1961, there was only one institution, the first university in the Americas, the Universidad Autonoma de Santo Domingo (UASD), which has operated under various names since 1538. This is an autonomous university that, although receiving public funds, is not accountable to the government. In 1975 there were seven universities with a total enrollment of 40 743 students, but in 1982, there were 15 recognized universities with an approximate enrollment of 100 000 students. Of these universities, one is public, five are private with partial government support, and nine are private receiving no public funds. To date, there are 24 higher education institutions with legal standing which offer technical, bachelor, magistral, and doctoral degrees with an approximate enrollment of 150 000 students of which, U A S D enrolls 67 000 students (Fernandez, 1990; Troxell, 1987). Higher education has its own laws and all institutions are autonomous in practice as they are largely independent of SEEBAC. There is no special supervisory or coordinating body at this level, but in 1983, the Consejo Nacional de Educacidn Superior (CONES, the 10 National Council on Higher Education) was founded under presidential decree to regulate private universities as well as to study the situation and suggest possible solutions. The actual approved universities vary in size, philosophy, calendar, and objectives. Some of them have physical facilities comparable to Canadian and U.S. institutions, some offer a wide variety of majors, while others specialize in one discipline or profession. In those which offer many fields of study, the specializations are subdivided by faculty. While some universities have full-time and part-time students, others have part-time students only as they were established for students who are already working full or part-time and can take only evening sessions. All Dominican universities offer full university degrees and possibly intermediate (professional certification programs, diploma programs, etc.) and graduate programs (Troxell, 1987). Purpose and Nature of the Study The purpose of the present study is to investigate gender and school differences in four affective variables in high school mathematics and students' intentions to enroll in a mathematics-related career in several Dominican classrooms. This study will provide information of students as learners of mathematics and their attitudes toward mathematics. Thus, the main goal of this study is to examine affective factors which may be related to patterns of high and low participation of Grade 12 students in choosing mathematics-related careers in the Dominican Republic. To address this issue, students' post-high school plans and future career choices, how they perceive mathematics in their future life, their experiences in mathematics courses during school, and their images of mathematics, will be investigated. Another goal of this study is to describe the patterns of intended participation by gender and by school type in choosing mathematics related-careers, (i.e., to determine the intended participation of female students, as compared to their male counterparts, in 11 mathematics-related careers). To address this issue, the intended participation rates of students (males and females) from different types of schools in mathematics-related careers will be investigated using the data gathered from questionnaires. Research Questions In order to assess students' attitudes toward mathematics and their future career choice at the Grade 12 level, the present study was designed to address the questions below. la) How do high school males and females differ in terms of their intended career choice? lb) How do high school students from different types of schools differ in terms of their intended career choice? 2) How do perceived confidence in learning mathematics, attitude toward success in mathematics, perception of mathematics as a male domain, and perceived usefulness of mathematics relate to gender, intended field of study (career choice), and school type? Below are the specific questions. (i) How does students' perception of confidence in learning mathematics vary between males and females, by intended career choice, and in the different types of schools? (ii) How does students' attitude toward success in mathematics vary between males and females, by intended career choice, and in the different types of schools? (iii) How does students' perception of mathematics as a male domain vary between males and females, by intended career choice, and in the different types of schools? (iv) How does students' perception of the usefulness of mathematics vary between males and females, by intended career choice, and in the different types of schools? 12 Significance of the Study The present study is concerned with gathering information about four affective variables in high school mathematics and patterns of intended participation in mathematics-related careers in the Dominican Republic. These affective variables and patterns are important components that need to be considered in educational decision-making by stakeholders. This study can provide a foundation on which to make curricular decisions and decisions about the ways teachers teach mathematics. Therefore it is important to understand how students perceive and value mathematics in their current and future life. In addition, it is also important to examine how affective variables might influence their choice to study mathematics. The rationale behind this study is the belief that too many students, particularly females, are avoiding careers for which they have to take more than the minimally required number of mathematics courses. This information will provide assistance to the Dominican educational authorities in identifying areas where attention and improvements are necessary. Examples of areas or ideas requiring improvements may include: dispelling stereotypes, affirmative action for females, increasing achievement levels, and so on. Further, the study will provide professionals and the public in general with information about four important affective variables and their relationships to students' career choices. This study is expected to produce findings of interest from practical perspectives because the information gathered can be important not just to mathematics educators and teachers but to anyone concerned about the participation of students, particularly female students, in mathematics-related careers. The results and conclusions of this study may have implications for choosing strategies to increase the participation of all students in mathematics-related careers. 13 Definitions of Terms Several variables were investigated in this study. The dependent variables (DV) were perceived confidence in learning mathematics, attitude toward success in mathematics, perceptions of mathematics as a male domain, and perceived usefulness of mathematics. The independent variables (IV) were gender, school type, and career choice. Definitions of the terms used throughout this study are provided below. Affective factors. Feelings, desires, emotions, attitudes, values, and appreciations (Allen, 1990, p.19; McLeod, 1992). Attitude toward Mathematics. A general emotional disposition toward the school subject of mathematics (Haladyna et al., 1983, p.20). Attitude toward Success in Mathematics (Attsmaf). The measure of the degree to which students fearfully or fearlessly anticipate positive or negative consequences to any mathematical task as a result of success in mathematics (Fennema & Sherman, 1976, p.325). Basic mathematics. Courses designed to provide a general review of the various fundamental topics in business mathematics, algebra, geometry, and trigonometry studied throughout middle and high schools. Students are expected to develop a functional knowledge of the language, operations, and concepts of mathematics required to solve problems in their chosen career field. Confidence in Learning Mathematics ("Confmaf). The measure of a student's perception of being able to learn new topics in mathematics, perform well in mathematics class, and do well on mathematics tests (Reyes, 1984, p.560). Developing country. A poor or primitive country that is developing better economic and social conditions (Allen, 1990, p.319). Gender difference. Non-biological distinction between females and males, focusing on the role played by the environment in which learning occurs (Leder, 1992, p.600). 14 High level or advanced mathematics. Courses designed to include the use of new material to generalize and develop the mathematical knowledge, skills, and devices mastered in secondary school. Students are expected to deal with complex topics and concepts to make abstractions, generalizations, and applications in situations involving quantitative laws. Such laws are dealt with in many disciplines (e.g., physics, control theory, mechanics, mathematics, etc.). Thus, the emphasis is on the development of mathematical theory and on improving its effectiveness when applied to real world situations. Mathematics achievement. The quality and quantity of a student's knowledge exhibited on mathematics tests. Mathematics as a Male Domain (MatrndonrO. The measure of the degree to which mathematics is viewed as appropriate for males and females (Fennema & Sherman, 1976, p.325). Mathematics-related careers: a) Low mathematics-related career (LMQ. In the Dominican context, an academic field of study which requires only one or two courses of basic mathematics (e.g., law, medicine, philosophy, social sciences, etc.). b) Middle mathematics-related career (MMQ. In the Dominican context, an academic field of study which requires many more than two courses of basic mathematics (e.g., accounting, architecture, business administration, etc.). c) High mathematics-related career (HMO. In the Dominican context, an academic field of study which requires a strong background of high level or advanced mathematics (e.g., engineering sciences, mathematics, physics, statistics, etc.). Mathematical beliefs. A tenet or body of tenets held by students about the ways they view mathematics and themselves as learners of mathematics. Participation in mathematics. The act of being (or intention of being) engaged in mathematics courses, mathematics activities, and/or mathematics-related careers. 15 School difference. Distinction among schools, focusing on characteristics that are amenable to change and on the role played by the environment in which learning occurs. School type. Four types of schools in the Dominican Republic were included in this study: Public Urban (PuU), Public Rural (PuR), Private Elite (PrE), and Private Non-elite (PrNE). Sex difference. Biological distinctions between females and males, focusing on characteristics that are not amenable to change (Leder, 1992, p.600). Survey research. The assessment of the current status of opinions, beliefs, and attitudes by questionnaires or interviews from a known population (McMillan & Schumacher, 1989, p.544). Tertiary education. Three or more years of post secondary education (e.g., diplomas and technical degrees), B.A./B.S. degree, and graduate education (Stromquist, 1989, p. 149). Usefulness of Mathematics (Usefmaf). The measure of a student's perception of the practical worth or applicability of mathematics in relation to her/his current or future life, future education, or other activities (Fennema & Sherman, 1976, p.326). 16 CHAPTER 2: REVIEW OF THE LITERATURE Overview Research on affective variables and gender issues in mathematics education has been conducted from a variety of perspectives. This chapter contains a review of selected literature which is directly related to the present study. It focuses on those studies which were concerned with gender and its relationship to attitudes toward, achievement in, and participation in mathematics. Mathematics and Gender A long held, general social belief has been that academic work is not appropriate for females. In much of the Third World, females still face educational disadvantages (Stromquist, 1989), and in most parts of the world males receive more education than females (Willms & Kerr, 1987). Division of the labor force within the home and various cultural norms work to the detriment of females who are defined as future mothers (Stromquist, 1989). Fennema and Hart (1994) assert that gender differences in mathematics still exist in the learning of complex mathematics and in career choices that involve mathematics. They further suggest that gender differences vary by ethnicity, by socio-economic status, by school, and by teacher. However, in recent years there has been an increased tendency for more females than males to stay in school until the end of high school (Hanna & Leder, 1990; Leder, 1992). Also, there are many females who are achieving well in mathematics and many who are pursuing mathematics-related careers (Fennema & Hart, 1994). Fennema and Hart (1994) indicate that gender differences in mathematics may be decreasing. The Research Advisory Committee of the NCTM (1989) contends that it is necessary to have clear descriptions of mathematics teaching and learning as it really occurs in schools with diverse populations. The present study is the first of its type at the senior 17 secondary level in the Dominican Republic. It attempts to investigate gender and school differences with respect to four affective, variables in high school mathematics as well as to document Dominican students' intended participation in mathematics-related careers. Therefore, four different factors that may be related to students' choice of mathematics-related careers, and patterns of intended participation by gender in mathematics-related careers were investigated in this study. As previously mentioned, these affective factors are: confidence in learning mathematics, attitudes toward success in mathematics, perception of mathematics as a male domain, and perception of the usefulness of mathematics. Performance in Mathematics Performance is included in the literature review because there is evidence suggesting that there may be important gender differences in the relationship between performance and participation (Fennema & Sherman, 1977; Lantz & Smith, 1981; Leder, 1982; Matthews, 1984; Sherman & Fennema, 1977), and in the relationship between performance and affective variables such as attitudes toward mathematics, stereotyping of mathematics, perceived usefulness of mathematics, confidence in learning mathematics, and so forth (Dossey et al., 1988; Fennema & Sherman, 1977, 1978; Lamb & Daniels, 1993; Leder, 1987; McLeod, 1992; Meyer & Koehler, 1990; Pedersen et al., 1985; Perl, 1982; Reyes, 1984; Reyes & Stanic, 1988a; Sherman & Fennema, 1977; Taylor & Robitaille, 1987). Dwinell and Higbee (1991) assert that during the last two decades, counselors and educators increasingly have been sensitized to the relationships between performance and affective variables in mathematics. In addition, because quantitative fields require extensive mathematical training, it is imperative to examine gender differences in mathematics performance (Dick & Rallis, 1991). 18 Existing research indicates that there are few differences in mathematics performance between males and females in the elementary school years. Differences in mathematics performance favoring males are more pronounced in the high school years, being more apparent in problem-solving tasks and applications (Friedman, 1989; Leder, 1982, 1985; Reyes & Stanic, 1988a). Sometimes the difference in mathematics achievement favoring males is attributed to underlying ability, and other times it is attributed to a social climate that does not encourage females to study mathematics (Fennema & Sherman, 1977). However, until age 10, either no differences are found, or the differences that are found favor females. In a meta-analysis of 98 recent studies on gender differences in mathematical tasks, Friedman (1989) found that the average gender difference was small and that gender differences in performance favoring males appeared to be decreasing over the years. Friedman (1989) argues that no gender differences would be found if females were to take the same number of mathematics courses as males. In addition, it appears that males and females assimilate the subject matter taught in class equally well (Hanna, 1989; Smith & Walker, 1988). Thus, out-of-class experiences or environmental variables seem to have more impact upon mathematics achievement than biological differences (Friedman, 1989; Hanna, 1989; Hart, 1989). Fennema and Sherman (1977) suggest that it is necessary to modify the belief that females have less aptitude for mathematics. They indicate that females have as much mathematical potential as males. They also assert that school systems should reassess the information and career planning advice regarding the importance of mathematics in social sciences and traditionally female areas such as nursing as well as in technical areas and the sciences. Their findings support the belief that socio-cultural factors are highly related to gender differences in mathematics achievement. Findings that emerged from two Dominican studies, The Teaching and Learning of Mathematics in the Dominican Republic (Gonzalez & Luna, 1984) and Mathematics Achievement in the Dominican Republic: Grade 12 (Crespo, 1990), reveal that the 19 mathematics achievement levels of Grade 8 and Grade 12 Dominican students were found to be below international norms. Further, Crespo (1990) found significant gender differences favoring males in mathematics achievement, independent of the school type and of the region in the country. In examining the data from three 1979 New York State Regents Mathematics Examinations, Smith and Walker (1988) found that Grade 10 males outperformed females in mathematics achievement, but Grades 9 and 11 females outperformed males. These types of conflicting findings may be attributable to the content or the format of the particular test administered. Moreover, the gap in mathematics is closing as can be seen by comparing the achievement scores from the First International Mathematics Study [FIMS] and Second International Mathematics Study [SIMS] (Willms & Kerr, 1987). According to these researchers, there were significant gender differences at all ages in the first IEA study, but in the second study, these differences were found only at the secondary level. Finally, it is important to note that many students, both males and females, perform very poorly in mathematics, not due to the lack of inherent ability, but rather due to complex interactions which develop as they study this subject at school. Studies reviewed in Lamb and Daniels (1993) have reported that gender differences in mathematics achievement were not due to ability but rather to some affective factors. Dwinell and Higbee (1991), for instance, explored the relationships between affective variables and performance in algebra by administering the Fennema-Sherman Mathematics Attitudes Scales to high-risk college freshmen (both males and females). They found that the affective variables together accounted for 34% of the variance in first-quarter mathematics grades. Further, Meyer and Koehler (1990) write, "We know that affective variables are related to achievement and participation and that these variables might have differing influence for females and males" (p.92). As Reyes (1984) and McLeod (1992,1994) state, affective issues can play a central role in mathematics learning and instruction. Therefore, 20 it is important to study affective variables in the hope of improving the learning of mathematics. Career Choice and Participation in Mathematics Gender differences in participation in mathematics continue to be a matter of concern (Fennema & Hart, 1994; Hanna & Leder, 1990; Leder, 1982). More males than females reported their intention to continue taking mathematics courses, irrespective of the attained level of performance (Leder, 1982; Sherman & Fennema, 1977). Other studies report that the percentage of females electing mathematics is significantly less than that for males (Cross, 1988, Kwiatkowski, Dammer, Mills, & Jih, 1993; Pedro et al. 1981; Perl, 1982; Rosenberg, 1987). Similarly, compared to white male students, Hispanics, blacks, and female students have traditionally enrolled in fewer optional mathematics courses (Matthews, 1984; Olson & Kansky, 1981; Reyes & Stanic, 1988b). However, Sherman and Fennema (1977) concluded that students' intent to study mathematics appears to be more related to attitudinal variables than to gender per se. Pedersen et al. (1985) found that males showed significantly higher interest than did females in science, technology, and trade. Females showed significantly higher interest in creative and applied art; in social, health, and personal services; and in business communications. However, Marrett & Gates (1983) found that females in their study were as likely as the males to elect mathematics courses. However, the bulk of the research suggests that, compared to males, females show less interest in continuing in mathematics. One recommendation by Gaskell et al. (1993) was the encouragement of more females into mathematics and physical science. Why? Gaskell et al. (1993) stated that, Mathematics and physical science are powerful forms of knowledge in our society. It is important that all people have access to those forms of knowledge so that they can participate equally in defining the kind of society in which we live. There is no inherent reason why women cannot participate equally in mathematics and science, (p.5) 21 Reyes & Stanic (1988a) also write, "Knowledge of mathematics is essential for all members of our society" (p.26). According to these researchers, one must be able to understand and apply mathematical ideas in order to fully participate in democratic processes and not to be restricted in career choice. However, there is no simple solution. Since females' underrepresentation in mathematics-related occupations is due to the inadequate preparation in mathematics received by many of them, they are often unable to enter mathematics-related careers (Fennema, Wolleat, Pedro, & Becker, 1981). Cross (1988), Fennema and Hart (1994), and Lamb and Daniels (1993) state that when females limit their academic choices in mathematics at adolescence, they also limit their occupational choices. For instance, Olson & Kansky (1981) reported that the occupational choices available to females were limited because of their poor mathematics background. In general, females and minorities study little mathematics and are seriously underrepresented in careers which use science and technology (Research Advisory Committee of the NCTM, 1989). For example, in 1990, the ratio of males to females enrolled in engineering and science in Canada was 7 to 1 (Hanna & Leder, 1990). Low participation rate of females in scientific and technical fields is hypothesized to be due to the traditional avoidance of mathematics by females (Armstrong & Price, 1982; Dick & Rallis, 1991; Fennema & Hart, 1994; Hart, 1989; Leder, 1985). Gaskell et al. (1993) also stated that students' experience in mathematics and physical science are shaped by their daily contact with their teachers. The ways the teachers approach these subjects and interact with the students influence their students. Fennema (1980) contends that teachers make an impact on students' feelings about mathematics and on their learning of mathematics. Research has indicated that teachers often interact differently with their female and male students (Burton, 1989; Hanna & Leder, 1990). Gaskell et al. (1993) reported that mathematics and science courses with female teachers had more females enrolled than did those with male teachers. Many students speculated that 22 females would have better experiences in mathematics and science if they were taught by female teachers because female teachers would inspire the females to pursue mathematics and science fields for themselves. In a study on female students in Nigerian secondary schools, Mallam (1993) found that the highest proportion of females demonstrating positive attitudes toward mathematics was in the schools where mathematics was taught by female teachers, while the lowest proportion was in the schools where mathematics was taught by male teachers. Swetz (1989), however, found that there does not seem to be gender-related biases associated with mathematics in Malaysia, and possibly in other non-Western societies. He states that cultural and societal constraints do not discourage females from participating in mathematics, but that on the contrary, these societies may encourage females' participation in mathematics fields. He also argues that in the traditional societies of Africa, Asia, and Latin America, sex-role modeling may be more conducive to familiarizing females with mathematics (and its uses) than it is in the West. Leder (1992) points out that differences in participation, favoring males, continue to be observed in more intensive, high level mathematics courses and related applied fields. Similarly, Fennema and Carpenter (1981) suggest that gender-related differences in course participation emerge in the most advanced mathematics courses. Hanna and Leder (1990) report that in the United States, Canada, England, and Australia, fewer females than males continue with intensive and advanced mathematics courses. Hanna and Leder (1990) also report that at the tertiary level in Canada, 50 percent of the students are females but that only 27 percent of these females are enrolled in undergraduate mathematics and science courses. Their findings also document the low participation of females in careers or university majors that require a strong mathematics background. Armstrong and Price (1982) concluded that parents can encourage their children to take mathematics by stressing its importance to future career options. Teachers and counselors can also encourage females' participation in mathematics. Similar conclusions 23 are reported by Pedro et al. (1981) and Rosenberg (1987). Students' attitudes toward mathematics and their decision to continue with mathematics have been found to be linked to their parents' perceived relevance of school mathematics (Armstrong & Price, 1982; Lantz & Smith, 1981; Rosenberg, 1987). Yong (1993) asserts that where students have a choice, counselors have great influence on students' enrollment of mathematics courses during the middle school years. Cross (1988), and Tracy and Davis (1989), on the other hand, suggest the use of role models as a tool to encourage the development of positive attitudes toward mathematics and equal opportunities in mathematics courses and mathematics-related careers for all students, both males and females. For instance, Gwizdala and Steinback (1990), and Lee and Lockeheed (1990, cited in Mallam, 1993) suggest that female mathematics teachers could serve as role models for females to actively pursue mathematics. Dick and Rallis (1991) concluded that for many females, the teacher makes a critical difference in the decision to pursue careers in quantitative fields. Marrett & Gates (1983), on the other hand, described male-female differences in enrollment in mathematics courses among students in predominantly black high schools, and they concluded that enrollment patterns seemed to vary more by school than by gender. Their findings suggest that participation in high school mathematics courses might reflect important characteristics of, and conditions within schools. Schools can differentiate between groups of male and female students in several ways through their organizational procedures (e.g., textbook selection and content, counselors' advice, time-tabling of courses, equipment and resources, methods of assessment. Confidence in Learning Mathematics Confidence in one's ability to do mathematics has been shown to influence the study of mathematics (Sherman & Fennema, 1977), and to correlate positively with mathematics achievement (Meyer & Koehler, 1990; Reyes, 1984; Schoenfeld, 1989). 