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EXPLAINING THE GENDER GAP IN HIGH SCHOOL MATHEMATICS ACHIEVEMENT: AN ANALYSIS OF THE EDUCATIONAL LONGITUDINAL STUDY Sanhita Gupta B.A., Sambalpur University, 2002 M.A., Benaras Hindu University, 2004 THESIS Submitted in partial satisfaction of the requirements for the degree of MASTER OF ARTS in SOCIOLOGY at CALIFORNIASTATEUNIVERSITY, SACRAMENTO SUMMER 2011 EXPLAINING THE GENDER GAP IN HIGH SCHOOL MATHEMATICS ACHIEVEMENT: AN ANALYSIS OF THE EDUCATIONAL LONGITUDINAL STUDY A Thesis by Sanhita Gupta Approved by: __________________________________, Committee Chair MridulaUdayagiri, Ph.D. __________________________________, Second Reader Randall MacIntosh, Ph. D. ____________________________ Date ii Student: Sanhita Gupta I certify that this student has met the requirements for format contained in the University format manual, and that this thesis is suitable for shelving in the Library, and credit is to be awarded for the thesis. __________________________, Graduate Coordinator ___________________ Amy Qiaoming Liu, Ph.D. Date Department of Sociology iii Abstract of EXPLAINING THE GENDER GAP IN HIGH SCHOOL MATHEMATICS ACHIEVEMENT: AN ANALYSIS OF THE EDUCATIONAL LONGITUDINAL STUDY by Sanhita Gupta This is a study of the gender gap in the mathematics achievement that exists in the tenth grade and the twelfth grade students. The study was done using data from the Educational Longitudinal Study of 2002. The findings state that not only a gender gap exists; this gap also increases from the tenth grade to the twelfth grade. _______________________, Committee Chair MridulaUdayagiri, Ph.D. _______________________ Date iv ACKNOWLEDGMENTS I would like to thank Dr. MridulaUdayagiri immensely for her support, encouragement, and patience during the entire course of this research. I am sincerely grateful to her for all her help. I would also like to thank Dr. Randall MacIntosh for being in my committee and providing a constant intellectual support. I would also like to acknowledge the help provided by Michael Small and thank him for his moral support. I would also like to thank Dr. Amy Liu for her help during my entry into the program. Most importantly, I would like to thank my family for being a constant source of encouragement to me at all times. v TABLE OF CONTENTS Page Acknowledgments ........................................................................................................................... v List of Tables ................................................................................................................................ viii List of Figures ................................................................................................................................. ix Chapter 1. INTRODUCTION ....................................................................................................................... 1 Significance of the Study............