24 According to Reyes (1984), confident students tend to learn more, be more interested in pursuing mathematics, and feel better about themselves as learners of mathematics than do those who lack confidence. Pedersen et al. (1985) found that of the affective factors involved in their study, confidence in learning mathematics had the highest correlation with mathematics achievement. Fennema and Sherman (1977, 1978) found positive correlations between mathematics achievement and confidence as measured by the Fennema-Sherman Confidence Scale (Fennema & Sherman, 1976). Males often score higher than females in confidence in mathematics (Hyde et al., 1990; Reyes, 1984). Fennema and Sherman (1977, 1978) found that consistently, at both the middle and high school levels, males have more self-confidence in their ability to learn mathematics than do females. Gonzalez and Luna (1984), Lantz and Smith (1981), and Mura (1987) had similar findings. These differences may be affected by students' and teachers' attitudes, and by mathematics applications which may favor the interests of males more than females. Pedersen et al. (1985), however, found that seventh grade females in their study scored significantly higher than their male counterparts on a scale of confidence in learning mathematics. Nevertheless, the bulk of research indicates that, compared to males, females are less confident about their ability to do mathematics. Meyer and Koehler (1990) state that confidence in learning mathematics is reflected by continued participation in mathematics courses and career aspirations in quantitative fields. Likewise, gender differences in confidence have also been found to predict gender differences in participation in non-compulsory mathematics courses (Armstrong & Price, 1982; Lantz & Smith, 1981). Finally, there is evidence of a drop in confidence in mathematical ability for both males and females from age 13 to age 17 (Dossey et al., 1988). However, this must be viewed with some caution because the data were not longitudinal. 25 Attitudes Toward Mathematics Attitudes have to do with feelings, and they are thought to exert a dynamic, directive influence on an individual's responses; thus attitudes may be related to the teaching and learning of mathematics. Studies have shown that students' attitudes toward mathematics are related to achievement (Dossey et al., 1988; Leder, 1987; Reyes & Stanic, 1988a; Taylor & Robitaille, 1987). Research also indicates that student attitudes play a significant role in the prediction of females' achievement in high school mathematics courses (Armstrong & Price, 1982; Becker, 1981). Attitudes toward mathematics may include liking algebra, being bored by geometry, disliking trigonometry, being curious about probability, enjoying problem solving, and so on. Early research treated attitude as a single variable, but since the mid-1970s many researchers have instead worked with specific dimensions of attitude. For example, Fennema and Sherman (1976) developed an instrument that would go beyond the measure of global attitudes, the Fennema-Sherman Mathematics Attitudes Scales. These attitudes scales can measure different constructs of mathematics attitudes related to the learning of mathematics as well as being able to differentiate between those students who elected to study mathematics and those who did not (Sherman & Fennema, 1977). Since the development of these scales, there has also been an increased interest in gender and its relationship to attitudes and achievement. However, the purpose of this study is not to determine if affective variables (attitudes) affect achievement, but rather to determine their relationship to intended participation in mathematics-related careers by gender and by school type. It is reasonable to hypothesize that students' attitudes toward mathematics affect their desire to pursue studies in mathematics-related areas. "Students' attitudes may influence their decisions in taking the types and number of mathematics and science courses in middle school through college, which in turn affect career choice" (Yong, 1993, p.53). 26 Thus, a student who really likes mathematics, and thinks it is easy and fun, will be more likely to take it than a student who dislikes it or thinks it is difficult. Many kinds of conditions may contribute to a general like or dislike of mathematics. But what about the fact that mathematics is a required course which students cannot avoid? In such courses, mathematics teachers could give a heavy emphasis to getting students more interested in mathematics by fostering a very positive environment. Students like mathematics primarily because they find it interesting, challenging, and fun (Schoenfeld, 1989). McLeod (1994) and Szetela (1991) note that the research literature on affective differences in mathematics suggests that attitudes toward mathematics are more positive in the primary grades but gradually decline in the middle grades and become even less positive in the upper grades. Dossey et al. (1988), Eccles (1983) and, Hyde et al. (1990) also found that students become more pessimistic and less positive about mathematics as they grow older. Hyde et al. (1990) also concluded that gender differences in attitudes toward mathematics favoring males increase with increasing age. A very distinctive factor between males' and females' attitudes toward mathematics is females' lower estimation of their own ability. Females are more anxious about mathematics and feel less confident about their ability to do mathematics. For example, Kwiatkowski et al. (1993) found that female students in their study showed less positive attitudes toward mathematics than did male students. Similarly, Gonzalez and Luna (1984) observed gender differences in attitudes toward mathematics among Dominican eighth graders in favor of males. Internationally, females have been found to have less positive attitudes toward mathematics than do males (Iben, 1991, cited in Mallam, 1993). However, females' lack of positive attitudes toward mathematics has been attributed to stereotyping rather than a lack of ability (Hyde et al., 1990; Lamb & Daniels, 1993). Haladyna et al. (1983) assert that a positive attitude toward mathematics may increase one's tendency to elect mathematics courses in high school and college as well as to choose careers in mathematics or mathematics-related fields. In fact, Ethington and 27 Wolfe (1988) found that for the females in their sample, more positive attitudes toward mathematics enhanced the likelihood of selection of quantitative fields. They also argue that it is necessary to increase efforts to shape more positive attitudes toward quantitative fields among young females as well as among their parents, since many parents tend to discourage their daughters from entering quantitative fields of study in college. Eccles (1983), Rosenberg (1987), and Yong (1993) suggest that parents and/or teachers could be influencing students' choices, self-concepts, and values by the types of general experiences they provide or encourage. Therefore, attitudes toward school mathematics seem to be formed and modified by many forces such as parents and other adults, classmates, teachers and the way they teach, and so on. Schoenfeld (1989), however, claims that students study mathematics for intrinsically valuable reasons rather than for extrinsic reasons, and that both the students and their parents believe that it is quite important to do well in mathematics. Dossey et al. (1988) and Schoenfeld (1989) report that many students think that learning mathematics is mostly memorizing, knowing and following the rules for solving mathematics problems. This emphasis on the memorization of algorithms might result in a dislike of mathematics. Mathematics as a Male Domain High school mathematics courses continue to attract fewer females than males (Becker, 1981; Gaskell et al., 1993; Isaacson, 1989; Leder, 1992). According to Becker (1981) and Burton (1989), the media, teachers, community, and school beliefs and values reinforce the traditional view of mathematics as a male domain, and mathematics is not seen as a subject in which females have an active role. Becker (1981) reported that the five geometry textbooks being used by the teacher and students in her study predominantly presented males in the historic and career essays. Also, the teachers involved in the study did not use other materials to counteract this gender bias. In addition, classroom materials 28 and bulletin boards presented gender-typed mathematics that was predominantly male and ignored the role of females in mathematics and society. Gender-role stereotypes have an early beginning when young children are treated in stereotypic ways by their families, peers, and teachers. Ironically, schools contribute to fostering these stereotypes by providing environments which perpetuate submissive female roles and gender stereotyping at the elementary levels, by not challenging females to take adequate science and mathematics courses at the secondary levels, and by continuing the use of gender-stereotyped textbooks. It has been observed that teachers treat male and female learners differently in such a way that it reinforces in both males and females the belief that mathematics is a male domain (Burton, 1989; Fennema, 1980; Fennema & Hart, 1994). In addition, school counselors have been found to steer female students away from advanced mathematics courses (Rosenberg, 1987). Females' perception of mathematics as a male domain is one of the principal factors that impede their enrollment in high school mathematics courses (Sherman & Fennema, 1977). As Ethington and Wolfe (1988) point out, sex-stereotyped expectations and opportunities have inhibited many females from entering quantitative fields of study, leading to their underrepresentation in such areas. It is reasonable to think that students are likely to enroll in courses in which they feel they belong, and avoid those in which they feel uncomfortable. Ethington and Wolfe (1988) claim that it is therefore necessary to change the climate within mathematics classrooms so that all students feel comfortable, and to look carefully at the content of the mathematics curriculum to ensure that it does not reflect a stereotypical traditional content (e.g., use of examples where males are portrayed as engineers and females as nurses and housewives). Rosenberg (1987) claims that a large part of blame for the stereotyping of mathematics as male domain rests on the intellectual and social environment created for females at school as well as at home. In general, mathematics is seen as a male domain by both male and female students. However, Dwinell and Higbee (1991), Hyde et al. (1990), and Pedersen et al. (1985) 29 found that significantly more males than females classified mathematics as a male domain. Kuendiger (1989) reached a similar conclusion in an analysis of the SIMS data for 12 countries. Further, Fennema and Sherman (1978), and Sherman and Fennema (1977), found that high school males openly stereotyped mathematics as a male domain. Nevertheless, there is no simple solution to this problem if females tend to be passive. For example, Cross (1988) writes, "Girls came to accept the male dominance stereotype as they progressed through their secondary education while at the same time more and more females opted for non-science and non-mathematics courses" (p.398). Gwizdala and Steinback (1990) found that females feel intimidated, dumb, uncomfortable, and hesitant in class with males. Fennema (1980) states that some females feel it is somehow unfeminine to appear to be too smart in mathematics, so they are reluctant to participate in mathematics classes. This is supported by Isaacson (1989) who claims that many females today reject stereotypical career choices, but then find themselves competing with males in a world where the rules have been made by males to fit in with the ways in which males are expected to behave. This type of behaviour does not encourage females to study mathematics or to enroll in mathematics-related subjects. Eccles (1985) points out that if a female stereotypes mathematics or mathematics-related careers as masculine and inconsistent with her own gender role values, it is likely that she will not value mathematics learning and will be less likely to continue her mathematical studies. In support of this suggestion, Boswell (1979, cited in Eccles, 1983) has found that career mathematicians are perceived as being decidedly unfeminine. In general, students capable of continuing with mathematics, but who believe that mathematics is not appropriate for them, are more likely to avoid mathematics courses and other areas for which mathematics is a prerequisite than do students who are comfortable about taking mathematics (Leder, 1992). 30 Usefulness of Mathematics Perception of the usefulness of mathematics has also been found to influence the study of mathematics (Sherman & Fennema, 1977). This important affective factor is reflected by the inclusion of "learning to value mathematics" (p.5) as one of the five major goals for all students in grades K-12 in the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989). For some students the practical value and usefulness of mathematics in out-of-class situations may contribute to the development of more positive attitudes toward mathematics. Therefore, making students aware of the uses of mathematics may be related to developing more positive attitudes. Corbitt (1984) reports that students perceived mathematics as the most important school subject to study. They also considered mathematics to be essential for getting a good job. The results of the 1986 NAEP (Dossey et al., 1988) also show a very positive view of the usefulness of mathematics by students. Armstrong and Price (1982) found that students ranked usefulness of mathematics as the most important reason in their decision to take more mathematics courses. Pedersen et al. (1985) agree that students' perceptions about the usefulness of mathematics currently and in relationship to their future education were important in the learning of mathematics. Eccles (1983), and Fennema and Sherman (1977; 1978), found that mathematics was perceived to be of less value for females than for males. Thus, there seems to be a suggestion of gender differences in perceived usefulness of mathematics and these perceptions may help to explain a female's decision to continue or not continue the study of mathematics. Perceptions of the usefulness of mathematics is strongly associated with mathematics participation and achievement for both sexes (Fennema & Sherman, 1978; Meyer & Koehler, 1990; Pedro et al., 1981). Perceptions of the usefulness of mathematics was also found to be a good predictor of election of mathematics courses in the National Longitudinal Study of Mathematics Achievement (Perl, 1982). Studies reviewed by Hyde et al. (1990) and Reyes (1984) show that males perceive mathematics to be more useful to 31 them than do females. Eccles (1983) also found that males rated the importance of future plans (college or career) in their decisions to take mathematics higher than did females. It is reasonable to think that students who see no application for mathematics in their personal lives or future careers are less likely to take optional or advanced mathematics courses than students who see mathematics as necessary for their future career plans. Those who see mathematics as necessary may enroll in optional or advanced mathematics courses even if they do not enjoy mathematics. The results in the 1990 British Columbia Mathematics Assessment: Technical Report (Taylor, 1991) show that the majority of students in Grade 10 recognize that most people use mathematics in their jobs and that mathematics is necessary in order to get a good job. However, only a few students indicated that they would like a job where they use mathematics. Of these few, males responded more positively than females. Then, students in general perceive mathematics as important and useful in their lives, but many prefer to avoid it. Also, it appears that males are more confident than females in their ability to apply mathematics outside the classroom (Taylor, 1991). Background on Education in Developing Countries Since the current study focuses on students in the Dominican Republic, it is important to look at developing countries in general and the Dominican Republic in particular. Two of the main goals in developing countries are to expand primary education to a larger proportion of the population and to reduce illiteracy. The problems affecting education in these countries undermine the quality of education and the efficiency of the educational systems. One fundamental fact in many developing countries is that a significant portion of their national budgets is allotted to education, because education is regarded as a prime factor for social mobility (Fernandez, 1990; Gallegos, 1984; Hungwe, 1989; Stromquist, 1989; Troxell, 1987). However, the problem is that regardless of the proportion of the budget spent on education it does not necessarily improve school quality 32 since the resources are often poorly allocated (Fuller & Heyneman, 1989). Fuller and Heyneman (1989) assert that more than 95% of most educational budgets is allocated to teacher salaries, but that very few studies have shown a positive relationship between student achievement and increases in teachers' salaries. Other educational problems facing developing countries are high rates of growth in child population, classroom shortages, economic decline, and lack of material resources available to schools such as textbooks, writing materials, and desks (Fuller & Heyneman, 1989). Another related problem is the fact that many unqualified and underqualified persons are employed as teachers because of teacher shortages (Hungwe, 1989). It has also been pointed out that educated individuals, including quite a number of researchers, many highly skilled professionals, and qualified teachers, emigrate to industrialized nations in order to obtain better jobs or greater monetary rewards (Benavot, 1989; Latapi, 1990). In Latin America, as in Africa and Asia, rural areas are being abandoned by those who can travel to live in urban areas, where life is assumed to be much better. However, this creates an imbalance between rural and urban advancement. It is suggested that this migration worsens the quality of life for these migrants as the number of unemployed grows, and the quality of education is lowered in the overcrowded schools of the cities (Gallegos, 1984). In addition, the national economy is severely affected since these countries have agriculturally-based economies which require a large rural population (Hungwe, 1989). Even though access to education in developing countries has improved, there are still many illiterates, and most people attain only two years of secondary education. In addition, the proportion of females with no schooling is consistently higher than that for men. In 17 countries in Latin America and the Caribbean, the percentage of population that receives no schooling is 24.3% for females and 20.2% for males. Stromquist (1989) asserts that for both males and females, participation in schooling is highest in primary, lower in secondary, and lowest in tertiary levels. She further explains that the Equal 33 Attainment [EA] index represents the access of females compared to that of males. It assumes that complete gender parity equals 1.0 and takes the proportion of males at any given point as the standard against which to judge the condition of females. The school completion rates at the primary and secondary levels in Latin America and the Caribbean are nearly even (48.5% females and 50.8% males at the primary level with an EA index of 0.95, 15.2% females and 15.8% males at the secondary level with an EA index of 0.96). However, the lowest EA index is generated at the tertiary level of education (3.8% males and 2.8% females have completed their tertiary education with an EA index of 0.74); the proportion of females completing tertiary education is less than that of males. In addition, the percentages at the tertiary level include those with three or more years of post secondary education (e.g., diplomas and technical degrees), those with a BA/BS degree, and those with graduate education (Stromquist, 1989). Bowman and Anderson (1980) argue that, in the Third World, males are more often literate than females, irrespective of place of residence. Also, regardless of gender, literacy is higher among urban residents. Nevertheless, Bowman and Anderson (1980) also contend that in parts of Central, Latin, and South America (and in three African countries) young adult females seem to be literate more often than their males counterparts. For example, Schiefelbein and Farrell (1980) state that females have long enjoyed relatively high levels of participation in the educational system of Chile. Overall, a higher proportion of females (53.3%) than males (46.6%) complete primary schooling in Chile. A similar assertion is reported for the Philippines by Bowman and Anderson (1980). It may be the case that dropout rates for males are higher than those for females, particularly in low income families who are more likely to withdraw males from school to work because they must help their parents. However, females are not exempt from this situation either, as they are demanded for domestic work. In some developing countries, it has been found that families prefer females to drop out if they have to repeat and males to repeat rather than drop out (Stromquist, 1989). In general, females appear to face more obstacles than males 34 during their journey through the education systems (Bowman and Anderson, 1980; Stromquist, 1989; Willms & Kerr, 1987). In traditional societies, early marriage is said to be a major impediment to expanding schooling of females, especially at upper primary or secondary years. In some places, married females remain in school several years before their marriage is consummated (Bowman & Anderson, 1980). However, female students in particular may be choosing not to pursue careers, feeling that it is more important to work in the home and raise a family. Finally, it is worth noting that the expansion of primary education, for both males and females, has a strong, positive effect on economic growth in developing countries (Benavot, 1989). Benavot (1989) points out that education increases females' participation in the labor force and raises their occupational aspirations. Problems in Education in the Dominican Republic Since the assassination of the dictator, Rafael L. Trujillo, in 1961, and the subsequent short-but-bloody civil war, the Dominican Republic has experienced many changes. These changes have taken place in many aspects of life, marking a fresh beginning in the Dominican way of life, and education has not been an exception to change. Theoretically, the Dominican educational system is based on a policy of formal equality of opportunities for all social sectors. However, Luna et al., (1990) concluded that the Dominican school system, in spite of its postulates, has developed a true selection procedure that deepens social inequalities. In recent years the quality of education in the Dominican Republic has been questioned by educators and concerned citizens. Diaz Santana (1987) claims that in the past two decades, the educational system in general, and especially public education, has systematically declined in quality. This situation is worsened by the educational system's struggle to provide equal access to education for all Dominican students. Problems such as 35 drop-outs and repetition rates present great threats to the system's efficiency, and are a source of constant concern for the authorities. For example, by the time students should be in Grade 8, less than 10 percent of them are still in school (Luna et al.,1990). These problems have been the focus of most educational reforms in the Dominican Republic and little attention has been paid to the problem of declining quality. However, the level of literacy has been rising from 43.2% in 1950 to 77.8% in 1978 (SEEBAC, 1984). The literacy levels for both males and females are comparable, but the same does not hold when comparing urban and rural rates, 80.3% and 56.6%, respectively. It is estimated that 12% of the secondary school population is rural and 88% urban (Diaz Santana, 1987). Diaz Santana (1987) also claims that the Dominican educational system presents drastic differences in quality and quantity between public and private schools, on the one hand, and between rural and urban schools, on the other hand, to the detriment of the public and the rural schools. However, it is worth noting that there are differences in quality among private schools. For example, private elite schools are found to be of better quality than most of the private non-elite schools (Diaz Santana, 1987). Many factors affecting the quality of Dominican education need to be taken into account to understand the overall system. The educational authorities exert very little control over the teaching-learning process, they are more concerned about quantity than about quality. Most of the private schools have excellent installations, better qualified teachers, and students with all the socio-economic conditions necessary to study in an optimum environment. Public schools in both urban and rural areas have deficient installations, most of their teachers have insufficient academic training, and students come with socio-economic conditions that discourage them from studying. Generally, public school students do not have books. Luna et al. (1990) report that 19% of eighth grade students in public urban schools possess a mathematics textbook as opposed to 63% (which is still very low) of eighth grade students in private schools. These researchers contend that teachers usually have a heavy teaching load and rely on the 36 textbook. Therefore, the methods and the emphases used for teaching are strongly influenced by the way the textbooks present the topics. Also, teachers spend most of the mathematics class copying the lesson and the exercises onto the blackboard for students to copy into their notebooks. This means that students spend most of the time copying from the blackboard rather than doing mathematics. Fuller and Heyneman (1989) have reported similar observations for other developing countries such as Nigeria and Thailand, where, on the average, teachers spent two thirds of their time lecturing the entire class. Thus, the chalk-and-talk pedagogical method is the most common employed by many Third World teachers (Fuller & Heyneman, 1989). However, the same also occurs in the developed world. For instance, Swafford, Silver, and Brown (1989) report that in the United States, the typical mathematics instruction consists of listening to teacher explanations, watching a teacher solve problems at the blackboard, and using mathematics textbooks (particularly at the secondary level). In addition, Swafford et al. (1989) and Dossey et al. (1988) found that many students reported never working on independent projects or doing mathematics laboratory activities. Thus, it can be easily seen why most students view mathematics as a mechanical and intimidating subject. Research in the Dominican Republic and Latin America Research is not independent of instruction, it is derived from and is applied to instruction. Very little educational research is carried out in the Dominican Republic, because, first, Dominican universities are primarily teaching as opposed to research institutions (Troxell, 1987); second, resources and funds are very limited; and third, there is no tradition of research work (Fernandez, 1990). The number of educational researchers in the country during the period of 1980 to 1985 was reported to be 66 (Aleman, 1988). Latapi (1990) points out that, to a certain degree, Latin American countries have maintained a relationship of dependence on developed countries regarding socio-educational research. This means that the type of research in these developing countries is 37 mostly replication or reproduction (and importing) of the fundamental theoretical paradigms prevailing in industrialized nations. This importation is done through postgraduate students who go to study in developed nations, joint research and technical assistance projects, and attendance at academic meetings or conferences. The main goal of the replication of studies has been to determine if findings of other studies also apply to Latin American countries. Moreover, due to the European-North American influence on Latin American schooling, it is often assumed that the educational needs in these developing countries are very similar to those in the developed ones (Gallegos, 1984). However, it is important and necessary to consider the social and cultural contexts in which education and research take place. Although educational research has had a slow development in Latin America, a growth of this type of work since 1970 has been reported by Egginton (1983). In an analysis of all publications on Latin American education included in the Handbook of Latin American Studies between 1970 to 1982, Egginton (1983) classified research as follows, 17.0% as descriptive, 10.4% as historical, and 1.1% as experimental. However, the remaining 71.5% could not be classified into these conventional research categories, raising concerns about the purity of educational research in Latin America. Egginton also stated that "there has been considerable disequilibrium among the countries of Latin America with respect to the extent of published research on education" (p. 127). This may suggest that in some of these countries, research on education varies from no research at all or very little research, to an abundance of research in other countries. Research in most of the Latin American countries is still restricted, has been severely affected by lack of funds, and has been questioned as to its effectiveness (Latapi, 1990). In addition, it has been pointed out that research in developing countries is about a decade behind the United States; particularly, school-effectiveness literature in examining classroom processes and school management (Fuller & Heyneman, 1989). Most of the research carried out in the Dominican Republic is focused on an analysis of the performance of the educational system and its implications to the labor market. 38 Furthermore, the bulk of research is undertaken by students in order to fulfill the requisites for their university degrees, and most of this research is not published (Fernandez, 1990). However, although the quality of research on Latin American education has been uneven, some progress is being made (Egginton, 1983). The present study is an attempt to contribute to the growing base of scientific knowledge in mathematics education by documenting results about affective factors that influence males and females in their intention to pursue a mathematics-related career in a developing country. The results of this study, it is hoped, will help researchers, teachers, educators and educational authorities understand some of the factors influencing students' career choices in the Dominican Republic. In general, findings would help educators and educational authorities gain insight toward enhancing interest, self-confidence, and mathematics attitudes of students, a valuable goal (Research Advisory Committee of the NCTM, 1989). Summary The literature on gender differences in mathematics achievement indicates that there is much overlap in the mathematical performance of males and females, but where it occurs, a gender gap that has been found is in favor of males. However, the literature also indicates that the gender gap has been decreasing over the years. Much research suggests that males tend to take more elective mathematics courses in high school than do females, and this discrepancy is greater for more advanced courses (Fennema & Sherman, 1977,1978; Hanna & Leder, 1990; Leder, 1982, 1992; Pedro et al. 1981; Perl, 1982). However, the difference between males and females in career choice is striking. The proportion of females choosing careers in engineering and science is much smaller than that for males (Dick & Rallis, 1991; Ethington & Wolfe, 1988; Gaskell et al., 1993; Fennema & Hart, 1994; Hanna & Leder, 1990; Mura, 1987). 39 The literature on the enrollment of females in mathematics in Latin America and the Caribbean is almost non-existent. However, it is known that females tend to lag behind males at all levels of education in developing countries, and that participation in schooling is highest at the primary level, lower at the secondary level, and the lowest at the tertiary level (Stromquist, 1989). There are many reasons for lower female enrollment in mathematics. These include early marriage and family decisions to remove females from schools particularly in traditional societies that question the effect of education on female roles and behaviors (Bowman & Anderson, 1980; Stromquist, 1989). In addition, families prefer females to drop out if they have to repeat and females are in high demand for domestic work. The development of students' desire to participate in mathematics or to avoid it whenever possible seems to begin very early. A number of scholarly papers and books have addressed the problem of mathematics avoidance. Affective variables such as attitudes toward success in mathematics, confidence in learning mathematics, and perceptions of the usefulness of mathematics have been presented among the reasons for enrollment or avoidance. Stereotypes of mathematics, and social and cultural sex role expectations are also among the explanations for students' actions (Armstrong & Price, 1982; Eccles, 1985; Fennema & Sherman, 1977, 1978; Haladyna et al., 1983; Hyde et al., 1990; Leder, 1985, 1992; Mura, 1987; Pedro et al., 1981; Sherman & Fennema, 1977). Confidence in learning mathematics plays a role in students' mathematics achievement. It shows one of the strongest positive relationships with mathematics achievement of any affective variable (Fennema & Sherman, 1977; Meyer & Koehler, 1990; Pedersen et al., 1985; Reyes, 1984). Also, it directly affects mathematics participation (Lantz & Smith, 1981) and, on the average, females are less confident about their ability to do mathematics (Fennema & Sherman, 1977, 1978; Leder, 1992). 40 Differences in attitudes toward mathematics are reflected in career expectations of males and females (Fennema & Sherman, 1977; Leder, 1985; Sherman & Fennema, 1977) and the differences between the attitudes toward mathematics of males and females increase as students progress in school (Hyde et al., 1990). Also, males consistently show greater interest and ability in mathematics and mathematical performance than do females (Fennema & Carpenter, 1981; Kwiatkowski et al., 1993). "Perceived usefulness of mathematics appears to be the variable having the strongest relationship with the mathematics plans of both sexes" (Pedro et al., 1981, p.215). Males generally perceive mathematics as more useful than do females (Eccles, 1983; Fennema & Sherman, 1978; Gonzalez & Luna, 1984; Reyes, 1984). "Perceived usefulness of mathematics" is then one of the most important affective variables, with its clear relationship to students' decisions to take mathematics courses, and thus it will help to explain gender differences in mathematics course election. Finally, males generally stereotype mathematics as a male domain more strongly than do females (Fennema & Sherman, 1978; Hyde et al., 1990; Kuendiger, 1989; Pedersen et al., 1985; Sherman & Fennema, 1977). These gender-role stereotypes begin very early when teachers, peers, families, and the society in general, treat children in different ways. School environment has been observed to reinforce the traditional view of mathematics as a male domain (Becker, 1981; Burton, 1989; Fennema, 1980). Cross (1988) found that female students became passive and allowed their male counterparts to take the lead and reinforce traditional stereotypes. This phenomenon has led to the underrepresentation of females in mathematics and quantitative fields of studies (Ethington & Wolfe, 1988; Fennema, 1980; Sherman & Fennema, 1977). 41 CHAPTER 3: METHODOLOGY The purpose of this study was to investigate gender and school differences in relation to four affective variables in high school mathematics. Also, to describe the patterns of high and low participation of Grade 12 students by gender and school type in choosing mathematics-related careers in the Dominican Republic. Research Design The present study employs the technique of survey research which falls under the category of non-experimental research. The independent variables (IV) are gender, type of school and career choice. The dependent variables (DV) are scores on a closed form questionnaire about attitudes toward, and perceptions of mathematics. This will be explained in more detail in the discussion on instrumentation. Subjects The target population was Grade 12 students enrolled in private and public schools in a major city of the Dominican Republic as well as in rural areas in the province in which the city is located. The sample procedures yielded 25 schools; 5 public urban schools (PuU), 7 public rural schools (PuR), 6 private elite schools (PrE), and 7 private non-elite schools (PrNE) located in the city of Santiago de los Caballeros, which is the second largest city of the country, and seven rural areas in the same province of Santiago. Selection Technique In selecting the sample, a stratified random sampling technique was used. The target population was taken from the province of Santiago and stratified according to school type resulting in four" cells. It was designed to ensure equal representation of the four types 42 of schools (PuU, PuR, PrE, PrNE). In this manner students in the sample represent a broad spectrum of socio-economic status (SES) as each school is representative of a different socio-economic condition. Within each school, 10 to 20 female students and 10 to 20 male students from the Grade 12 class(es) were randomly selected. The strata were constructed according to the information available and provided by the Ministry of Education concerning the number of students per grade and per school in the specific province. The sampling procedure resulted in the selection of 25 schools: a total of 808 students (404 females and 404 males). See Table Bl in Appendix B. While this procedure did not produce numbers of Grade 12 students that were representative of the whole country population, it did ensure that sufficient numbers of students were available within each group of concern in this study in order that appropriate comparisons could be made. Selection of Schools and Subjects In selecting schools for this study, the primary criterion was type of school since each school operates in a particular context (with a particular group of parents, teachers, and students) and is representative of a different socio-economic condition. The intent was to sample from schools that represent urban and rural areas, and different socio-economic levels. The main focus of the study was on those affective factors which impact on both students' choice of careers and gender issues. The available evidence indicates that there are significant gender differences in mathematics achievement favoring males, independent of the school type and of the region in the Dominican Republic (Crespo, 1990). In each school, a random sample of students was selected stratified by gender. In all schools, the same number of males as females was selected to allow comparisons between males and females since the patterns of females' choices appear to be different from those of males (Dick & Rallis, 1991; Gaskell et al., 1993; Hanna & Leder, 1990; Mura, 1987). Those students who were invited to participate in the study were randomly 43 selected by applying a table of random numbers to class lists obtained directly from the schools involved in the study (Glass & Hopkins, 1984). Alternates were selected under the same selection procedures in order to be included in the study in cases where selected students were unavailable. Confidentiality was guaranteed. Instrumentation Each student was surveyed with a questionnaire containing closed questions. The questionnaire was developed by adopting or adapting existing research instruments so that it was suitable for this study and for the Dominican context. McMillan and Schumacher (1989) state that in many cases, instead of preparing a new questionnaire, existing ones could be used or adapted for use. Further, they suggest that if one can locate an existing questionnaire, one will save time and money and may find an instrument with established validity and reliability. The instruments used (both the original questionnaire, and the translated version can be found in Appendices C and D, respectively) were the Fennema-Sherman Mathematics Attitudes Scales (Fennema & Sherman, 1976) designed for middle and high school students. These are paper-and-pencil tests developed by Fennema and Sherman in an attempt to assess various dimensions of attitude toward mathematics. The main purpose of their study was to get information concerning variables related to the election of mathematics courses and information about the learning of mathematics by females. The instrument consists of nine different scales and each scale contains 12 Likert-type items with five possible responses ranging from "strongly disagree" to "strongly agree." Scoring is reversed for negative items and individual scores on each scale are obtained by summing the item values. The scores on each scale can range from 12 to 60, where lower scores are indicative of negative attitude and higher scores are indicative of positive attitude. 44 However, high scores on the Perception of Mathematics as a Male Domain scale indicate a less stereotypic view of mathematics. The nine scales are: 1) The Attitude toward Success in Mathematics Scale, 2) The Mathematics as a Male Domain Scale, 3) The Mother Scale, 4) The Father Scale, 5) The Teacher Scale, 6) The Confidence in Learning Mathematics Scale, 7) The Mathematics Anxiety Scale, 8) The Effectance Motivation in Mathematics Scale, and 9) The Usefulness of Mathematics Scale. Fennema and Sherman (1976) supplied strong statistical evidence supporting the content validity and reliability of the instrument. Only four of the nine scales were used to develop the questionnaire for this study. These constructs were chosen because they are the affective variables that have been found to be most related to participation in mathematics with other populations (Armstrong & Price, 1982; Becker, 1981; Eccles, 1985; Fennema & Sherman, 1977, 1978; Hanna & Leder, 1990; Lantz & Smith, 1981; Leder, 1992; Meyer & Koehler, 1990; Pedro et al., 1981; Perl, 1982; Sherman & Fennema, 1977). The meaning and nature of these constructs have been discussed frequently and thoroughly (Fennema & Sherman, 1976, 1978; Hyde et al., 1990; Meyer & Koehler, 1990; Reyes, 1984). The items were selected to represent students' feelings about mathematics and about themselves as learners of mathematics, background information, post-high school plans, as well as intention to pursue mathematics. The affective questionnaire scores were used as dependent measures in the analysis, which were from section 2 of the questionnaire: Perceived Confidence in Learning Mathematics (items 1 to 12), Attitude toward Success in Mathematics (items 13 to 24), Perception of Mathematics as a Male Domain (items 25 to 36), and Perceived Usefulness of Mathematics (items 37 to 48). Translation, Validation and Reliability of the Questionnaire There is a need to be sure the questionnaire is valid as well as reliable, that is, that each scale and the questionnaire in general measures what it is supposed to measure, 45 consistently (Norusis, 1993). Prieto (1992) argues that accurate translation of instruments to other languages is critical. She contends that one of the central problems of studies of non-English speaking individuals is the equivalence of measurement. Therefore, a multistep approach was used which permitted the establishment of a translation equivalency and ruled out translation problems as a source of data contamination. This multistep approach to translate instruments was decided by following the recommendations given by Prieto (1992). The intent was to produce the best possible product. It should be noted, however, that the purpose of the present study was not to determine the comparability of the Spanish translation of the Fennema-Sherman Mathematics Attitudes Scales to the (original) English version. The multistep approach for the translation of the questionnaire included: (a) three original translations from English to Spanish, (b) three blind back-translations (translation from the Spanish translation to English without knowledge of the original English version), (c) translation review and modification, and (d) field-testing. The process is fully described as follows. English-Spanish translation. The direct translation was performed independently by three individuals. The translators were instructed to provide a translation that was as literal as possible, without adding or deleting words or phrases. This resulted in three Spanish versions of the original questionnaire. Blind back-translation. Three other independent individuals accomplished the blind back translation of the three Spanish versions of the questionnaire. They translated the Spanish questionnaires back into English without having seen the original English version. These back-translators were asked to provide a literal translation that neither corrected translation errors nor interpreted the intent of the English/Spanish translators. Translation review and modification. The blind back-translations were checked by the main researcher for equivalency. The items that produced equivalent English/Spanish-Spanish/English translations were immediately selected. The remaining items were 46 amended through discussion with one of the first translators and one of the back-translators. Some minor changes were made so that these items were suitable to Spanish-speaking respondents (in this case, Dominicans). Thus, despite the few changes necessitated by the translation of the original questionnaire to Spanish, the underlying structure of the new instrument remains virtually identical to its parent. The questionnaire was initially translated into Spanish for sole use in the Dominican Republic. However, it can be easily adapted for use in any other Spanish speaking country. The whole process of translation included individuals from Spanish and English speaking countries such as Canada, Chile, Costa Rica, Dominican Republic, El Salvador, the United States, and Venezuela. Two of these individuals are magistral students in mathematics education, one is a doctoral student in mathematics education, one holds a Ph.D. degree in science education, one is a non-Hispanic bilingual with a master's degree in education, one is a non-Hispanic bilingual with a B.Sc. degree in computer science, and the others are Hispanic bilinguals with bachelor's degrees. Two of these individuals are from the Dominican Republic because it is suggested that utilizing a translator familiar with the community and the culture will often improve translation quality (Brislim, 1980, cited in Prieto, 1992). The different techniques summarized by Prieto (1992) have proven to be efficient in many other studies. Field-testing. The final Spanish questionnaire was field tested for reliability in September, 1994 in the Dominican Republic. "Reliability refers to the consistency of measurement, the extent to which the results are similar over different forms of the same instrument or occasions of data collection" (McMillan & Schumacher, 1989, p. 168). The main goal of the field-testing was to identify initial problems in the administration of the questionnaire, to test the basic methodology and tools to be used, and to collect basic information to help refine the final questionnaire for the present study. The Spanish form was administered to 230 students at one of the major universities in the Dominican Republic, the Pontificia Universidad Catolica Madre y Maestra (PUCMM), located in the 47 city of Santiago de los Caballeros. The students had just completed their high school degree between June and August, 1994 and were just starting their first year of university aiming at many different careers. In addition, the students came from a variety of schools representing private and public schools, from rural and urban areas, and from many parts of the country, not only the province of Santiago. The decisions to be made in the selection of the sample included: 1) the university in which the field testing was conducted, the PUCMM, was arbitrarily selected because it was a familiar environment for the researcher. This was an advantage considering the relatively short period of time available to complete the pilot study, 2) it is at this university where the research centre for which the researcher works is located, 3) the intent was to include a sample in the pilot study similar to the one used in the main study. The subjects were randomly selected within the university and were asked to complete the questionnaire anonymously. Reliability of the Questionnaire (Scales) An analysis of the reliability of the items in the new instrument was conducted to ensure that the stability of the scales was not significantly affected by the translation from English to Spanish. The reliability coefficient of the affective questionnaire was calculated using the responses of the 230 students in the field-testing to the questionnaire. The reliability coefficient for the total set of items, as well as subset (scales) reliabilities, were calculated. The reliabilities were computed using Cronbach's alpha (a) ANOVA procedure which was performed using the SPSS Windows 6.0 computer package (Norusis, 1993). This procedure indicates internal consistency using analysis of variance (items were given equal weights) and is algebraically equivalent to the Hoyt estimate and the Kuder-Richarson 20 (KR-20) analyses (Norusis, 1993). Results are presented in Table 3.1. 48 Table 3.1 Reliability of the Affect Questionnaire (SPSS Output) SPSS Windows 6.0 TOTAL TEST STATISTICS Affect Questionnaire Number of individuals = 227 Number of items = 48 Mean = 198.67 Highest score = 239 Standard deviation = 20.43 Lowest score = 131 Source of variance D.F. S.S. M.S. Individuals 226 1964.51 8.69 Items 47 1297.51 27.61 Residual 10622 9021.62 0.85 Total 10895 12283.63 1.13 Alpha estimate of reliability = 0.90 Cronbach's a for composite = 0.90 As Table 3.1 shows, the total questionnaire was found to be highly reliable, with an alpha estimate of reliability of 0.90. The reliabilities of the scales (shown in Table 3.2) ranged from 0.77 to 0.92. Table 3.2 shows that the Perceived Confidence in Learning Mathematics scale, with a Cronbach's alpha coefficient of 0.92 was the most reliable of the four scales, while the Attitude toward Success in Mathematics scale had the lowest reliability, with a Cronbach's alpha coefficient of 0.77. However, considering that each scale consisted of only 12 items, their reliabilities coefficients of 0.92, 0.77, 0.78, and 0.89, respectively, were relatively high. In addition, scales with Cronbach alpha coefficients around 0.70 are considered to be internally consistent (Kline, 1976). 49 Table 3.2 Total Questionnaire and Scales Reliabilities, Means, Standard Deviations, and Number of Cases Number Mean Standard Alpha Lowest Highest Number of Items Deviation Reliability Score Score of Cases Total Questionnaire 48 198.67 20.43 0.90 131 239 227 Scale 1: Perceived Confidence in Learning Mathematics Scale 2: Attitude toward Success in Mathematics Scale 3: Perception of Mathematics as a Male Domain Scale 4: Perceived Usefulness of Mathematics 46.62 9.30 0.92 50.89 6.16 0.77 50.42 6.65 0.78 50.62 7.88 0.89 18 60 229 35 60 228 26 60 229 21 60 228 Dimensionality of the Questionnaire (Scales) A factor analysis of the items in the total questionnaire and within each of the scales was conducted at the next stage of analysis of the pilot data. The purpose of this process was to determine common underlying dimensions on which of the criterion variables were located. Eigenvalues represent variance, and an eigenvalue of 1.0 or greater is a commonly used criterion for factor identification (Norusis, 1993; Tabachnick & Fidell, 1989). Using this criterion, items were grouped into factors in the total questionnaire and within each of the scales. The loading of an item into its respective factor was considered significant if its correlation with the factor was greater than 0.30. Tabachnick and Fidell (1989) indicate that factor loadings above 0.30 are eligible for interpretation. Also, when an item loaded into more than one factor at the 0.30 level, it was assigned to the factor into which it loaded at 50 the highest level. The factors or dimensions intended to be measured by the questionnaire are: Perceived Confidence in Learning Mathematics (Confmat), Attitude toward Success in Mathematics (Attsmat), Perception of Mathematics as a Male Domain (Matmdom), and Perceived Usefulness of Mathematics (Usefmat). Thus, factors other than the four specified above were of no interest in the analysis. The factor extraction technique performed through SPSS Windows 6.0 on the 48 items was principal components analysis (PCA). PCA analyzes variance and its goal is to extract maximum variance from a data set with each component. The solution is mathematically unique. According to Tabachnick and Fidell (1989), the principal components are ordered so that the first component extracts the most variance and the last component the least variance. Further, their use in other analyses (e.g., as DVs in MANOVA) greatly facilitate interpretation of results. In order to improve the interpretability of the solution, rotation was used after extraction. The rotation technique used was varimax which is a variance maximizing procedure. Tabachnick and Fidell (1989) write, "The goal of varimax rotation is to simplify factors by maximizing the variance of the loadings within factors, across variables" (p. 628). These authors also explain that varimax reapportions variance among factors so that they become relatively equal in importance. The first (exploratory) factor analysis was performed on the total questionnaire comprising the 48 affective items. No factor analysis was conducted on the five background variables (school type, gender, age, post-high school plans, and career choice) because these variables are categorical variables and no factor structure among them was of interest to the present study. Also, three of these variables are used as independent variables in further analyses in order to answer research question number 2. Results of the first principal components analysis are shown in Table 3.3 on page 52. 51 The data in Table 3.3 show that the maximum number of factors (eigenvalues greater than 1) is 11. However, retention of 11 factors seems unreasonable given there are only 48 items, so sharp breaks in size of eigenvalues are sought. The differences between the first four factors' eigenvalues are large (i.e., >0.7), but there is little difference in variance explained between factors 4 and 5 and thereafter. That is, factor 5 adds little to factors 1 to 4, and so on. In addition, the data in Table 3.3 also show that 44.4% of the total variance is attributable to the first four factors. The remaining seven factors together account for only 21.1% of the variance. This is taken as evidence that the 48 items would yield four strong factors with a cumulative variance of 44.4 percent. A varimax rotation grouped the items (after 11 iterations) as shown in Table 3.4 on page 53. A second (confirmatory) factor analysis on the 48 items of the total questionnaire was performed by setting the analysis to four factors. The purpose of this was to verify that the 48 items were measuring four distinctive constructs as suggested by the first analysis. The results are the same as those shown in Table 3.3. The PCA extracted four factors (Confmat, Attsmat, Matmdom, and Usefmat) with a cumulative variance of 44.4 percent, and the varimax rotation converged in ten iterations grouping the items in four clusters as reported in Table 3.5 on page 54. However, the fact that some items loaded in two factors and some items failed to correlate either uniquely or significantly higher with the proposed scale may reflect that such items may be poorly worded, especially five of the negatively worded items intended to measure Matmdom (Q19, Q20, Q22, Q23, and Q24) and one of the negatively worded items intended to measure Usefmat (Q47). The next three pages show Table 3.3, Table 3.4, and Table 3.5 corresponding to PCA and varimax rotated factor loadings for all 48 items in the total questionnaire. 52 Table 3.3 Principal Components of the Total Questionnaire Factor Eigenvalue Percent of Variance Cumulative Percent 1 10.5057 21.9 21.9 2 4.5321 9.4 31.3 3 3.7903 7.9 39.2 4 2.4974 5.2 44.4 5 2.1721 4.5 49.0 6 1.6722 3.5 52.4 7 1.4438 3.0 55.4 8 1.3352 2.8 58.2 9 1.2576 2.6 60.8 10 1.1662 2.4 63.3 11 1.0696 2.2 65.5 0.9723 2.0 67.5 0.9404 2.0 69.5 0.8989 1.9 71.4 0.8638 1.8 73.2 0.7851 1.6 74.8 0.7587 1.6 76.4 0.7464 1.6 77.9 0.7021 1.5 79.4 0.6494 1.4 80.7 0.6129 1.3 82.0 0.6087 1.3 83.3 0.5770 1.2 84.5 0.5304 1.1 85.6 0.5027 1.0 86.6 0.4486 0.9 87.6 0.4434 0.9 88.5 0.4333 0.9 89.4 0.4145 0.9 90.3 0.4048 0.8 91.1 0.3639 0.8 91.9 0.3404 0.7 92.6 0.3339 0.7 93.3 0.3217 0.7 93.9 0.3178 0.7 94.6 0.2995 0.6 95.2 0.2711 0.6 95.8 0.2584 0.5 96.3 0.2468 0.5 96.9 0.2231 0.5 97.3 0.2135 0.4 97.8 0.2039 0.4 98.2 0.1862 0.4 98.6 0.1653 0.3 98.9 0.1518 0.3 99.2 0.1378 0.3 99.5 0.1237 0.3 99.8 0.1059 0.2 100.0 53 Table 3.4 Varimax Rotated Factor Loadings of the Total Questionnaire Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 Factor 9 FactorlO Factorl 1 Ql 0*6513 0.0860 0.1319 0.0823 0.0576 -0.1067 -0.0368 0.4068 -0.0236 -0.0197 0.1962 Q2 e t n a * 0.2960 0.1231 0.0391 -0.0112 -0.0648 0.0372 0.3619 0.0979 0.0744 0.2667 Q3 0.3936 0.1108 0.1334 0.1755 0.0149 -0.0073 -0.0414 0.0336 -0.0103 -0.1584 Q4 0.4210 0.2461 0.0889 0.1186 -0.0373 -0.1212 0.0698 0.2134 0.1096 0.0779 Q5 0.4203 0.3410 0.1848 0.1234 0.1202 0.0281 0.1058 mm -0.1705 -0.1045 0.0024 06 0.7364 0.2164 0.1328 0.1399 0.0290 -0.0360 0.0913 0.2986 -0.0844 -0.0490 0.0781 Q7 mm 0.0700 0.0009 0.0664 0.0295 0.0379 0.0198 0.0992 0.1193 0.0155 0.0514 Q8 0.7213 0.1564 0.0332 0.1846 0.1060 -0.0252 0.0311 0.1468 -0.0092 0.0060 0.0740 09 %35$6 0.0330 -0.0724 0.1512 0.0949 -0.0271 0.0625 0.1680 0.0885 -0.1191 -0.1040 Q10 08374 0.1216 0.0119 0.1361 -0.0342 -0.0561 0.0274 0.0278 0.1025 -0.0305 0.0366 QH o . ? m 0.1232 0.0036 0.1718 0.1081 0.0085 0.0519 -0.1432 -0.0305 0.0463 -0.0683 Q12 &T937 0.2058 0.0042 0.1735 0.0871 -0.0826 0.0129 -0.0566 0.0197 0.0131 -0.0777 Q13 0.0738 -0.0006 -0.0049 -0.0989 -0.0382 -0.0922 0.1972 0.1757 0.1970 -0.3188 Q14 0.0305 0.0262 0.0486 0.0251 -0.0600 -0.1539 0.2183 0.0281 0.1756 -0.4573 Q15 -0.0339 0.1160 turn 0.1273 -0.0075 0.0037 0.0758 0.0639 -0.0785 -0.0723 -0.0866 Q16 0.0193 0.2219 mm 0.1364 0.0617 -0.015 0.0578 0.0217 -0.0439 -0.0656 0.0852 Q17 0.1051 0.1353 0.8292 0.0758 -0.0388 -0.066 0.1443 -0.0216 -0.0397 -0.0806 0.1082 Q18 0.0325 0.1366 0.7151 0.0516 -0.0893 0.1128 0.1197 -0.0358 0.1435 -0.1102 0.2636 Q19 0.1523 0.0534 0.1430 0.0515 0.1352 0.0447 0.2451 -0.0655 0.7085 0.0418 0.0795 Q20 0.0356 0.0144 -0.0826 0.1058 0.1655 0.0632 0.1998 0.1319 &7402 -0.0725 -0.0566 Q21 0.1423 -0.0080 0.1422 0.0890 0.0497 0.0497 &745S -0.0954 0.1373 -0.1468 -0.0758 Q22 0.0286 -0.0961 0.1132 0.1101 0.1040 -0.0293 0.7344 -0.0127 0.2022 0.0494 0.1473 Q23 -0.0821 0.3124 0.0227 -0.0866 0.2768 0.0605 0.4957 0.0846 0.2842 -0.0614 -0.3145 Q24 0.0409 0.0538 -0.0267 0.0165 0.0970 0.0965 0.7043 0.1186 0.0149 0.2071 0.0371 Q25 -0.0241 -0.1304 0.0966 0.0049 0.0881 0.73S8 -0.0049 -0.0494 0.1131 0.1080 0.0556 Q26 -0.0815 -0.0711 0.0296 0.0570 0.1179 0 J o » r -0.0076 0.0257 -0.0131 0.0272 0.0499 Q27 -0.0438 0.0900 -0.0993 -0.1314 0.1893 0,«265 0.0874 0.0108 -0.0685 0.0645 -0.0130 Q28 -0.0437 0.1282 -0.0259 -0.0714 0.1793 J0J9UI 0.0731 -0.0708 0.0666 0.1212 -0.0635 Q29 -0.0369 0.1045 -0.0980 0.0168 0.0711 6.1304 -0.0372 0.0421 0.0358 07114 0.0008 Q30 -0.1064 0.1374 0.0340 0.0667 0.1830 0.2352 0.1560 -0.0662 -0.1314 0.5508. 0.1288 Q31 0.1009 -0.0626 -0.0098 -0.0099 0.0712 0.1848 0.0514 -0.0077 0.3291 -0.1029 Q32 0.1910 0.0400 -0.0182 0.0370 0 4043 0.0831 0.0400 0.0659 0.0236 0.1763 mm Q33 0.0358 -0.0741 -0.0660 0.0650 06702 0.2073 -0.0007 -0.0250 0.1200 0.2701 0.1449 Q34 0.0523 0.0518 0.0111 0.0550 0.7560 0.1730 0.1303 0.0860 -0.0557 -0.0899 0.1335 Q35 0.0176 0.0016 -0.0406 0.0941 0.77K4 0.1286 0.0754 0.0851 0.0847 0.0163 0.0219 Q36 0.1851 0.0177 -0.0159 0.0474 0.6447 0.0796 0.0010 -0.2026 0.2209 -0.0400 -0.0652 Q37 0.2739 067*7 0.1350 0.2570 0.0648 -0.0306 -0.1057 -0.0124 0.0127 0.1308 -0.0213 Q38 0.2810 0.2617 0.0948 0.0025 -0.0283 0.1774 0.1129 -0.1503 0.0257 -0.0909 Q39 0.1800 0 7477 0.1988 0.1520 -0.0367 -0.0423 -0.0677 0.0941 0.1028 0.1102 0.1012 Q40 0.1314 0.0792 0.1494 0.0766 0.0931 0.1471 0.0762 -0.1319 -0.0302 -0.3582 Q41 0.1941 0.7060 0.1130 0.3226 -0.1155 -0.0292 -0.1042 0.0702 0.0501 0.0258 0.1105 Q42 0.1455 0<WH9 0.0327 0.2870 -0.0203 0.0523 0.0514 0.1530 0.1627 0.0492 0.1077 Q43 0.2326 0.2387 0.0598 0.1198 -0.0220 0.0734 0.0309 0.0401 -0.0445 0.0542 Q44 0.1936 0.3153 0.1359 -0.0334 -0.0069 0.0351 -0.0405 0.0029 -0.0903 -0.0252 Q45 0.1755 0.3106 0.0727 0.7O41 0.0306 -0.0575 -0.0219 0.1995 0.0236 0.0803 0.0156 Q46 0.1760 0.1912 0.1567 063% 0.2277 0.0613 0.0722 0.2119 -0.0950 -0.0841 -0.1114 Q47 0.2113 -0.0117 0.0102 0.5504 0.0185 -0.0474 0.2523 0.0127 0.1288 0.3055 -0.0185 Q48 0.3167 0.2091 0.1442 05*67 0.0233 -0.1349 -0.0777 -0.0325 0.2310 0.1147 0.1265 Note: Greater salient loadings are shaded and the dotted lines indicate the breaks between the theoretical constructs of the items. 54 Table 3.5 Confirmatory Varimax Rotated Factor Loadings of the Total Questionnaire Item Factor 1 Factor 2 Factor 3 Factor 4 Communality Ql 0.7145 0.1723 -0.0414 0.0805 0.6767 Q2 0,5792 0.2924 0.0128 0.1130 0.5798 Q3 0.2606 -0.0310 0.1692 0.6387 Q4 0.2764 -0.0087 0.1695 0.7439 Q5 &5tl% 0.4007 0.0595 0.2046 0.6960 . Q6 &7S73 0.2819 0.0078 0.1134 0.7416 Q7 0+76U3 0.1102 0.0884 -0.0349 0.6948 Q8 0,7232 0.2378 0.0812 -0.0071 0.6199 Q9 0 7767 0.0717 0.0713 -0.0493 0.6793 Q10 0.1531 -0.0126 -0.0136 0.7533 Q l l 0.1891 0.1138 -0.0554 0.7134 0.2408 0.0334 -0.0362 0.7268 Q13 0.0444 0.1229 -0.1115 f>*y64 0.7617 Q14 0.0009 0.1934 -0.1085 i 0.7911 Q15 -0.0349 0.2163 -0.0468 % o/mi 0.6060 Q16 0.0261 0.3031 -0.0007 0,7687 0.7804 Q17 0.0839 0.1881 -0.0298 0.7844 0.7653 Q18 0.0200 0.1547 0.0447 0.6722 Q19 0.2717 -0.1007 0.3725 0.2882 0.6438 Q20 0.2333 -0.1279 0.1259 0.6645 Q21 0.2431 -0.1855 0.3417 % 0.6648 Q22 0.2015 -0.2379 0.3460 0.6512 Q23 0.0508 0.0287 0.2698 0.6289 -0.0675 04*47 0.1800 0.5789 Q25 -0.2233 0.0499 IKS*'** 0.0195 0.6104 Q26 -0.2726 0.1398 0.54*2 -0.0474 0.6880 Q27 -0.2655 0.1623 0,-6219 -0.1501 0.7728 Q28 -0.2578 0.2004 QA277 -0.0663 0.7139 Q29 -0.1024 0.2330 QMH -0.1634 0.5548 Q30 -0.1790 0.2510 {)Aim -0.0266 0.4906 Q31 0.1226 -0.0385 0.5185 -0.0105 0.4592 Q32 0.2439 0.0755 0.4148 -0.1197 0.5989 Q33 0.0538 0.0029 fi 4575 -0.1416 0.6165 Q34 0.1304 0.0427 o . * m -0.0147 0.6634 Q35 0.1200 0.0110 0,6405 -0.0481 0.6541 Q36 0.1992 -0.0373 0,5144 -0.0417 0.5547 Q37 0.2720 Q 7ttSK 0.0183 0.0839 0.6514 Q38 0.2867 UJ5763 0.0063 0.2890 0.6434 Q39 0.2178 -0.0300 0.1801 0.7036 Q40 0.1248 0+5*>7 0.0977 0.1490 0.6486 Q41 0.2406 0.7417 -0.1012 0.0927 0.6983 Q42 0.2418 ft,#7$3 0.0952 0.0859 0.6627 Q43 0.3664 UASiS 0.1301 0.0890 0.5700 Q44 0.2820 -0.0014 0.1591 0.6128 Q45 0.3354 t>>mi 0.0298 0.0923 0.6800 Q46 0.3084 0.1867 0.1832 0.6354 Q47 0*337* 0.2016 0.2016 0.0907 0.5245 Q48 <U2u2 0.3948 0.0156 0.1231 0.5612 Note: Greater salient loadings are shaded and the dotted lines indicate the breaks between the theoretical constructs of the items. In addition, the scree test (Cattell, 1966 cited in Norusis, 1993; and in Tabachnick & Fidell, 1989) of eigenvalues plotted against factors was used as a second criterion to find the number of factors measured by the questionnaire. Experimental evidence indicates that 55 the scree begins at the &th factor, where k is the true number of factors (Norusis, 1993). Figure 3.1 shows the screen output for the pilot data produced by SPSSX FACTOR. What one is looking for is the point where a line drawn through the points changes direction. As can be seen in Figure 3.1, the first four eigenvalues are around the same line. After that, three other different lines, with noticeably different slopes, best fit the remaining seven points. That is, the plot shows a distinct break between the steep slope of the large factors and the gradual trailing off of the rest of the factors. Therefore, there appear to be about four factors (Confmat, Attsmat, Matmdom, and Usefmat) in the questionnaire as indicated in pilot data of Figure 3.1. 12 -r 10 + E 8 + g e n v 6 + a u e s 4 4-2 4-0 H 1—I—i-H 1—I—I 1—I h 1 2 3 4 5 6 7 8 9 10 11 \—\ Factors Figure 3.1 Screen output for pilot data produced by SPSSX FACTOR. 56 The third factor analysis involved the 12 items measuring Perceived Confidence in Learning Mathematics. Table 3.6 lists the results of the principal components analysis. Table 3.6 Principal Components of the Perceived Confidence in Learning Mathematics Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 6.5916 54.9 54.9 2 1.2239 10.2 65.1 0.7023 5.9 71.0 0.6227 5.2 76.2 0.5197 4.3 80.5 0.4817 4.0 84.5 0.4084 3.4 87.9 0.3693 3.1 91.0 0.3302 2.8 93.7 0.3142 2.6 96.4 0.2379 2.0 98.3 0.1982 1.7 100.0 Table 3.6 shows that the 12 items yield two factors with eigenvalues greater than 1. However, by looking at the results of the data in Table 3.6, it appears that this scale is, in fact, unidimensional with a large proportion of the variance (54.9%) accounted for by a single factor (Confmat). This satisfies Reckase's (1979) minimum criterion for establishing the unidimensionality of the scale. Reckase's (1979) indicates that when a dominant first factor is present, fit is directly related to the first eigenvalue. The second eigenvalue, 1.2239, accounted for 10.2% of the total variance. After three iterations the rotated factor matrix grouped the items into the two clusters shown in Figure 3.2. 57 Factor 2 Factor 1 Scale i tem Figure 3.2 Correlations of the Perceived Confidence in Learning Mathematics scale's items with factors. The fourth factor analysis involved the 12 items measuring Attitude toward Success in Mathematics. Results of the principal components analysis are shown in Table 3.7. Table 3.7 Principal Components of the Attitude toward Success in Mathematics Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 3.8213 31.8 31.8 2 2.5068 20.9 52.7 3 1.0944 9.1 61.9 0.9324 7.8 69.6 0.7643 6.4 76.0 0.6233 5.2 81.2 0.5655 4.7 85.9 0.5113 4.3 90.2 0.4430 3.7 93.9 0.3593 3.0 96.8 0.1946 1.6 98.5 0.1838 1.5 100.0 58 The principal components analysis extracted three factors with eigenvalues greater than 1.0, which accounted for a cumulative variance of 61.9 percent. The first and second eigenvalue, 3.8213 and 2.5068 respectively, accounted for 52.7% of the variance. Thus, the data in Table 3.7 show that this scale is defined by the first two factors. Factor 1 shows significant loadings for items Q13 to Q18, Factor 2 correlated significantly with items Q21 to Q24 while Factor 3 correlated higher with items Q19 and Q20. This suggests that there is an underlying attribute common to the items in each of the three factors. A varimax rotation grouped the items (after 7 iterations) as shown in Figure 3.3. 0.9 - -0.8 • • 0.7 - -eu 0.6 .9 •a 0.5 CQ t 0.4 S3 0.3 - -C3 0.2 0.1 i l Factor 1 S Factor 3 E U Factor 2 co £J co CM CM CM o o o o o o o o o o o o • r - T - T - - i - - > - - ' - C M C M Scale item Figure 3.3 Correlations of the Attitude toward Success in Mathematics scale's items with factors. The twelve items measuring Perception of Mathematics as a Male Domain were then factor analyzed in the fifth step and the principal components analysis is shown in Table 3.8. 59 Table 3.8 Principal Components of the Perception of Mathematics as a Male Domain Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 3.9993 33.3 33.3 2 1.7670 14.7 48.1 3 1.1031 9.2 57.2 0.8132 6.8 64.0 0.7950 6.6 70.6 0.7230 6.0 76.7 0.7003 5.8 82.5 0.6235 5.2 87.7 0.4850 4.0 91.7 0.4136 3.4 95.2 0.3439 2.9 98.1 0.2331 1.9 100.0 Similarly, the PCA extracted three factors (eigenvalues > 1.0) accounting for a cumulative variance of 57.2%. Table 3.8 suggests that this scale is defined by only two factors with the first accounting for the larger proportion of the variance (33.3%). After five iterations the rotated factor matrix grouped the items into clusters shown in Figure 3.4. 0.9 j 0.8 -• 0.7 -• 0.6 --0.5 -• 0.4 --0.3 --0.2 --0.1 •• 0 --ee a •3 ee o u © u ee b LO CD s OO O) o t— CM CO LO <n CJ CM CM CM CM CO 00 CO CO OO CO CO o o o o o o a o o o a o Factor 2 Factor 3 Factor 1 Scale item Figure 3.4 Correlations of the Perception of Mathematics as a Male Domain scale's items with factors. 60 The last factor analysis involved the 12 items measuring Perceived Usefulness of Mathematics. The principal components analysis is reported in Table 3.9. Table 3.9 Principal Components of the Perceived Usefulness of Mathematics Scale's Items. Factor Eigenvalue Percent of Variance . Cumulative Percent 1 5.4493 45.4 45.4 2 1.3720 11.4 56.8 0.8820 7.4 64.2 0.7795 6.5 70.7 0.6196 5.2 75.9 0.5746 4.8 80.6 0.5087 4.2 84.9 0.4467 3.7 88.6 0.4076 ' 3.4 92.0 0.3717 3.1 95.1 0.3058 2.5 97.6 0.2825 2.4 100.0 Based on the results reported in Table 3.9, a one-factor solution is suggested. The PCA of these 12 items resulted in two eigenvalues greater than 1.0. The first eigenvalue, 5.4493, accounted for 45.4% of the variance. This clearly satisfies Reckase's (1979) minimum criterion for establishing the unidimensionality of the scale. Therefore, this scale is also unidimensional with a large proportion of the variance (45.4%) accounted for by a single factor (Usefmat). The second eigenvalue, 1.3720, accounted for 11.4% of the total variance. A varimax rotation grouped the items (after 3 iterations) as shown in Figure 3.5. 61 Factor 1 Factor 2 Scale item Figure 3.5 Correlations of the Perceived Usefulness of Mathematics scale's items with factors. Analysis of the reliability as well as factor analyses were also performed on the main data, following the same procedures used here with the pilot data. The results of these analyses on the main data resemble those of the pilot data and therefore confirm that the instrument used in the present study is very stable. The results of the reliability and factor analyses for the main data are reported in Appendix F. In summary, the reliability tests and the factor analyses performed on the pilot and main data indicate that the Spanish questionnaire is reliable and measures four distinct affective factors. The factor analyses performed on the pilot data were used to determine the dimensionality of the scales and to validate and finely tune the multidimensional instrument. Results of the factor analyses showed strong support for the theoretical structure of the scales. It was hoped that the approach used for the translation of the instrument would guarantee that the resulting questionnaire would keep the validity reported for the original English version. This is supported by the reliability tests and the factor analyses reported in this section. 62 Data Gathering and Procedures This research project was carried out by the principal researcher with the assistance of staff members from the Research and Curriculum Development Centre for Mathematics Education at PUCMM in Santiago de los Caballeros, Dominican Republic. With the approval of all the sampled schools, students who agreed to participate in the main study responded to a questionnaire form designed to assess their attitudes toward mathematics, their post-high school plans, and intended career choice; it was designed to explore the context within which students develop their interest in mathematics courses. Students completed the survey during class time in all schools. Each student responded to all 52 items, and the average time taken to do so was 23 minutes. Great effort was made in the sample schools to ensure that the questionnaire would be administered in a consistent manner across schools. The questionnaire had written instructions on how to respond to the items as well as an example showing how to mark the answers. The questionnaire administrator(s) read these instructions aloud after distributing the questionnaire to the students. A 100% response rate was achieved. This means that when a questionnaire administrator arrived at a selected school, randomly selected forty students, gave the selected students the questionnaires to complete, and received the forty completed questionnaires back in the allotted time for this purpose. More specifically, 808 questionnaires were distributed to the random sample of students and 808 completed questionnaires were returned. In surveying students from each school the intent was to investigate their likes and dislikes about mathematics, their views and perceptions about the subject, their intention to pursue a mathematics-related career, and the differences in the results between males and females and by school type. To encourage honest responses all subjects were instructed to respond anonymously. 63 Data Analyses For the analyses and interpretation of the data a combination of approaches was used with inferential statistics being the main approach for analyses. The statistical procedure for simultaneously analyzing the variables involved in this study was multivariate analysis of variance (MANOVA) conducted using the SPSS MANOVA program. For testing differences in the four affective variables among schools and by gender, a 2x3x4 (Gender x Career choice x School type) factorial MANOVA was performed with the mean scores of four measures in the affective questionnaire of the students being the unit of analysis. Multivariate statistical techniques were used because they allow one to deal with all of the data in a single analysis instead of a series of univariate analyses; thus avoiding the increased probability of obtaining a spurious result. Tabachnick and Fidell (1989) note "with the use of multivariate statistical techniques, complex interrelationships among variables are revealed and are accounted for in statistical inference" (p.4). Further, Tabachnick and Fidell (1989) contend that multivariate techniques were mainly developed for use in non-experimental research, the most common form being the survey. Bray and Maxwell (1985) and Tabachnick and Fidell (1989) point out that the response variables are usually interrelated in highly complex ways, and univariate or bivariate statistics are not sensitive to this complexity. Limitations of the Design One limitation is the fact that by using a closed form questionnaire the respondent cannot provide an in-depth explanation of some issues of interest. The closed form questionnaire obviously relies on the honesty of the individual in expressing his/her feelings. "A questionnaire is relatively economical, has standardized questions, can assure anonymity, and questions can be written for specific purposes" (McMillan & Schumacher, 64 1989, p.254). Dick and Rallis (1991) suggest that given the inherent limitations of surveys and the rarity of females choosing careers in engineering and science, interviews with these females might prove to be the best step toward gaining a more detailed picture of the forces and factors forming their career choices. A second limitation is that the sample does not represent all students in Grade 12 attending public and private schools in the Dominican Republic because of differences among regions. The schools in the sample are only from one city and seven rural areas of a province in the country; also, only students in the Traditional program were selected to participate in the study. Thus, although the sample is representative, the results should be cautiously extrapolated to the whole country's population of Grade 12 students. 65 CHAPTER 4: RESULTS This chapter is concerned with reporting the description of the data, the results on the mathematics attitudes scales, and the statistical analyses. Summaries of results of data analyses are presented by means of tables and figures with their corresponding interpretations. They are presented following the order of the research questions that give shape to this study. Description of the Data The data were obtained at the beginning of the second half of the 1994-1995 school year. The sample used in the main study consisted of 808 Grade 12 students (404 males and 404 females) from 25 schools located in the city of Santiago de los Caballeros and seven rural areas in the same province. The schools represent four different types of schools in the country: Public Urban (PuU), Public Rural (PuR), Private Elite (PrE), and Private Non-elite (PrNE). These have all been explained in more detail in chapter three. The data base consisted of five background variables and means of four affective measures from males and females in 25 schools at the Grade 12 level. Table 4.1 and Figure 4.1 combined provide information about the distribution of four of the five background variables. Table 4.1 summarizes the post-high school plans of the students by school type and gender of the subject. As could be expected, a very high proportion of Grade 12 students indicated that they would go on to the university (91.8% altogether). However, this includes the 5.1% who plan to take a year off and then go to the university. Therefore, 86.7% of Grade 12 students plan to go on to the university immediately after having completed high school. This is consistent with the report that 85% of secondary school graduates in the Dominican Republic go on to higher education (SEEBAC, 1984; Troxell, 1987). 66 Table 4.1 Post-High School Plans of Students by School Type and Gender Post-high school plans School Type P u R P u U P r N E P r E Gender Gender Gender Gender M F (n= 101) (n= 101) M F (n= 101) (n= 101) M F (n= 101) (n= 101) M F (n= 101) (n= 101) - go on to university (n= 394) - seek part-time job & go to university (n= 307) - seek full-time job (n=5) - take year off & then go to university (n=41) - take year off & then seek a job (n=2) -1 have other plans (n= 33) -1 have not decided (n= 26) 32.7% 37.6% 46.5% 49.5% 0.0% 0.0% 7.9% 4.0% 1.0% 0.0% 5.0% 2.0% 6.9% 6.9% 35.6% 45.5% 43.6% 50.5% 2.0% 1.0% 6.9% 1.0% 0.0% 0.0% 5.0% 1.0% 6.9% 1.0% 55.4% 50.5% 31.7% 39.6% 0.0% 2.0% 7.9% 3.0% 1.0% 0.0% 4.0% 4.0% 0.0% 1.0% 62.4% 70.3% 22.8% 19.8% 0.0% 0.0% 5.0% 5.0% 0.0% 0.0% 6.9% 5.0% 3.0% 0.0% Across school types, a greater proportion of females than males indicated that they will study in the university immediately after completing high school. Furthermore, a greater proportion of students (regardless of gender) from the private schools indicated that they will continue to study in the university immediately after having completed high school (88.1% private vs. 85.4% public). On the other hand, a greater proportion of students from the public schools indicated their intentions to get a part-time job and go to the university (28.5% private vs. 47.5% public). Most of the undecided or who have other plans are from the public schools and most of them are males. Nevertheless, many of these students indicated by writing on the questionnaire that they plan to go to a technical or vocational post-high school institution in order to pursue studies. Thus, that increases the proportion of students who chose a future 67 field of study to 98.3% altogether. This fact reflects a minor flaw in this section of the questionnaire. It can be seen that less than 1% (0.87%) indicated their intention to get a full-time job (0.50% males and 0.37% females). Not surprisingly, none of these students come from the PrE schools. Figure 4.1 Age of students by school type As can be seen in Figure 4.1, the largest proportion of young students (15 - 17 years old) are in the private schools (73.9%) while the older students (18 or more years old) are in the public schools (67.1%). In general, most of the students in the private schools are 16 - 17 years old whereas most of the students in the public schools are 68 18 - 19 years old. For example, in the PuR schools, 28.0% are 18 and 24.0% are 19, in the PuU schools, 22.9% are 18 and 27.9% are 19 whereas in the PrNE schools, 17.9% are 18 and 14.4% are 19, and in the PrE schools, 9.5% are 18 and 2.5% are 19. Further, it is interesting to note that 16.5% (PuR), 14.9% (PuU), 7.0% (PrNE), and 1.0% (PrE) are 20 years old or more. While it is not within the scope of this study, it is important to point out that these figures reflect the discrepancy of unequal entry time of the students into the elementary school system, and the subsequent results. It has to do with the fact that the students in the private schools begin pre-school when they are 4 years old leading to an early start in Grade 1, while the students in the public schools do not go to pre-school and are not eligible for entry into Grade 1 until they are 7 years old. Therefore, this leads to an unequal Grade 12 finishing age between private and public school students (see Appendix A). This reflects one of the disadvantages that public school students (not able to pay for private education) face. This also contradicts the policy of formal equality for all social sectors in which the Dominican educational system is said to be based. Even when comparing the combined number of students who are 18 years and up in the private schools versus those who are 19 years and up in the public schools, the difference between the two groups is still in detriment of the public school students (26.1% private vs. 41.7% public respectively). This has far-reaching implication for post secondary prospects and career expectations, and underscores the problem in the Dominican Republic school system. Students' answers to questions 1 and 4 in Section 1 of the questionnaire were used in the analyses of the data to answer research questions la (How do high school males and females differ in terms of their intended career choice?) and lb (How do high school students from different types of schools differ in terms of their intended career choice?). The statistical technique used for testing differences in proportions was the chi-square test of association (Glass & Hopkins, 1984) by using the SPSS Windows 6.0 computer package. 69 Research Question la How do high school males and females differ in terms of their intended career choice? Table 4.2 Males' and Females' Career Choice (or Intended Field of Study) HMC MMC LMC N Males 60.7% 21.6% 17.8% 394 (n=239) (n=85) (n=70) Females 31.5% 32.3% 36.3% 400 (n=126) (n=129) (n=145) Overall 46.0% 27.0% 27.1% 794 (n=365) (n=214) (n=215) Chi-square = 70.15; df = 2; p< 0.0001 Notes: i) LMC indicates low-mathematics related career choice, it includes careers requiring only one or two basic courses of mathematics, such as music, law, medicine, sociology, etc. ii) MMC indicates middle mathematics-related career choice, it includes careers requiring many more than two courses of basic mathematics, but not requiring a strong background of advanced mathematics, such as accounting, architecture, public administration, banking, etc. iii) HMC indicates high mathematics-related career choice, it includes careers requiring a strong background of advanced mathematics, such as computer science, electronic engineering, mathematics, physics, etc. Students were asked to report their intended future career (or field of study) in the survey questionnaire (section 1, question 4). As can be seen in Table 4.2, there is a significant gender difference regarding students' career choice %2 (2, N = 794) = 70.15; p < 0.0001. A greater proportion of female students than male students indicated that they intended to pursue a LMC (36.3% females versus 17.8% males) or a MMC (32.3% females versus 21.6% males) while a greater proportion of males (60.7%) than females (31.5%) indicated that they intended to pursue a HMC. The ratio of males to females choosing a HMC was nearly 2 to 1. It has been reported that the ratio of males to females electing careers in science and engineering approaches 3 to 1 in the United States 70 (Dick & Rallis, 1991; Rosenberg, 1987) and 7 to 1 in Canada (Hanna & Leder, 1990). This pattern can also be seen by school type. Table 4.4 shows that in all types of schools, a greater proportion of males than females intend to pursue a HMC whereas a greater proportion of females than males intend to enroll in the other two choices (MMC and LMC). By examining Table 4.4, it can be seen that across all types of schools, LMC is the least chosen and HMC is the most chosen by males. The opposite holds for females, except in the PuU schools in which 36.6% chose a HMC and 27.7% chose a LMC. Research Question lb How do high school students from different types of schools differ in terms of their intended career choice? Table 4.3 School Type Students' Career Choice (or Intended Field of Study) HMC MMC LMC N PuR 48.0% 23.0% 29.0% 200 (n=96) (n=46) (n=58) PuU 52.0% 26.5% 21.5% 200 (n=104) (n=53) (n=43) PrNE 47.7% 26.4% 25.9% 193 (n=92) (n=51) (n=50) PrE 36.3% 31.8% 31.8% 201 (n=73) (n=64) (n=64) Overall 46.0% 27.0% 27.1% 794 (n=365) (n=214) (n=215) Chi-square = 13.30; df = 6; p < 0.05 The data in Table 4.3 show significant school differences regarding career choice X 2 (6, N = 794) = 13.30; p < 0.05). In general, a greater proportion of students from the 71 public schools than from the private schools intend to pursue a HMC. In addition, a greater proportion of students from the PuU schools (52.0%) than from the PuR schools (48.0%) intend to pursue a HMC and a greater proportion of students from the PrNE schools (47.7%) than from the PrE schools (36.3%) also plan to enroll in a HMC. Students in the private schools come from families of high and middle socio-economic status. Moreover, most of their parents are professionals (engineers, lawyers, physicians, accountants, etc.) and business people, as opposed to the students in the public schools whose parents have lower levels of schooling (many of them are illiterates), and are rather workers in both the public and private sectors. However, the finding that a greater proportion of students from the public schools than from the private schools intend to pursue a HMC may be attributable to students coming from families of low socio-economic status perceiving mathematics and science as a way to a high paying career (computers, electronics, civil engineering, etc.). In contrast, students coming from families of high and middle socio-economic status often do not have to worry about making money and are therefore more inclined toward the humanities and the arts (intellectual, creative areas) or politics and business which do not require advanced mathematics and science. Concerning the other two categories of career choice, the results are mixed. The largest proportion of students planning to pursue a MMC as well as a LMC are from the PrE schools (31.8% for each of MMC and LMC). The lowest proportion of students planning to pursue a MMC are from the PuR schools (23.0%). There is not any difference between the PuU and the PrNE schools regarding the MMC. Similarly, the lowest proportion of students planning to enroll in a LMC are from the PuU schools (21.5%) followed by the PrNE schools (25.9%). Surprisingly, the data in Table 4.3 also show that, in general, HMC is the most frequently chosen (46.0%) by Grade 12 students in the Dominican Republic. There is not any difference between the MMC (27.0%) and LMC (27.1%) choices. Table 4.4 shows the percents of the intended career choices by school type and gender. 72 Table 4.4 Intended Career Choice by School Type and Gender School Type Gender Percent choosing HMC Percent choosing MMC Percent choosing LMC PuR Males (n= 99) 59.6 22.2 18.2 Females (n= 101) 36.6 23.8 39.6 PuU Males (n= 99) 67.7 17.2 15.2 Females (n= 101) 36.6 35.6 27.7 PrNE Males (n= 95) 64.2 20.0 15.8 Females (n= 98) 31.6 32.7 35.7 PrE Males (n= 101) 51.5 26.7 21.8 Females (n= 100) 21.0 37.0 42.0 Note: The differences in n's in the table above is due to the deletion of 14 cases for which the career choice datum was missing as explained in the rational and methodology in page 75. Affective Variables As described earlier, four constructs that have been found to be most related to participation in mathematics with other populations (Armstrong & Price, 1982; Fennema & Sherman, 1976, 1977, 1978; Hanna & Leder, 1990; Hyde et al., 1990; Lantz & Smith, 1981; Leder, 1992; Meyer & Koehler, 1990; Pedro et al., 1981; Perl, 1982; Reyes, 1984; Sherman & Fennema, 1977) were chosen for this study. The instrument used to measure attitudes toward mathematics was a subset of the mathematics attitude scales developed by Fennema and Sherman (1976). The authors supplied strong statistical evidence supporting the content validity and rehabihty of the instrument. Both validity and reliability coefficients are listed in the technical manual. Since the study only focused on four affective variables, it was decided that only a subset of the original scales was to be used, so a total of four scales (48 items) were put into a survey questionnaire. The four scales (found in Section 2) are: Perceived Confidence 73 in Learning Mathematics (items 1 to 12), Attitude toward Success in Mathematics (items 13 to 24), Perception of Mathematics as a Male Domain (items 25 to 36), and Perceived Usefulness of Mathematics (items 37 to 48). Each response is given a score from 1-5 and, on each scale, the weight of 5 is given to the response that is hypothesized to have a positive effect on the learning of mathematics. Scoring is reversed for negative items and a student's total score on each scale is the cumulative total of the item scores. Possible scores range from a high of 60 to a low of 12. Lower scores are indicative of negative attitudes, and higher scores are indicative of more positive attitudes. In addition, high scores on the Perception of Mathematics as a Male Domain scale indicate a less stereotypic view of mathematics. Reliabilities and factor analyses of these scales and the total questionnaire used in this study have been reported in chapter 3 and in Appendix F. Table 4.5 shows the descriptive statistics (Ns, means, and standard deviations for the subjects) for the four affective variables by gender, career choice, and school type. Table 4.5 Descriptive statistics for the four affective variables Gender (G) Career (C) School (S) Affective M F HMC MMC LMC PuR PuU PrNE PrE variable (n=394) (n=400) (n= 365) (n=214) (n=215) (n=200) (n=200) (n=193) ( n= 201) Confmat x/60 47.1 44.0 49.1 43.9 41.0 44.8 45.3 45.7 46.3 SD 8.3 9.2 7.2 8.6 9.3 9.6 7.5 9.0 9.4 Attsmat x/60 50.5 51.1 51.3 51.0 49.6 49.8 50.5 50.7 52.0 SD 5.6 6.2 5.5 5.8 6.5 6.3 5.3 5.9 5.9 Matmdom x/60 44.8 50.4 46.9 48.7 48.2 45.5 47.5 47.3 50.0 SD 7.3 6.3 7.4 7.2 7.3 8.1 7.2 7.1 6.1 Usefmat x/60 50.3 48.1 52.2 49.8 43.4 49.0 49.9 49.2 48.6 SD 7.0 8.0 5.7 6.7 8.0 7.8 6.2 7.2 8.9 Notes: 1) The differences in n's in the table above is due to the deletion of 14 cases for which the career choice datum was missing as explained in the rational and methodology in page 75. 2) Confmat = Perceived Confidence in Learning Mathematics Attsmat = Attitude toward Success in Mathematics Matmdom = Perception of Mathematics as a Male Domain Usefmat = Perceived Usefulness of Mathematics 74 Table 4.6 Ns, Means, and Standard Deviations for All Variables Confmat Attsmat Matmdom Usefmat School Career Gender Gender Gender Gender Type Choice M F M F M F M F X / 6 0 49.4 47.8 51.3 51.4 43.0 49.3 51.9 51.8 SD 7.1 8.7 5.3 5.6 8.2 7.0 4.9 6.3 HJVH-. N 59 37 59 37 59 37 59 37 X / 6 0 42.6 44.5 48.7 49.3 41.5 48.7 49.3 50.5 PuR M M C SD 10.1 8.8 6.7 7.2 8.5 7.0 8.3 8.1 N 22 24 22 24 22 24 22 24 X / 6 0 37.6 40.1 47.9 47.9 44.1 46.6 46.3 42.6 L M C SD 9.1 9.9 6.3 7.1 6.7 7.8 7.8 8.3 N 18 40 18 40 18 40 18 40 X / 6 0 47.6 46.8 49.6 51.3 44.1 50.6 51.0 52.6 H M C SD 6.7 6.8 5.3 5.2 6.7 6.3 5.6 4.8 N 67 37 67 37 67 37 67 37 X / 6 0 47.3 42.6 49.9 52.3 46.7 50.8 52.5 49.4 PuU M M C SD 6.9 6.8 4.3 5.3 6.4 5.9 4.2 5.9 N 17 36 17 36 17 36 17 36 X / 6 0 44.1 40.5 49.7 49.8 43.3 50.3 46.5 44.9 L M C SD 8.3 8.2 4.8 6.0 7.4 6.9 6.9 6.5 N 15 28 15 28 15 28 15 28 X / 6 0 49.8 48.4 52.2 51.8 46.0 51.2 52.3 51.9 H M C SD 6.5 8.5 4.7 7,3 5.9 5.94 5.6 6.3 N 61 31 61 31 61 31 61 31 X / 6 0 47.3 41.8 50.3 49.1 41.4 49.7 49.3 49.2 PrNE M M C SD 7.9 8.2 5.0 5.1 7.7 6.2 6.3 6.8 N 19 32 19 32 19 32 19 32 X / 6 0 43.9 39.7 48.9 49.8 41.9 49.5 43.3 44.1 L M C SD 10.0 9.4 6.7 6.5 9.3 5.1 6.5 7.2 N 15 35 15 35 15 35 15 35 X / 6 0 51.4 53.0 51.0 54.2 46.5 53.4 54.0 53.3 H M C SD 6.9 4.8 6.1 3.6 6.9 4.2 6.5 4.7 N 52 21 52 21 52 21 52 21 X / 6 0 44.2 44.2 52.1 54.0 48.6 51.8 48.7 50.5 PrE M M C SD 8.2 10.3 5.0 5.4 4.4 5.7 7.0 6.1 N 27 37 27 37 27 37 27 37 X / 6 0 41.5 42.4 48.5 52.2 48.0 53.1 42.0 41.1 L M C SD 8.4 9.9 7.0 6.1 6.7 3.6 8.3 9.4 N 22 42 22 42 22 42 22 42 Note: Confmat = Perceived Confidence in Learning Mathematics Attsmat = Attitude toward Success in Mathematics Matmdom = Perception of Mathematics as a Male Domain Usefmat = Perceived Usefulness of Mathematics 75 Table 4.6 shows the descriptive statistics for the four affective variables across all the possible combinations of the independent variables (gender, career choice, and school type). Statistical Assumptions In order to answer the research question 2 [How do perceived confidence in learning mathematics, attitude toward success in mathematics, perception of mathematics as a male domain, and perceived usefulness of mathematics relate to gender, intended field of study career choice, and school type)?], a 2x3x4 (Gender x Career choice x School type) factorial MANOVA was performed on the data with mean scores of the students in four affective variables being the unit of analysis for testing differences in the variables among schools, career choices, and gender. Each significant MANOVA was followed with ANOVAs on each of the dependent variables (DV) for interpreting group differences. This follow-up method is often referred to as the protected F since the overall multivariate test provides protection from an inflated alpha level on the univariate tests which ignore any relationships among the DVs (Bray & Maxwell, 1985). ln addition, in order to uncover differences among individual means, post hoc comparisons (or multiple comparisons) were made. Duncan and Scheffe (McMillan & Schumacher, 1989) aproaches were the post hoc tests used to test each possible pair of means. However, before proceeding with MANOVA, the variables were assessed with respect to practical limitations. That is, an evaluation of assumptions was performed on the data. SPSS FREQUENCIES was run with SORT and SPLIT FILE to divide cases into groups. Data and distributions for each DV within each group were inspected for missing values, shape, and variance. For the 808 students who were administered the survey questionnaire, the run revealed the presence of 14 cases for which the career choice datum was missing. Deletion of the cases with the missing value, reduces the available sample 76 size to 794. For the 48 affective items, the run only revealed 0.29% of missing response data which was reflected in no deletion of any subject by SPSS. Sample sizes are equal for gender and for the four school types. However, there were differences in group sizes by career choice, with a ratio of 1.7:1:1. There are 365 in HMC, 214 in MMC, and 215 in LMC in the sample. This is due to the fact that gender and school type can be (and were) controlled, whereas career choice cannot be controlled. Nevertheless, with the small differences in variance (for no DV does the ratio of largest to smallest variance approach the standard of 20:1. In fact, the largest ratio is about 2.4:1) and the use of a two-tailed test, the discrepancy in these sample sizes does not invalidate the use of MANOVA (Tabachnick & Fidell, 1989). The sample size of 794 includes at least 15 cases for each cell of the 2x3x4 between-subjects design which meets the suggested level to assure multivariate normality of the sampling distribution of means (Tabachnick & Fidell, 1989). Further, the distributions from the full run produced no cause for alarm. Skewness and kurtosis were not extreme and were roughly the same for the DVs (skewness ranged from -1.16 to 0.76 while kurtosis ranged from -0.68 to 1.62). In addition, neither multicollinearity nor singularity was judged to be a problem since the correlations among the DVs were small to moderate (0.14, 0.16, 0.29, 0.32, 0.33, 0.55). Therefore, no DV was found to be redundant. Tabachnick and Fidell (1989) suggest that two variables with a bivariate correlation of 0.70 or more should not be included in the same analysis. A second approach was used to examine dependencies among the dependent variables. Thus, a principal components analysis of the DVs within-cells correlation/covariance matrix was performed. It was found that none of the eigenvalues (1.9316, 0.8610, 0.6931, and 0.5143) was close enough to 0 to cause concern about the error matrix being singular. Also, each variable loads highly on only one of the components, suggesting that none is redundant or highly correlated with the others. Finally, no outliers were found. 77 Research Question 2 How do perceived confidence in learning mathematics, attitude towards success in mathematics, perception of mathematics as a male domain, and perceived usefulness of mathematics relate to gender, intended field of study (career choice), and school type? The results of the MANOVA test produced by SPSS MANOVA are presented in Table 4.7. Table 4.7 Multivariate Analysis of Variance Testing Main and Interaction Effects Source of Variation Degrees of freedom Multivariate F P Gender (G) 4 39.00 0.0001 * Career (C) 8 28.52 0.0001 * School (S) 12 6.16 0.0001 * G x C 8 0.46 0.884 G x S 12 2.44 0.004 * C x S 24 1.84 0.008 * G x C x S 24 1.28 0.166 *Note: a was set at 0.05 for all multivariate F's. The MANOVA table (Table 4.7) shows that this analysis yielded significant multivariate main effects by gender of subject, F (4, 767) = 39.00, p < 0.0001, by career choice, F (8, 1534) = 28.52, p < 0.0001, and by school type, F (12, 2030) = 6.16, p < 0.0001. The analysis also yielded significant interactions between gender of subject and school type, F (12, 2030) = 2.44, p < 0.004, and between intended career choice and 78 school type, F (24, 2677) = 1.84, p < 0.008. However, the interaction between gender of subject and intended career choice as well as the 3-way interaction did not approach statistical significance at the 0.05 level. Because omnibus MANOVA shows significant main and interaction effects, univariate F's were used to further investigate the nature of the relationships among the IVs and DVs. Table 4.8 presents the results of the follow-up ANOVA tests produced by SPSS MANOVA. Table 4.8 Follow-up Univariate Analysis Confmat Attsmat Matmdom Usefmat Source of Variation df F P F P F P F P Gender (G) 1,770 3.90 0.05 * 5.92 0.02 * 130.60 0.0001 * 0.69 0.41 Career (C) 2,770 61.75 0.0001 * 9.07 0.0001 * 1.25 0.29 97.46 0.0001 * School (S) 3,770 2.70 0.05 * 6.06 0.0001 * 16.54 0.0001 * 1.11 0.34 G x S 3,770 3.83 0.01 * 2.60 0.05 * 0.77 0.51 0.33 0.81 C x S 6,770 2.01 0.06 1.63 0.14 1.60 0.15 2.33 0.03 * Notes: 1) a was set at 0.05 for all univariate F's. 2) Confmat = Perceived Confidence in Learning Mathematics Attsmat = Attitude toward Success in Mathematics Matmdom = Perception of Mathematics as a Male Domain Usefmat = Perceived Usefulness of Mathematics Three of the four univariate F ratios revealed significant gender differences for the affective variables. These variables include the measures of Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, and Perception of Mathematics as a Male Domain. Also, subsequent univariate analyses showed that the effect of career choice was also significant for three of the four dependent measures: Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, 79 and Perceived Usefulness of Mathematics. Similarly, follow-up univariate analyses revealed that the effect of school type was significant for three of the four dependent measures: Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, and Perception of Mathematics as a Male Domain. With the exception of the main effect for gender, when significant univariate F's were found, a multiple comparison approach was then carried out to learn which means differed significantly. Duncan and Scheffe tests were then performed on each variable for the comparison of means at the 0.05 level (see Appendix H). Finally, follow-up univariate analyses showed that the interaction of gender by school type was significant for two of the four dependent measures: Perceived Confidence in Learning Mathematics and Attitude toward Success in Mathematics while follow-up univariate analyses revealed that the interaction of career choice by school type was significant for one of the four dependent measures: Perceived Usefulness of Mathematics. The significant and non-significant gender by school interactions as well as career by school interactions are illustrated in Figures 4.2, 4.3, 4.4, and 4.5 which present the means for the four affective variables. Research Question 2(i) How does students' perception of confidence in learning mathematics vary between males and females, by intended career choice, and in the different types of schools? Table 4.8 shows that significant gender, career, and school differences were found for Perceived Confidence in Learning Mathematics. Results and inspections of the appropriate means by gender in Table 4.5 indicate that males were significantly more confident of their ability to learn mathematics than were females (47.1 vs. 44.0), (F (1, 770) = 3.90, p < 0.05). 80 In addition, as expected, results by career choice (F (2, 770) = 61.75, p < 0.0001) were significant. Duncan's and Scheffe's tests revealed that students intending to pursue a high mathematics-related career differed significantly (p < 0.05) from students intending to pursue a middle mathematics-related career and from those aiming at a low mathematics-related career. Also, students intending to pursue a middle mathematics-related career differed significantly from students intending to pursue a low mathematics-related career. The data in Table 4.5 clearly indicate that students intending to pursue a high mathematics-related career scored higher on the confidence scale (49.1) than students intending to pursue a middle or a low mathematics-related career. On the other hand, students intending to pursue a low mathematics-related career scored the lowest on the confidence scale (41.0) as compared to students intending to pursue a high or a middle mathematics-related career. Students intending to pursue a middle mathematics-related career also obtained low mean scores in Perceived Confidence in Learning Mathematics (43.9), but higher than the LMC students. Likewise, an examination of the means by school type (Table 4.5) indicates that the students from the private schools scored higher on Perceived Confidence in Learning Mathematics than the students from the public schools, (F (3, 770) = 2.70, p < 0.05). Duncan's and Scheffe's tests revealed that students from the PrE schools differed significantly from those from the PuR schools, and that students from the PrNE schools differed significantly from those from the PuR schools. The students from the PrE schools obtained the highest mean scores in Perceived Confidence in Learning Mathematics (46.3) followed by the PrNE schools (45.7) and then by the PuU schools (45.3). The students from the PuR schools obtained the lowest mean scores in Perceived Confidence in Learning Mathematics (44.8). Females' confidence mean scores were higher in the PrE and PuR schools than in the PuU and PrNE schools. The most confident females were found to be in the PrE schools. 81 (a) (b) Figure 4.2 Mean score of students by gender, career choice and school type on Perceived Confidence in Learning Mathematics (Confmat). Table 4.8 also shows that the gender by school interaction was significant, (F (3,770) = 3.83, p < 0.01). Figure 4.2a shows that within each school type mathematics confidence was significantly higher for the males than for the females. However, it can be noticed that the highest mean scores for the males can be found in the PrNE schools (48.4) where the lowest mean scores for the females also exist (43.1). Thus, the largest difference between males and females exists in the PrNE schools and then in the PuU schools. The smallest difference between males and females was found in the PuR schools. The highest mean scores for the females can be found in the PrE schools (45.3) followed by the PuR schools (44.1) where the lowest mean scores for the males exist (45.6). Table 4.6 presents an interesting picture of the Perceived Confidence in Learning Mathematics factor. Within each school type, Perceived Confidence in Learning Mathematics was consistently higher for both males and females intending to pursue a HMC followed in order by those planning to pursue a MMC and those planning to pursue a LMC. Also, it can be noticed that males intending to pursue a HMC from the PuR, PuU, 82 and PrNE schools scored higher than their females counterparts. In contrast, the females intending to pursue a HMC from the PrE schools scored higher than their male peers. Of those students intending to pursue a MMC, the males from the PuU and the PrNE schools scored higher than the females, but the females from the PuR and the PrE schools scored higher than the males. Similarly, of those students intending to pursue a LMC, the males from the PuU and PrNE schools scored higher than the females while the females from the PuR and PrE schools scored higher than the males. Research Question 2(ii) How does students' attitude toward success in mathematics vary between males and females, by intended career choice, and in the different types of schools? Follow-up analyses of variance (see Table 4.8) revealed significant gender, career, and school differences for Attitude toward Success in Mathematics. Inspections of the appropriate means by gender in Table 4.5 indicate that males were less likely to hold more positive attitude toward success in mathematics than did females (50.5; 51.1), (F (1,770) = 5.92, p < 0.02). Also, as could be expected, the effect of career choice was significant (F (2,770) = 9.07, p < 0.0001). Duncan's and Scheffe's tests revealed that students intending to pursue a high mathematics-related career differed significantly from students intending to pursue a low mathematics-related career (51.3 vs. 49.6). Similarly, students aiming at a middle mathematics-related career differed significantly from students intending to pursue a low mathematics-related career (51.0 vs. 49.6). No significant difference was found between students intending to pursue a high and a middle mathematics-related career. Likewise, an examination of the means by school type (Table 4.5) indicates that the students from the private schools scored higher than the students from the public schools (F (3,770) = 6.06, p < 0.0001). Duncan's and Scheffe's tests revealed that students from 83 the PrE schools differed significantly from those from the PuR, PuU, and PrNE schools. No significant differences were found among students from the PuR and PuU schools, PuR and PrNE schools, and PuU and PrNE schools. The students from the PrE schools obtained the highest mean scores in Attitude toward Success in Mathematics (52.0), followed in order by the students from the PrNE schools (50.7), those from the PuU schools (50.5), and the students from the PuR schools (49.8). Attsmat Attsmat ' Male - Femald r PuR PuU PrNE PrE PuR PuU PrNE PrE (a) (b) Figure 4.3 Mean score of students by gender, career choice and school type on Attitude toward Success in Mathematics (Attsmat). The gender by school interaction was also significant for Attitude toward Success in Mathematics, (F (3,770) = 2.60, p < 0.05). Figure 4.3a shows that Attitude toward Success in Mathematics mean scores were higher for males at the PuR and PrNE schools (50.0 vs. 49.6; 51.3 vs. 50.2, respectively) while they were higher for females at the PuU and PrE schools (51.3 vs. 49.7; 53.3 vs. 50.7, respectively). The males obtaining the highest mean scores in Attitude toward Success in Mathematics were found to be from the PrNE schools (51.3) while the males obtaining the lowest mean scores were found to be from the PuU schools (49.7). On the other hand, the females obtaining the highest mean 84 scores in Attitude toward Success in Mathematics were from the PrE schools (53.3) and the females obtaining the lowest mean scores were from the PuR schools (49.6). Table 4.6 presents a very mixed picture of the attitude toward success in mathematics factor. For example, students (males and females) intending to pursue a HMC from the PuR and PrNE schools scored higher than those planning to pursue a MMC and those planning to pursue a LMC. Also, it can be noticed that in the PuU and PrE schools, males and females intending to pursue a MMC obtained higher mean scores in Attitude toward Success in Mathematics than those intending to pursue the other two categories of career choice. In addition, the females from the PuU and PrE schools consistently scored higher than the males across the three categories of career choice. The opposite holds for the males in the PuR and PrNE schools. Research Question 2(iii) How does students' perception of mathematics as a male domain vary between males and females, by intended .career choice, and in the different types of schools? Table 4.8 shows that follow-up analyses of variance were significant for gender of subject and school type for Perception of Mathematics as a Male Domain. The results and inspections of the means (the reader is reminded that the scoring on this section yielded results where the lower the scores the stronger the student stereotyped mathematics as a male domain) by gender in Table 4.5 indicate that males significantly stereotyped mathematics as a male domain more than did females (44.8 vs. 50.4), (F (1,770) = 130.6, p < 0.0001). Further, it is also evident that the students from the public schools together perceived mathematics as a male domain more strongly than did the students from the private schools (F (3,770) = 16.54, p < 0.0001). Duncan's and Scheffe's tests revealed that students from the PrE schools differed significantly from those from the PuR, PuU, 85 and PrNE schools, and that students from the PrNE schools differed significantly from those from the PuR schools. In addition, students from the PuU schools differed significantly (p < 0.05) from those from the PuR schools. No significant difference was found between students from the PuU and PrNE schools (47.5 and 47.3, respectively). The students who had the strongest stereotyping of mathematics as a male domain were found to be from the PuR schools (45.5) while the students who had the lowest stereotyping of mathematics as a male domain were found to be from the PrE schools (50.0). Matmdom 40 4 30 PuR Matmdom — ' I — Male - 0 Female] 40 4 PuU PrNE PrE PuR PuU PrNE PrE (a) (b) Figure 4.4 Mean score of students by gender, career choice and school type on Perception of Mathematics as a Male Domain (Matmdom). Figure 4.4a clearly shows that males consistently stereotyped mathematics as a male domain more strongly than females in all school types. The males who had the strongest stereotyping of mathematics as a male domain were found to be in the PuR schools followed by the males in the PrNE and PuU schools, respectively. Similarly, the females who had the strongest stereotyping of mathematics as a male domain were found to be in the PuR schools followed by the females in the PrNE and PuU schools, respectively. 86 The males and females with the lowest stereotyping of mathematics as a male domain can be found in the PrE schools. On the other hand, Perception of Mathematics as a Male Domain was not significant for the effect of career choice. It can be seen in Table 4.5 that students intending to pursue a high mathematics-related career view mathematics as a male domain at similar levels as students intending to pursue a middle and a low mathematics-related career. In addition, none of the interactions was significant for Perception of Mathematics as a Male Domain. Table 4.6 shows that across all school types and across all categories of career choice, males consistently stereotyped mathematics as a male domain more strongly than did females. Additionally, by examining the means by school type in Table 4.6, it can be seen that in the PuR schools, females intending to pursue a LMC stereotyped mathematics as a male domain more strongly than those planning to pursue a MMC, and these in turn stereotyped it as a male domain more strongly than those planning to pursue a HMC. Males, on the other hand, had the strongest stereotyping of mathematics as a male domain when intending to pursue a MMC followed in order by those planning to pursue a HMC and then by those planning to pursue a LMC. In the PuU schools, there was not any difference among the three categories of career choice for the females. But males intending to pursue a LMC stereotyped mathematics as a male domain more strongly than those planning to pursue a HMC, and these in turn stereotyped it as a male domain more strongly than those planning to pursue a MMC. In the PrNE schools, the females intending to pursue a LMC and a MMC showed no difference, but they had a stronger stereotyping of mathematics as a male domain than the females intending to pursue a HMC. Similar results can be found for the males. Finally, in the PrE schools, the females intending to pursue a LMC and a HMC showed no difference and had a lower stereotyping of mathematics as a male domain than the females intending to pursue a MMC. For the males in the PrE schools, those intending to pursue a HMC had a stronger stereotyping of mathematics as a male domain than those intending to pursue a LMC and a MMC. 87 Research Question 2(iv) How does students' perception of the usefulness of mathematics vary between males and females, by intended career choice, and in the different types of schools? Table 4.8 shows that follow-up analyses of variance for Perceived Usefulness of Mathematics were significant only for the career effect (F (2,770) = 97.46, p < 0.0001) and for the career by school interaction (F (6,770) = 2.33, p < 0.03). As could be expected, Duncan's and Scheffe's tests revealed that students intending to pursue a high mathematics-related career differed significantly from students intending to pursue a middle mathematics-related career and from students intending to pursue a low mathematics-related career. Similarly, students intending to pursue a middle mathematics-related career differed significantly from students intending to pursue a low mathematics-related career. Inspections of the appropriate means by career choice in Table 4.5 indicate that students intending to pursue a high mathematics-related career perceived mathematics to be more useful to them than the students intending to pursue a middle mathematics-related career (52.2 vs. 49.8), and the latter scored much more higher than those students aiming at a low mathematics-related career (49.8 vs. 43.4). Usefmat Usefmat 40 4 30 n ——1|—— Male n Female] r 50 4 40 4 PuR PuU PrNE PrE PuR PuU PrNE PrE (a) (b) Figure 4.5 Mean score of students by gender, career choice and school type on Perceived Usefulness of Mathematics (Usefmat). 88 The career by school interaction indicated that the career-related differences in the Perceived Usefulness of Mathematics showed similar profiles across all school types (see Figure 4.5b). Usefulness scores showed little difference among schools when comparing students intending to pursue a MMC. Figure 4.5b shows that within each school type, the students intending to pursue a HMC obtained the highest mean scores in Perceived Usefulness of Mathematics while those students intending to pursue a LMC obtained the lowest mean scores. In addition, the highest and the lowest mean scores for the HMC students were 53.8 (in the PrE schools) and 51.5 (in the PuU schools), respectively. The highest and the lowest mean scores for the MMC students were 50.4 (in the PuU schools) and 49.3 (in the PrNE schools) respectively, while the highest and the lowest mean scores for the LMC students were 45.5 (in the PuU schools) and 41.4 (in the PrE schools), respectively. It is worth noting that students from the private schools intending to pursue a HMC perceived mathematics as more useful than their counterparts from the public schools. The opposite holds when comparing the students intending to pursue a LMC, students from the public schools perceived mathematics as more useful than their counterparts from the private schools. By examining the means by school types in Table 4.6, an interesting pattern can be seen for the perception of the usefulness of mathematics. Across all school types, the females intending to pursue a HMC scored higher than the females planning to pursue a MMC, and these in turn scored higher than the females planning to pursue a LMC. Similar results can be found for the males, except in the PuU schools. In the PuU schools, the males intending to pursue a MMC scored higher than the males intending to pursue a HMC, and the latter scored higher than the males intending to pursue a LMC. It is interesting to note that Figure 4.5a shows that the Perceived Usefulness of Mathematics mean scores were higher for the males than for the females across all school types. The largest discrepancy between males and females can be found in the PrE schools 89 while the smallest gap can be found in the PuU schools. However, the results of the analyses for Perceived Usefulness of Mathematics show that this variable is a stronger predictor of intended career choice than is gender per se. 90 CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS The main goal of the present study was to investigate, through the use of survey data, at the Grade 12 level in the Dominican Republic the relationships among four affective variables in mathematics and gender of student, school type, and students' intention to pursue a mathematics-related career. Four specific affective variables that have been shown to be related to participation in mathematics with other populations were examined. To achieve this goal, a survey was conducted among Grade 12 students from twenty-five public and private schools in a large city and seven rural areas in the same province of the country. In addition, gender, school type, and career choice differences in the affective variables as well as intended participation in mathematics-related careers were studied. In the following sections, a summary of the findings is presented, and conclusions are drawn based on the information gathered through the survey, as well as from the available literature on the subject. Implications of the results are then discussed, and finally, suggestions for further research are presented. Summary of the Findings First of all, it is important to note that the findings reported in the present study refer to male and female groups of similar backgrounds in mathematics, but different in socio-economic background (as explained in Chapter 1, "The Educational System of the Dominican Republic"). The data showed that 86.8% of Dominican Grade 12 students plan to go on to a university immediately after having completed high school. A greater proportion of females than males indicated their intention to go on to a university, and a greater proportion of students from the private schools made this decision. A greater proportion of students from the public schools indicated their intention to get a part-time job and go on to the university. 91 The data also showed that the students from the private schools tend to be younger than the students from the public schools. The initial research questions (la and lb) asked whether there were gender and school differences in terms of intended career choice. The chi square indicated that a greater proportion of males than females intended to enroll in a high mathematics-related career, whereas a greater proportion of females than males indicated their intentions to enroll in a middle or a low mathematics-related careers. The ratio of males to females choosing a high mathematics-related career was nearly 2 to 1. This gender discrepancy was marked along all school types, with the difference being more striking in the private schools. This is consistent with previous findings (Dick & Rallis, 1991; Rosenberg, 1987). It is possible that when females elect not to pursue a high mathematics-related career, they are responding to a reality factor of pressure from their male peers and to pressure of the social context and cultural norms. Or alternatively, this may be so because females see jobs in MMC and LMC as more economically rewarding. In addition, the greater number of students intending to pursue high mathematics-related careers were from the public schools (especially from the PuU schools). A direct result of the finding is that a greater number of students intending to pursue middle and low mathematics-related careers were from the private schools (especially from the PrE schools for both MMC and LMC). Another question addressed in this study was whether there were gender, career choice, and school type differences in four important affective variables (Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, Perception of Mathematics as a Male Domain, and Perceived Usefulness of Mathematics). The results of the MANOVA analysis indicated significant gender, career choice, and school type effects suggesting that males and females, students intending to pursue one of the three categories of career, and students from the four types of schools differed on one or more of 92 the four affective variables. Also, two significant interactions were found, gender by school and career by school. For Perceived Confidence in Learning Mathematics, significant gender, career choice, and school type differences were found. The gender by school interaction was also found to be significant for this measure. Mathematics confidence was consistently found to be significantly higher for males than for females. Similarly, the students intending to pursue a high mathematics-related career were more confident of themselves in regard to mathematics than the students intending to pursue a middle or a low mathematics-related career. Those intending to pursue a low mathematics-related career obtained the lowest mean scores on Perceived Confidence in Learning Mathematics. In general, the students from the private schools were significantly more confident of their ability to learn mathematics than were their counterparts from the public schools. In addition, Perceived Confidence in Learning Mathematics was significantly higher in males than in females at the four types of schools and tended to be the highest in the PrNE schools. These findings are consistent with those reported by Fennema and Sherman (1977; 1978), Gonzalez and Luna (1984), Hyde et al. (1990), and Reyes (1984). For Attitude toward Success in Mathematics, significant gender, career choice, and school type differences were found. The gender by school interaction was also found to be significant for this measure. Females were found to hold more positive attitudes toward success in mathematics than males. In addition, the students intending to pursue a middle or a high mathematics-related career were found to have more positive attitude toward success in mathematics than the students intending to pursue a low mathematics-related career. However, no significant differences were found between the students intending to pursue a middle and a high mathematics-related career. Similar to some of the findings of Fennema and Sherman (1977), Attitude toward Success in Mathematics was significantly higher in females than in males at the PuU and PrE schools while it was significantly higher in males than in females at the PuR and PrNE 93 schools. Further, it was found that Attitude toward Success in Mathematics was significantly higher for the students from the private schools than for their counterparts from the public schools. The students from the PrE schools were found to have the highest mean scores while the students from the PuR schools obtained the lowest mean scores. School environment seems to be an important factor in relation to this construct. For Perception of Mathematics as a Male Domain, only significant gender and school differences were found. In all four types of schools, males consistently stereotyped mathematics as a male domain more strongly than did females. This lends support to the findings of Fennema and Sherman (1977; 1978), Hyde et al. (1990), Pedersen et al. (1985), and Yong (1993). Similarly, students from the public schools together perceived mathematics as a male domain more strongly than did the students from the private schools. However, students from the PrE schools differed significantly from those from the PuR, PuU, and PrNE schools. In addition, students from the PrNE and PuU schools differed significantly from those from the PuR schools. No significant difference was found between students from the PuU and PrNE schools. The students who had the strongest stereotyping of mathematics as a male domain were found to be from the PuR schools while the students who had the lowest stereotyping of mathematics as a male domain were found to be from the PrE schools. Lamb and Daniels (1993), and Rosenberg (1987) contend that the stereotyping of mathematics as a male domain is the strongest factor in the choice a high school female makes not to take mathematics. Thus, Perception of Mathematics as a Male Domain differentiated males and females, and among school types, but it failed to differentiate between those intending/nonintending to pursue a mathematics-related career. Therefore, it may be that stereotyping mathematics as a male subject is a mediating variable affecting other affective variables, for example, Perceived Usefulness of Mathematics and/or Perceived Confidence in Learning Mathematics. In addition, it appears that the school environment (as each school type represents a different socio-economic condition) plays a 94 significant role in shaping students' attitudes and perceptions of mathematics. Rosenberg (1987), for example, claims that a large part of the blame for the stereotyping of mathematics as a male domain rests on the social and intellectual environment at schools. Fennema (1980), on the other hand, found that student's feeling's about themselves as learners of mathematics, their perception of the usefulness of mathematics, and their willingness to continue the study of mathematics are all directly influenced by teachers. For Perceived Usefulness of Mathematics, only significant career effect and a significant career by school interaction were found. The students intending to pursue a high mathematics-related career perceived mathematics as being more useful than did the students intending to pursue a middle or a low mathematics-related career. Those intending to pursue a low mathematics-related career had the lowest perception of mathematics being useful to them. This finding is consistent with that of Sherman and Fennema (1977), who found that Perceived Usefulness of Mathematics differentiated between those intending and not intending to continue the study of mathematics. Further, across all school types, the students intending to pursue a high mathematics-related career obtained the highest mean scores in Perceived Usefulness of Mathematics, while those students intending to pursue a low mathematics-related career obtained the lowest mean scores. In addition, the highest and lowest mean scores for the HMC students were found in the PrE and PuU schools, respectively. The highest and the lowest mean scores for the MMC students were found in the PuU and the PrE schools, respectively while the highest and the lowest mean scores for the LMC students were found in the PuU and the PrE schools, respectively. It is evident that Perceived Usefulness of Mathematics related better to career than to gender and to school type. However, it is not clear why this measure failed to differentiate between males and females and among school types. The nonsignificant gender differences are also interesting. The nonsignificant gender differences in Perceived Usefulness of Mathematics indicate that there was little 95 direct evidence that this construct is an important variable influencing Dominican high school females' decision to continue the study of mathematics. This contradicts previous U.S. findings (Fennema & Sherman, 1977, 1978; Hyde et al., 1990; Pedersen et al., 1985; Reyes, 1984; Sherman & Fennema, 1977). This may reflect important characteristics within the Dominican context. Finally, even though among all students in general and in all school types males' mean scores on Perceived Usefulness of Mathematics were higher than females' mean scores, it can be concluded that Perceived Usefulness of Mathematics did not influence females' decision to pursue a mathematics-related career, since gender differences were not significant for this variable. Conclusions Very few students have the privilege of finishing Grade 12 in the Dominican Republic and these few students constitute a privileged group with schooling (Luna et al., 1990). However, the data of this study and previous reports ( S E E B A C , 1984; Troxell, 1987) show that of those few students who finish Grade 12, about 85% of them intend to go on to higher education immediately after having completed high school. There are several conclusions highlighted by the results of the present study. Grade 12 Dominican females did not intend to pursue a high mathematics-related career as often as did males, while the middle and low mathematics-related careers attracted more females than males. This gender discrepancy was found across all types of schools. Perhaps Dominican females view careers such as engineerings and sciences as too hard and unfeminine, whereas careers such as accounting, business, education, law, medicine, etc. are viewed as more appropriate and conducive to their perceived female roles, or more rewarding and prestigious careers. However, it could also be that the effects of social and cultural forces in influencing career choice is subtle, yet extremely powerful. For example, females across a wide range of socio-economic status conditions may be affected by these forces very early in their childhood. 96 Nevertheless, the phenomenon described in the previous paragraph could be explained by what Isaacson (1989) calls coercive inducement and double conformity. Isaacson (1989) suggests that females are induced by the system of rewards and approval to accept a more passive role and to choose stereotypically feminine occupations. Further, Isaacson (1989) claims that the learning of mathematics cannot be divorced from the social context in which that learning takes place. Rosenberg (1987) contends that the social climate teaches young females that mathematics is not useful to them and that mathematics is a male domain. Thus, females learn at an early age that mathematics is for males and that they will be rewarded if they pursue traditional female roles. Mathematics carries a strong male image which is reinforced by traditional male dominance. Burton (1989) writes, "the images in the media, in language, in advertising reinforce the roles and behaviour of active, powerful, controlling men and attentive, submissive and attractive women" (p.184). For example, Stromquist (1989) notes that a common characteristic of textbooks in developing countries is their portrayal of females as mothers, wives, and submissive individuals. However, books in developed countries like the United States have also been found to be stereotyped (Rosenberg, 1987). Stromquist (1989) also adds that females' career choices are significantly affected by social and cultural norms. The present results show that the Dominican context is not an exception to this social stereotyping of mathematics as a male domain. Further, the greater number of students intending to pursue high mathematics-related careers were from the public schools, while the number of students intending to pursue the other two categories of career choice were mixed across all school types. This finding, and the fact that gender differences were similar across all school types, lead to the speculation that other factors (not investigated in the present study) are more important than school (teacher, counselor) and home (father, mother) environments in shaping students' career choice. Some of these factors may be salaries, availability of jobs, and genuine interest. 97 From the pattern of findings in this study and that of other studies (Dick & Rallis, 1991; Fennema & Sherman, 1977, 1978; Gaskell et al., 1993; Sherman & Fennema, 1977) , it can be concluded that the four affective variables studied are associated with students' decision to pursue studies in mathematics. Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, and Perceived Usefulness of Mathematics were the most important variables differentiating between students intending/nonintending to pursue a mathematics-related career. On the other hand, Perceived Confidence in Learning Mathematics, Attitude toward Success in Mathematics, and Perception of Mathematics as a Male Domain were the most important variables differentiating between males and females, and among types of schools. In fact, males across all school types were significantly more confident of their ability to learn mathematics than were females, while females across all school types consistently viewed mathematics as less of a male domain and tended to hold more positive attitude toward success in mathematics, but elected not to pursue studies in mathematics more often than did males. Nevertheless, the males' stereotyping of mathematics as a male domain undoubtedly has a strong influence on females (Fennema & Sherman, 1977, 1978) . For all students, particularly for females, it is important to be aware of the relationship between confidence and plans to pursue studies in mathematics in the future. There is evidence that females underestimate their ability in mathematics (Fennema & Sherman, 1977). Implications Gender differences in career choice were found in this study. The finding that females did not intend to pursue a high mathematics-related career as often as did males indicates that females will continue to be underrepresented in the mathematics-related careers and restricted to careers which use little mathematics, as well as to traditionally female areas. Unless proper steps are taken, gender differences in mathematics will 98 continue to exist, and most of the mathematics-related professions or occupations will continue to be dominated by males in the Dominican society. The findings also support previous reports that males express more interest in mathematics than females. Differences between males' and females' affective responses in mathematics were also found. These differences were most marked in Perceived Confidence in Learning Mathematics and Perception of Mathematics as a Male Domain. It was concluded that this might be related to males' and females' experiences out of school. Differences were found in all types of schools and in all career choices. They may be related to the rigid social and cultural gender-role expectations which are so widely spread in the Dominican culture. The finding that PrNE schools and PuU schools have similar mean scores in the four affective variables studied merits further examination. It suggests that students paying tuition for their education may not be getting the type of experience and instruction they expect. It implies that students attending PrNE schools are paying for the same educational environment and experience that students in the PuU schools obtain for free. In fact, Diaz Santana (1987) claims that the Dominican educational system presents drastic differences in quality and quantity between public and private schools to the detriment of the public schools. However, the present study is not about achievement in mathematics but it investigated different constructs of mathematics attitudes which relate to the learning of mathematics as well as differentiations between those who elect to study mathematics and those who do not (Sherman & Fennema, 1977). Further research is needed into the factors within a school milieu that provides information in relation to the learning of mathematics by males and females. Definitely the school must provide equity in access and encouragement to students to pursue academic coursework in mathematics so that all students have the full range of career options open to them. The educational goal is to encourage as many students as possible, both males and females, to enjoy mathematics and to participate in mathematics-related careers (Research Advisory Committee of the NCTM, 1989). 99 Further, intervention efforts to improve the representation of females in mathematics-related careers (e.g., engineering, sciences) may require earlier efforts if they are to be successful. Although females have not received a great deal of support and encouragement in pursuing mathematics-related careers, as suggested by the literature (Dick & Rallis, 1991; Fennema & Hart, 1994, Rosenberg, 1987), it is imperative that the family and the school play a larger role in encouraging and stimulating early interest and further coursework in mathematics. In fact, Fennema et al. (1981) suggest that if females' knowledge about gender differences in mathematics was increased and attitudes toward mathematics were improved, the females' willingness to take mathematics courses would increase. Likewise, it could be speculated that these females would likely pursue studies in mathematics. Finally, Dwinell and Higbee (1991) suggest that patterns of behaviors in affective variables can be identified through early administration of the appropriate Fennema-Sherman scale. Thus, mathematics teachers are encouraged to consciously use these scales to monitor and measure attitudes their students hold about mathematics. These paper-and-pencil instruments, as well as interviews and journals, can reveal much that might not be apparent under normal circumstances. The results of the present study imply that the other five Fennema-Sherman Mathematics Attitudes Scales (Fennema & Sherman, 1976), as well as other instruments, can be adapted for use not only in the Dominican Republic but in any Spanish-speaking country by following the procedures outlined in this study. The translation of existing instruments provides one solution to the problem of assessment of non-English speaking subjects. Thus, it also implies that these popular and reliable instruments can be made available for use in countries such as the United States and Canada for cases in which the English version is inappropriate (e.g., new Hispanic immigrants). In addition, Fennema and Sherman (1977) and Nebres (1988) suggest that recognizing the role of a set of cultural conditions which makes the study of mathematics seem inappropriate for females is a fair approach. 100 Going Beyond Nebres (1988) suggests that it is important to be much more aware of non-cognitive factors such as affective factors and take them into account in the development of school mathematics in developing countries. The findings of the present study can be of interest not just to mathematics educators and teachers but to anyone concerned about the participation of students, particularly female students, in mathematics-related careers. The results and conclusions of this study together with research reviewed in the literature may have implications for choosing strategies to increase the participation of all students in mathematics-related careers. Some example of such strategies are: (a) to adjust the curriculum so that the subject can be made more attractive, interesting, or challenging to female students; (b) to make careers which involve the use or prerequisite demands of mathematics more attractive and worthwhile; (c) to use techniques (e.g., competitions) to support and encourage young students into mathematics; and (d) to make school teachers aware of this problem since many teachers are themselves frightened of mathematics and pass this fear on to their students (especially elementary teachers), or they treat males and females differently and thus, reinforce the belief that mathematics is a male domain. As suggested by the NCTM (1989), it is important that at all grade levels, all students (a) learn to value mathematics, and (b) become confident in their ability to learn mathematics. Likewise, Stromquist (1989) concluded that specific strategies are necessary to encourage teachers to adopt teaching styles and curriculum content that will foster greater gender and school equity in their societies. Suggestions for Further Research The results of this study have provided additional information regarding four important affective variables and their relationship to male and female students' decisions to enroll in mathematics-related careers. In addition, the study has provided information about 101 the relationship between students' career choice or future field of study and the school type they attend. This work, however, suggests a variety of additional questions which may have implications for further research. The focus of this research was specifically on four affective factors (i.e., Perceived Confidence in Learning Mathematics, Attitudes towards Success in Mathematics, Perception of Mathematics as a Male Domain, and Perceived Usefulness of Mathematics), gender issues, school type, and intended future career choice. Research which encompassed affective variables other than those involved in this study would broaden the framework of knowledge regarding affective factors and the learning of mathematics. Attitude scales, such as the Fennema-Sherman Mathematics Attitude Scales Fennema and Sherman (1976), which examine a wide range of constructs of attitude and which have statistical evidence supporting their vahdity and reliability would be useful for this purpose. Likewise, the sample which formed the basis of this study involved Grade 12 students in the Traditional system only. Further work involving students at different grade levels in both the Traditional and Reform systems is needed as it will shed light on the possible similarities and differences between the systems and among grade levels. A more empirical study would allow for more specific information regarding affective factors and their effect on male and female students' decisions to enroll in mathematics-related careers. One further question which could be addressed is that of the causality of the relationship between affective factors and intended participation in mathematics-related careers. Although this may be a difficult question to precisely answer, it warrants an examination. Certainly, investigations of the relationship of affective factors and participation in mathematics-related careers is an important contribution to the growing literature aimed at isolating factors related to the study of mathematics by all students, particularly females. 102 Another issue that may prove to be important is to investigate teachers' attitudes toward mathematics and their relation to students' attitudes toward mathematics and their future career choice (e.g., when teachers like mathematics, does a majority of their students prefer it?). In addition, a follow-up study that may be worthy to carry out in the Dominican context is to investigate if any relationship exists between attitudes toward mathematics and achievement, since no previous study in the country has directly dealt with this relationship. Finally, future research is needed to ascertain whether the findings of the present study can be replicated in other samples. 103 REFERENCES Aleman, J. L. (1988). 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Focus on Learning Problems in Mathematics, 15, 52-61. 113 Appendix A School Educational Structure in the Dominican Republic Traditional System Primary Education Public School Intermediate Education Secondary Education First Grade Second Grade, Third Grade Fourth Grade Fifth Grade Sixth Grade Seventh Grade Eighth Grade 7 8 9 10 11 12 13 14 ge ^ Ninth Grade Tenth Grade Eleventh Grade, Twelfth Grade 15 16 17 18 years Primary Education Private School Intermediate Education Secondary Education Pre-school First Rrade Second Grade Third Grade, Fourth Grade, Fifth Grade Sixth Grade, Seventh Grade, Eighth Grade 4 to 5 6 7 8 9 10 11 12 13 Age Ninth Tenth Eleventh Twelfth Grade Grade Grade, Grade 14 15 16 17 years Reform System Public School Primary Education Secondary Education First Grade, Second Grade Third Grade Fourth Grade Fifth Grade Sixth Grade, 7 8 9 10 11 12 Seventh Grade Eighth Grade, Ninth Grade, Tenth Grade 13 14 15 16 lEleventh Grade Twelfth Grade Specialization 17 18 years 114 Appendix B Table Bl Distribution of Students and Sampled Schools. School Enrollment of Grade 12 students Selected random sample Total Females Males Females Males Total P R 1 142 90 52 20 20 40 P R 2 68 34 34 20 20 40 P R 3 48 26 22 17 17 34 P R 4 27 13 14 10 10 20 P R 5 70 37 33 10 10 20 P R 6 37' 19 18 13 13 26 P R 7 80 56 34 11 11 22 P U 1 68 36 32 21 21 42 P U 2 180 101 79 20 20 40 P U 3 94 70 24 20 20 40 P U 4 55 27 28 20 20 40 P U 5 66 28 38 20 20 40 P N E 1 72 34 38 20 20 40 P N E 2 40 20 20 15 15 30 P N E 3 44 27 17 10 10 20 P N E 4 69 24 35 16 16 32 P N E 5 79 43 36 20 20 40 P N E 6 34 22 12 10 10 20 P N E 7 26 14 12 10 10 20 P E 1 68 39 29 20 20 40 P E 2 35 20 15 13 13 26 P E 3 30 15 15 10 10 20 P E 4 137 81 56 20 20 40 P E 5 63 39 24 20 20 40 P E 6 43 23 20 18 18 36 Overall 1675 938 737 404 404 808 APPENDIX C School's Letter and Student Questionnaire (Original) 118 Name of School Please do not complete this space -For office use only 1 2 3 4 O O O O SECTION 1: Background information 1) What is your gender? O male O female 2) Your age is 015 years or less 0 1 6 years 0 1 7 years O 18 years O 19 years O 20 years or more 3) What are your plans when you finish high school? Fill in only one of the bubbles below. O go on to the university O take a year off and then seek a job O seek a full-time job OI have other plans O seek a part-time job and go to the university O I have not decided anything O take a year off and then go to the university 4) If you are going to the university, in what career do you plan to enroll? Fill in the bubble that accompanies the set of careers that includes yours. O Civil engineering, Chemical engineering, Electronics engineering, Electro-Mechanical engineering, Geology & Mining engineering, Industrial engineering, System & Computer engineering, Mathematics, Physical Sciences, Statistics. O Accounting, Agricultural engineering (various fields), Architecture, Banking, Business Administration, Economics, Education (Mathematics & Physics), Hotel Administration, Public Administration. O Bilingual Executive secretary, Education (Biology & Chemistry, English, French, Philosophy & Letters, Plastic Arts, Social Sciences), Executive Secretarial Studies, Interior Design, Law, Music, Philosophy, Political Science, Psychology, Sociology, Social Communication, Social Work, Theater, Tourism. O Bioanalysis, Estomatology, Medicine, Medical Technology, Nursing, Pharmacy, Veterinary Medicine, X- Ray Technology. SECTION 2: This section contains a series of statements. There are no correct answers for these statements. They have been set up in a way which permits you to indicate the extent to which you agree or disagree with the ideas expressed. As you read the statement, you will know whether you agree or disagree. Blacken the bubble corresponding to the answer that best describes your feeling. Remember that there are no "right" or "wrong" answers. The only correct responses are those that are true for you. For the following items, a five-point rating scale is provided for you to record your responses. Please interpret it to have the following meaning: (1) (2) (3) (4) (5) Strongly agree Agree Undecided Disagree Strongly disagree 2.1 am sure I could do advanced work in mathematics O O O O O 3.1 am sure that I can learn mathematics O O O O O 4.1 think I could handle more difficult mathematics O O O O O 5.1 can get good grades in mathematics O O O O O 6.1 have a lot of self-confidence when it comes to math 0 0 0 0 0 7. I'm no good in math O O O O O 8.1 don't think I could do advanced mathematics O O O O O 9. I'm not the type to do well in math O O O O O 10. For some reason even though I study, math seems unusually hard for me O O O O O (1) (2) (3) (4) (5) Strongly agree A g r e e U n d e c i d e d D i s a g r e e Strongly d isagree 1 2 3 4 5 11. Most subjects I can handle O.K., but I have a knack for flubbing up math O O O O O 12. Math has been my worst subject O O O O O 13. It would make me happy to be recognized as an excellent student in mathematics O O O O O 14. I'd be proud to be the outstanding student in math O O O O O 15. I'd be happy to get top grades in mathematics 0 O O O O 16. It would be really great to win a prize in mathematics O O O O O 17. Being first in a mathematics competition would make me pleased O O O O O 18. Being regarded as smart in mathematics would be a great thing O O O O O 19. Winning a prize in mathematics would make me feel unpleasantly conspicuous O O O O O 20. People would think I was some kind of a grind if I got A's in math O O O O O 21. If I had good grades in math, I would try to hide it O O O O O 22. If I got the highest grade in math I'd prefer no one knew O O O O O 23. It would make people like me less if I were a really good math student O O O O O 24. I don't like people to think I'm smart in math O O O O O 25. Females are as good as males in geometry O O O O O 26. Studying mathematics is just as appropriate for women as tor men O O O O O 27.1 would trust a woman just as much as I'd trust a man to figure out important calculations O O O O O 28. Girls can do just as well as boys in mathematics O O O O O 29. Males are not naturally better than females in mathematics O O O O O 30. Women certainly are logical enough to do well in mathematics O O O O O 31. It's hard to believe a female could be a genius in mathematics O O O O O 32. When a woman has to solve a math problem, it is feminine to ask a man for help O O O O O 33.1 would have more faith in the answer lor a math problem solved by a man than a woman O O O O O 34. Girls who enjoy studying math are a bit peculiar O O O O O 35. Mathematics is for men; arithmetic is for women O O O O O [36.1 would expect a woman mathematician to be a masculine type of person O O O O O 37. I'll need mathematics for my future work O O O O O J38.1 study mathematics because I know how useful it is O O O O O 39. Knowing mathematics will help me earn a living O O O O O 40. Mathematics is a worthwhile and necessary subject O O O O O 41. I'll need a firm mastery of mathematics for my future work O O O O O 42.1 will use mathematics in many ways as an adult O O O O O 43. Mathematics is of no relevance to my life O O O O O 44. Mathematics will not be important to me in my life's work O O O O O 45.1 see mathematics as a subject I will rarely use in my daily life as an adult O O O O O 46. Taking mathematics is a waste of time O O O O O 47. In terms of my adult life it is not important for me to do well in math in high school O O O O O 48.1 expect to have little use for mathematics when I get out of school O O O O O APPENDIX D School's Letter and Student Questionnaire (Translated) 123 Liceo o Colegio. 12 3 4 No complete cstc cspacio por favor O O O O 1. tCual es lu sexo? O Masculino O Fcmcnino 2. Tuedades 015ariosomenos Ol6afios Ol7aflos Ol8aflos Ol9aflos O20anosomas 3. iCuales son tus planes para cuando termines cl bachillcralo? (Selecciona sOlo una de las siguientes opcioiies). S estudiar en la universidad buscar un empleo de medio tiempo e ir a la universidad O buscar un empleo a liempo compleio descansar un afio y luego ir a la universidad dcscansar un ano y luego buscar un empleo lengo otros planes no he decidido nada 4. Si vas a la universidad, j,en que" carrcra piensas matricularte? (Rcllena la burbuja que acompafia el conjunto de carreras que incluye la tuya). O Ciencias Ffsicas, Ciencias Matcmdticas, Estadfsticas, Ingenierfa Civil, Ingenierfa ElectrxJnica, Ingenierfa Electro-Mecanlca, Ingenierfa de Geologfa y Mina, Ingemeria Industrial, Ingenierfa Qufmica, Ingenierfa dc Sistcma y Computes, Telemauca. O Administracion de Empresas, Adminisiracion Hotelera, Administration Publics, Arquitcctura, Banca, Contabilidad, Economla, Education (Matematicas y Ffsicas), Ingenierfa Agron6mica (cualquiera de varias concentraciones), Mercadeo. O Ciencia Polftica, Cotnunlcacidn Social, Derecho, Diseflo de Interiorcs, Education (Artes Plasticas, Biologfa y Qufmica, Ciencias Sociales, Filosoffa y Lelras, Frances, Inglgs), Filosoffa, Miisica, Psicologfa, Secretariado Ejecutivo (BilingOc), Sociologfa, Teatro, Trabajo Social, Turismo. O Bioanilisis, Enfermerfa, Estomatologfa, Farmacia, Medicina, Medicina Veterinaria, Tecnologfa M6dica, Tecnologfa de Rayos X. Esta section contiene una serie de declarations para las cuales no hay una respuesta "correcta" o "incorrecta". Las tinicas respuestas correctas son aquellas que son ciertas para ti. Las mismas cstan discfiadas para perrnitirte indicar que tan de acuerdo o en desacuerdo estas tu con las ideas expresadas. Segun leas las declaraciones, sabras si estas de acuerdo o en desacuerdo con ellas. Rellena la burbuja correspondiente ala respuesta que mejor describe his sentimicntos. Para los siguientes Items se te proporciona una escala de puntuacion de cinco puntos. Por favor intcrprdtala para que tenga el siguiente signillcado: May de acuerdo De acuerdo 3 Indeciso En desacuerdo May on desncuerdu 1. Generalmente me he sentido seguro(a) cuando trabajo con matimatica 2. Estoy seguro(a) de que yo podrfa hacer trabajos avanzados en matematica 3. Yo estoy seguro(a) de que puedo aprender matematica 4. Soy capaz de aprender matematica mds complicada de la que he aprendido hasta ahora 5. Yopucdo sacar buenas calificaciones en matematica M. 6. Tengo mucha conflanza en mi cuando se trata de matema'tica 7. No soy bueno(a) para la maternities 8. No creo que yo podrfa hacer materndticas avanzadas 9. No soy del tipo de persona que le va bien en mutemiltica 10. Por alguna razon aunque estudio, la matematica parece extraordinariamente diffcil para mi Continua al dorso Pagina 1 124 SECCION 2 ... Muy de acuerdo De acuerdo 3 Indeciso En desacuerdo Muy en desacuerdo 11. Me va bien en la mayorfa de las asignaturas, pero tengo una destrezaunica parahacer | ; 2 ^ 4 i disparates en matematica 12. Matemftica siempre ha sido mi peor asignatura 13. Me harfa muy feliz ser reconocido(a) como un(a) estudiante excelente en matematica. 14. Estarfa orgulloso(a) dc ser un(a) estudiante sobresaliente en matematica 15. Estarfa contento(a) de obtener altas califlcaciones en matematica OCX £ 2 £ 4 ' £ 16. Seria realmente grandioso ganar un premio en matematica QQv 17. Me encantarfa mucho ganar el primer lugar en una compctencia dc matematica 18. Seria estupendo ser considerado(a) corao inteligente para la matemStica 19. Ganarme un premio en matematica me harfa sentir desagradablemente notable 20. La gente pensarfa que soy un(a) comelibros si yo sacara notas sobresalientes en matematica 21. Si yo tuviera buenas califlcaciones en matemaiica, trataria de ocultarlo QOC 22. Si yo sacara la calificacifin mas alia cn mi clasc de matematica, preferirfa que nadie lo supiera .. 23. Harfa que yo le guste menos a la gente si yo fuera un estudiante de matematica realmente bueno. 24. No me gusta que la gente piense que soy inieligente para la matematica 25. Las hembras son tan capaces como los varones en matematica jll2pa|4!fi 26. El estudiar matematica esapropiado tanto para las mujeres como para los hombres.., 27. Yo confiaria en una mujer tanto como confiarfa en un hombre para resolver cllculos | | j 2 H§ 4 H numericos importantes 28. A las muchachas les puede ir tan bien como a los muchachos en matematica 29. Los varones no son naturalmente mejores que las hembras en matematica 30. Ciertamente, las mujeres son bastante 16gicas para irles bien en matematica 31. Es diffcil creer que una mujer pueda ser un genio en matematica ( ^ X ] ) 0 O O 32. Cuando una mujer tiene que resolver un problema matematico, es femenino (apropiado) 3L- 2 3> 4 W-pedirle a un hombre que la ayude Q O C ^ O C j 33. Yo tendrfa mas fe en la respuesta a un problema matematico resuelto por un hombre que 2 :$<.4 ' por una mujer 34. Las muchachas que distrutan estudiar matematica son un poquito extraflas 35. La matematica avanzada es para los hombres; la aritmdtica es para las mujeres. ^syM1 rtv^A Ny-"As; 36. Yo esperarfa que una mujer matematica de profesi<3n sea un tipo de persona masculino 2 |fF 4 t?1 (una marimacho) 37. Necesitare' la matematica para mi trabajo futuro (porvenir). 38. Estudio matematica porque si lo util que es 39. Saber matematica me ayudard a ganarme la vida 40. La matematica es una asignatura valiosa y necesaria t 2 3 4 5 41. Necesitare' un dominio firme de matematica para mi trabajo futuro (porvenir) 42. Utilizarg la matematica de muchas maneras en mi vida adulta 43. La matematica no tiene ninguna relevancia en mi vida 44. La matematica no me seri importante para mi trabajo de por vida , 45. Veo la matematica como una asignatura que rara vez utilizare en mi vida diaria adulta . t 2 3 4i 46. Tomar cursos de matematica es una perdida de tiempo 47. En tcrminos de mi vida adulta no importa que me vaya bien en la matematica del bachillerato.... 48. Yo espero usar poca matematica cuando saiga de la escuela Pagina 2 APPENDIX E Tables for Figures in Chapter 126 Table for Figure 3.1 Screen output for pilot data produced by SPSSX FACTOR Eigenvalues Factors 10.5057 1 4.5321 2 3.7903 3 2.4974 4 2.1721 5 1.6722 6 1.4438 7 1.3352 8 1.2576 9 1.1662 10 1.0696 11 Table for Figure 3.2 Correlation of the Perceived Confidence in Learning Mathematics scale's items with factors. Item Factor 1 Factor 2 Ql 0.5325 0.5683 Q2 0.3912 0.5779 Q3 0.1892 0.7706 Q4 0.2056 0.8541 Q5 0.2669 0.7481 Q6 0.6683 0.5123 Q7 0.7657 0.2742 Q8 0.7172 0.3294 Q9 0.7376 0.2640 Q10 0.8047 0.2879 Qll 0.7901 0.1515 012 0.7935 0.2423 Table for Figure 3.3 Correlation of the Attitude Toward Success in Mathematics scale's items with factors. Item Factor 1 Factor 2 Factor 3 Q13 0.7316 -0.2464 0.3865 Q14 0.7089 -0.3279 0.3434 Q15 0.7734 0.0933 -0.0632 Q16 0.8620 0.1339 -0.0872 Q17 0.8468 0.1963 -0.1006 Q18 0.7144 0.1904 0.0159 Q19 0.0814 0.3558 0.6440 Q20 -0.0927 0.2268 0.7635 Q21 0.1422 0.7605 0.1612 Q22 0.0907 0.7326 0.1488 Q23 0.0541 0.4782 0.4313 024 -0.0178 0.6570 0.1574 127 Table for Figure 3.4 Correlation of the Perception of Mathematics as a Male Domain scale's items with factors. Item Factor 1 Factor 2 Factor 3 Q25 0.1090 0.7665 0.0164 Q26 0.0994 0.8188 0.0473 Q27 0.1505 0.8224 0.1608 Q28 0.2027 0.7591 0.1777 Q29 0.0698 0.0520 0.8309 Q30 0.1787 0.2152 0.7109 Q31 0.5643 0.1153 0.1955 Q32 0.5512 0.0116 0.1634 Q33 0.6967 0.2405 0.1441 Q34 0.7210 0.1609 0.0407 Q35 0.7926 0.1218 0.0431 036 0.6800 0.0815 -0.0790 Table for Figure 3.5 Correlation of the Perceived Usefulness of Mathematics scale's items with factors. Item Factor 1 Factor 2 Q37 0.7330 0.3042 Q38 0.7515 0.1596 Q39 0.7844 0.2070 Q40 0.7053 0.1173 Q41 0.7398 0.3284 Q42 0.7046 0.3095 Q43 0.2359 0.7107 044 0.3482 0.6490 Q45 0.3462 0.7212 Q46 0.2541 0.6672 Q47 0.0283 0.6416 Q48 0.2072 0.6903 APPENDIX F Reliability and Factor Analyses of the Main Data 129 Table Fl Reliability of the Affect Questionnaire (Main Data) SPSS Windows 6.0 TOTAL TEST STATISTICS Affect Questionnaire Number of individuals = 723 Number of items = 48 Mean = 193.72 Highest score = 239 Standard deviation = 20.25 Lowest score =121 Source of variance DP. S.S. M.S. Individuals Items Residual Total 722 47 33934 34703 6169.34 6316.57 30117.64 42603.55 8.55 134.40 0.89 1.23 Alpha estimate of reliability = 0.90 Cronbach's a for composite = 0190 Table F2 Total Questionnaire and Scales Reliabilities, Means, Standard Deviations, and Number of Cases (Main data) Number Mean Standard Alpha Lowest Highest Number of Items Deviation Reliability Score Score of Cases Total Questionnaire 48 193.72 20.25 0.90 121 239 723 Scale 1: Confidence in learning mathematics Scale 2: Attitude toward success in mathematics Scale 3: Mathematics as a male domain Scale 4: Usefulness of mathematics 45.72 8.79 0.89 50.79 5.91 0.75 47.78 7.17 0.80 49.35 7.51 0.86 15 60 785 27 60 .786 20 60 784 18 60 781 130 Table F3 Principal Components of the Total Questionnaire (Main data) Factor Eigenvalue Percent of Variance Cumulative Percent 1 9.3451 19.5 19.5 2 4.5283 9.4 28.9 3 3.2067 6.7 35.6 4 2.4937 5.2 40.8 5 2.0630 4.3 45.1 6 1.4488 3.0 48.1 7 1.3315 2.8 50,9 8 1.2317 2.6 53.4 9 1.0801 2.3 55.7 10 1.0400 2.2 57.9 0.9711 2.0 59.9 0.9261 1.9 61.8 0.8936 1.9 63.7 0.8349 1.7 65.4 0.8047 1.7 67.1 0.7694 1.6 68.7 0.7412 1.5 70.2 0.7355 1.5 71.8 0.7241 1.5 73.3 0.7007 1.5 74.7 0.6265 1.3 76.0 0.6136 1.3 77.3 0.6002 1.3 78.6 0.5968 1.2 79.8 0.5772 1.2 81.0 0.5501 1.1 82.2 0.5435 1.1 83.3 0.5293 1.1 84.4 0.5132 1.1 85.5 0.5044 1.1 86.5 0.4948 1.0 87.5 0.4732 1.0 88.5 0.4353 0.9 89.4 0.4169 0.9 90.3 0.4042 0.8 91.1 0.4009 0.8 92.0 0.3804 0.8 92.8 0.3750 0.8 93.6 0.3667 0.8 94.3 0.3499 0.7 95.0 0.3465 0.7 95.8 0.3384 0.7 96.5 0.3313 0.7 97.2 0.3134 0.7 97.8 0.2787 0.6 98.4 0.2690 0.6 99.0 0.2558 0.5 99.5 0.1059 0.2 100.0 Table F4 Varimax Rotated Factor Loadings of the Total Questionnaire (Main data) 131 Item Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 Factor 9 FactorlO Ql &67J5 0.2994 -0.0502 0.0742 -0.1473 -0.1161 0.2506 0.0651 0.1283 0.0207 Q2 0.4328 0.3096 -0.0482 0.1259 -0.0862 0.0249 0.1351 0.0404 0.0646 Q3 0.2697 0.2006 0.1253 0.0758 0.0304 0.0406 0.6938 -0.1228 0.0810 -0.0564 Q4 0.2954 0.2215 -0.0072 0.1388 0.0670 0.1707 9.6642 -0.0075 -0.0200 0.0891 Q5 0.3238 0.1330 0.0439 0.0604 0.0814 0.0979 06928 0.0389 0.0128 -0.0398 06 0.3224 -0.0247 0.0982 -0.0956 -0.1078 0.3142 0.0892 0.0825 0.0408 Q7 0,7453 0.0943 0.0572 0.0541 0.0143 0.1123 0.0637 0.0471 -0.1064 -0.0653 Q8 0.5254 0.0861 0.0800 0.0416 0.0818 0.3333 0.2800 0.0834 -0.1485 -0.0446 09 ami 0.0467 0.0993 0.0507 . 0.0730 0.1453 0.0926 0.0209 0.0467 -0.0647 QIO 07619 0.0563 0.0575 -0.0023 0.1455 0.1293 0.0787 -0.0542 0.0117 -0.0007 Qll 0.6826 0.0608 -0.0127 0.0056 0.0612 0.1539 0.0493 0.0007 0.1908 0.0828 Q12 0.1721 0.0163 0.0239 0.1093 0.0542 0.1293 -0.0444 0.0900 -0.0481 Q13 0.0601 0.1302 0.0329 &roa 0.0429 0.0453 0.0097 0.0371 -0.1097 -0.0483 Q14 0.0393 0.1007 0.0635 0.1315 0.1091 0.0242 -0.0074 -0.0152 0.0382 Q15 0.0527 0.1026 0.1141 wsm 0.1145 0.0558 -0.0605 -0.0804 0.1619 -0.0817 Q16 0.0267 0.1133 0.0716 0.7462 0.0011 0.0288 0.0248 -0.0310 0.0039 0.0724 Q17 0.0529 0.1306 0.0221 §zm 0.0462 -0.0011 0.0994 -0.0076 0.0525 -0.0007 Q18 0.0243 0.1001 0.0682 OfiHCB 0.0864 0.0350 0.2014 0.1269 -0.0009 0.0365 Q19 0.2733 0.0752 0.0185 0.1726 0.1049 0.1497 -0.1465 -0.0530 &sm 0.1459 Q20 0.0325 0.0350 0.0795 -0.0662 0.1641 0.0094 0.1358 0.0151 0.0600 Q21 0.0761 0.0273 0.1513 0.1166 mm 0.0110 0.0099 -0.0927 0.0733 -0.1081 Q22 0.0428 0.0521 0.0467 0.1039 0.0144 -0.0207 -0.0309 -0.0309 -0.0516 Q23 0.0940 0.0159 0.0615 0.0866 &S38* 0.0980 0.1216 0.2784 0.2303 0.0665 Q24 0.0774 -0.0669 -0.0116 0.1922 0.56-54 0.1293 0.0711 0.2321 0.1871 0.2447 Q25 0.0524 0.0185 0.0227 0.0031 -0.0169 -0.0056 -0.0140 0.0065 0.1110 Q26 -0.0034 0.1337 076$5 0.1402 -0.0165 -0.1148 -0.0114 -0.0816 -0.0326 0.1038 Q27 0.0707 0.0361 0.7646 0.0987 0.0381 -0.0441 0.0073 0.0810 -0.0044 0.0858 Q28 0.0161 0.0321 0.0281 0.1220 0.0260 0.0313 -0.0364 -0.0129 0.0733 Q29 -0.0624 -0.0281 0.1310 -0.0432 -0.0189 -0.0141 0.0179 -0.0354 0.1294 Q30 0.0166 -0.0129 0.4369 0.0957 0.0325 0.0550 -0.0324 0.0873 -0.0245 83521 Q31 -0.0023 -0.0671 0.3462 0.0038 0.2026 0.2279 0.0650 03508 0.3101 -0.1201 Q32 0.0502 0.0481 0.1109 0.0034 0.0808 -0.0596 -0.0256 -0.1027 0.0529 Q33 0.0256 -0.0195 -0.0092 0.0240 0.1655 -0.0733 0.5192 0.2028 -0.0217 Q34 0.1243 0.0196 mm -0.0112 -0.0258 0.2565 0.0016 0.3559 0.3546 -0.1237 Q35 -0.0034 -0.0277 &6537 0.0401 0.0679 0.2059 0.1227 0.2602 0.0863 -0.0540 Q36 -0.0342 0.0240 mmi 0.1412 0.0971 0.3122 0.1680 0.2206 0.2693 -0.0577 Q37 0.1092 mm 0.0508 0.1199 0.0166 0.2170 0.0242 -0.0973 -0.0394 -0.0268 Q38 0.1052 0.0410 0.0797 0.0907 -0.0549 0.2116 -0.0552 0.0503 0.0269 Q39 0.0374 -0.0444 0.1551 -0.0547 0.0476 0.0723 0.0066 0.0236 -0.0865 Q40 0.0554 turn 0.1309 0.1751 0.0193 -0.0560 0.2178 0.0385 0.0946 -0.1484 Q41 0.1540 ami -0.0234 0.1287 -0.0460 0.1942 0.0263 0.0167 -0.0651 0.1138 Q42 0.1783 0.0185 0.0774 -0.0086 0.1413 0.0485 0.0347 -0.0177 0.1570 Q43 0.0462 0.1455 0.0864 0.0420 0.0525 &S390 0.0812 -0.0111 0.1564 -0.0580 Q44 0.2051 0.4798 -0.0276 0.0480 0.1029 0.0712 0.0121 0.0028 -0.0176 Q45 0.2495 0.3054 0.0385 0.0347 0.0888 OJS27 0.1003 0.0332 -0.0255 0.1289 Q46 0.1145 (M«57 0.1305 0.0638 0.0341 0.2289 0.0153 0.0945 0.0710 -0.1725 Q47 0.2630 0.1796 0.0259 0.1783 -0.0151 &sm 0.0016 0.0446 0.0364 0.0471 Q48 0.4058 05206 -0.0520 0.0544 0.0415 0.2980 0.1175 0.0364 0.0343 0.0477 Note: Greater salient loadings are shaded and the dotted lines indicate the breaks between the theoretical constructs of the items. 132 Table F5 Confirmatory Varimax Rotated Factor Loadings of the Total Questionnaire (Main data) Item Factor 1 Factor 2 Factor 3 Factor 4 Communality Ql &G532 0.3058 -0.0819 -0.0296 0.5278 Q2 0.3638 -0.0338 0.0587 0.4263 Q3 0.47O9 0.2881 0.0637 0.0921 0.3173 Q4 05124 0.3174 -0.0011 0.1627 0.3897 Q5 0-547H 0.1935 0.0450 0.1027 0.3501 Q6 0.6587 0.3291 -0.0560 0.0141 0.5456 Q7 0,6773 0.1230 0.0113 0.0063 0.4740 Q8 0.6088 0.1675 0.0958 0.0457 0.4099 Q9 0.0573 0.0869 0.0458 0.5808 Q10 0.7372 0.0321 0.0311 0.0427 0.5473 Qll 0.6850 0.0378 0.0392 0.0247 0.4728 Q12 &7532 0.1343 -0.0066 0.0453 0.5874 Q13 -0.0128 0.2780 -0.0269 mm 0.4617 Q14 0.0099 0.2318 0.0322 0.7*35 0.5640 Q15 0.0068 0.1847 0.0745 0.6651 0.4820 Q16 -0.0430 0.2790 0.0118 0.6382 0.4871 Q17 0.0230 0.2671 -0.0257 0.6604 0.5087 Q18 0.0432 0.2400 0.0754 0,6321 0.4647 Q19 -0.0029 0.1512 0.2485 0.1814 Q20 0.2252 -0.1038 0.2546 0.0925 0.1349 Q21 0.2120 -0.1980 0.1873 0.4839 0.3534 Q22 0.1855 -0.1998 0.1079 0.4957 0.3317 Q23 0.2957 -0.1613 0.2660 0.3809 0.3293 Q24 0.2487 -0.2080 0.2008 0.4712 0.3674 Q25 -0.0232 0.0838 0.6549 0.0037 0.4365 Q26 -0.1187 0.2229 0.6322 0.0846 0.4705 Q27 -0.0068 0.1042 0.703* 0.0744 0.5118 Q28 -0.0185 0.0845 0.7092 0.0609 0.5141 Q29 -0.0712 -0.0104 0.3362 -0.0427 0.5581 Q30 -0.0395 0.0565 0.4804 0.0726 0.2408 Q31 0.1544 -0.1190 0.5317 0.1463 0.3421 Q32 0.0758 -0.0238 03241 0.0073 0.1114 Q33 0.0708 -0.0306 (MW37 0.0129 0.4873 Q34 0.2112 0.0258 0.5898 0.0073 0.3932 Q35 0.0705 0.0400 0.7176 0.0722 0.5268 Q36 0.1242 0.0775 0.5865 0.2073 0.4084 Q37 0.1648 0.74*45 0.0269 0.0946 0.5331 Q38 0.1943 0-5370 0.0128 0.1046 0.3372 Q39 0.0934 0.7116 -0.0652 0.0916 0.5278 Q40 0.1432 0.5755 0.0996 0.1605 0.3873 041 0.2008 -0.0129 0.0630 0.5777 Q42 0.2343 04379$ 0.0418 0.0433 0.5204 Q43 0.2408 0.2127 0.2085 0.1134 0.1596 Q44 0.3693 0.4942 0.0750 0.0977 0.3958 Q45 04014 0.3618 0.1478 0.0769 0.3198 Q46 0 1985 0-4562 0.1726 0.0734 0.2827 Q47 £338* 0.2856 0.1189 0.1594 0.2355 048 0.4905 0.4979 0.0095 0.0660 0.5008 Note: Greater salient loadings are shaded and the dotted lines indicate the breaks between the theoretical constructs of the items. 133 Similar to the pilot data, the scree test (Cattell, 1966 cited in Norusis, 1993; and in Tabachnick & Fidell, 1989) of eigenvalues plotted against factors was used as a second criterion to find the number of factors measured by the questionnaire. Experimental evidence indicates that the scree begins at the kth factor, where k is the true number of factors (Norusis, 1993). Figure 1 shows the screen output for the main data produced by SPSSX FACTOR. What one is looking for is the point where a line drawn through the points changes direction. As can be seen in Figure 1, the first four eigenvalues are around the same line. After that, three other different lines, with noticeably different slopes, best fit the remaining six points. That is, the plot shows a distinct break between the steep slope of the large factors and the gradual trailing off of the rest of the factors. Thus, there appear to be about four factors (Confmat, Attsmat, Matdom, and Usefmat) in the questionnaire as indicated in main data of Figure 1. 1 2 3 4 5 6 7 8 9 10 Factors Figure Fl Screen output for main data produced by SPSS x FACTOR. 134 Table F6 Principal Components of the Perceived Confidence in Learning Mathematics Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 5.6941 47.5 47.5 2 1.3266 11.1 58.5 0.8629 7.2 65.7 0.7838 6.5 72.2 0.5758 4.8 77.0 0.4822 4.0 81.0 0.4731 3.9 85.0 0.4169 3.5 88.5 0.4014 3.3 91.8 0.3663 3.1 94.9 - 0.3492 2.9 97.8 0.2678 2.2 100.0 Factor 1 Factor 2 Scale item Figure F2 Correlations of the Perceived Confidence in Learning Mathematics scale's items with factors. 135 Table F7 Principal Components of the Attitude toward Success in Mathematics Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 3.7700 31.4 31.4 2 2.9952 16.6 48.0 3 1.0908 9.1 57.1 0.8362 7.0 64.1 0.8052 6.7 70.8 0.7088 5.9 76.7 0.6174 5.1 81.9 0.5491 4.6 86.4 0.5017 4.2 90.6 0.4074 3.4 94.0 0.3802 3.2 97.2 0.3380 2.8 100.0 60 .= T3 et o u o u CS U. 0.9 j 0.8 --0.7 --0.6 •• 0.5 --0.4 --0.3 •• 0.2 --0.1 •• 4- + CO m co + 1 - T - i - C M C M C M C M C M o o o o o o o o a a o o Factor 1 Factor 3 Factor 2 Scale item Figure F3 Correlations of the Attitude toward Success in Mathematics scale's items with factors. 136 Table F8 Principal Components of the Perception of Mathematics as a Male Domain Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 4.3838 36.5 36.5 2 1.3871 11.6 48.1 3 1.0616 8.8 56.9 0.9036 7.5 64.5 0.7406 6.2 70.6 0.6441 5.4 76.0 0.5906 4.9 80^9 0.5548 4.6 85.6 0.5170 4.3 89.9 0.4909 4.1 94.0 0.3782 3.2 97.1 0.3478 2.9 100.0 .a 03 u o u CS 0.9 T 0.8 --0.7 •-0.6 •-0.5 •-0.4 --0.3 •-0.2 --0.1 --Factor 1 Factor 3 Factor 2 un t D r - o o o o i - C M c o T j - L o c o C M ( M N t M N W f f l W o n n n O 0 0 0 0 0 0 0 0 0 0 0 Scale item Figure F4 Correlations of the Perception of Mathematics as a Male Domain scale's items with factors. 137 Table F9 Principal Components of the Perceived Usefulness of Mathematics Scale's Items. Factor Eigenvalue Percent of Variance Cumulative Percent 1 4.8645 40.5 40.5 2 1.3166 11.0 51.5 0.8810 7.3 58.9 0.7887 6.6 65.4 0.7232 6.0 71.5 0.6334 5.3 76.7 0.5811 4.8 81.6 0.5273 4.4 86.0 0.5046 4.2 90.2 0.4182 3.5 93.7 0.4069 3.4 97.0 0.3544 3.0 100.0 Factor 1 Factor 2 Scale item Figure F5 Correlations of the Perceived Usefulness of Mathematics scale's items with factors. APPENDIX G Tables for Figures in Chapter 139 Table for Figure 4.1 Age of students by school type School 15 years or less 16 years 17 years 18 years 19 years 20 years or more PR 0 8.5 23 28 24 16.5 PU 3.5 11.9 18.9 22.9 27.9 14.9 PNE 1.5 23.9 35.3 17.9 14.4 7 PE 1.5 31.3 54.2 9.5 2.5 1 Table for Figure 4.2 Mean score of students by gender, career choice and school type on Perceived Confidence in Learning Mathematics School male female HMC MMC LMC PR 45.6 44.1 48.8 43.6 39.3 PU 47.0 43.6 47.3 44.1 41.7 PNE 48.4 43.1 49.3 43.8 41.0 PE 473 453 51.8 44.2 42.01 Table for Figure 4.3 Mean score of students by gender, career choice and school type on Attitude toward Success in Mathematics School male female HMC MMC LMC PR 50.0 49.6 51.3 49.0 47.9 PU 49.7 51.3 50.2 51.6 49.8 PNE 51.3 50.2 52.1 49.5 49.5 PE 50J 53.3 52.0 53,2 50.9 140 Table for Figure 4.4 Mean score of students by gender, career choice and school type on Perception of Mathematics as a Male Domain. School male female HMC MMC LMC PR 42.7 48.2 45.4 45.3 45.8 PU 44.4 50.6 46.4 49.5 47.9 PNE 44.4 50.1 47.7 46.6 47.2 PE 4TA 52J 48,5 50.5 51.3 Table for Figure 4.5 Mean score of students by gender, career choice and school type on Perceived Usefulness of Mathematics School male female HMC MMC LMC PR 50.2 48.0 51.8 50.0 43.7 PU 50.6 49.3 51.5 50.4 45.5 PNE 50.3 48.2 52.2 49.3 43.8 PE 5O0 47J 53$ 49J 41.4. APPENDIX H Duncan and Scheffe Post Hoc Comparisons for Career Choice and School Type 142 Table HI Comparison of Career Choice Means on Perceived Confidence in Learning Mathematics Comparison Career Choice Mean Career Choice LMC MMC HMC 41.1 LMC 44.1 MMC * 49.2 HMC * * Note: * denotes pairs of groups significantly different at the 0.05 level. Table H2 Comparison of Career Choice Means on Attitude toward Success in Mathematics Comparison Career Choice Mean Career Choice LMC MMC HMC 49.6 LMC 51.0 MMC * 51.3 HMC * Note: * denotes pairs of groups significantly different at the 0.05 level. 143 Table H3 Comparison of Career Choice Means on Perception of Mathematics as a Male Domain Comparison Career Choice Mean Career Choice LMC MMC HMC 48.2 LMC 48.2 MMC 46.9 HMC Note: No two groups were significantly different at the 0.05 level. Table H4 Comparison of Career Choice Means on Perceived Usefulness of Mathematics Comparison Career Choice Mean Career Choice LMC MMC HMC 43.3 LMC 49.6 MMC * 52.2 HMC * * Note: * denotes pairs of groups significantly different at the 0.05 level. 144 Table H5 Comparison of School Means on Perceived Confidence in Learning Mathematics Comparison School Type Mean School Type PuR PuU PrNE PrE 44.8 PuR 45.3 PuU 45.7 PrNE * 46.3 PrE * Note: * denotes pairs of groups significandy different at the 0.05 level. Table H6 Comparison of School Means on Attitude toward Success in Mathematics Comparison School Type Mean School Type PuR PuU PrNE PrE 49.7 PuR 50.5 PuU 50.6 PrNE 52.0 PrE * * * Note: * denotes pairs of groups significandy different at the 0.05 level. 145 Table H7 Comparison of School Means on Perception of Mathematics as a Male Domain Comparison School Type Mean School Type PuR PuU PrNE PrE 45.5 PuR 47.5 PuU * 47.2 PrNE * 50.0 PrE * * * Note: * denotes pairs of groups significandy different at the 0.05 level. Table H8 Comparison of School Means on Perceived Usefulness of Mathematics Comparison School Type Mean School Type PuR PuU PrNE PrE 48.8 PuR 49.9 PuU 49.0 PrNE 48.5 PrE Note: No two groups were significantly different at the 0.05 level. 

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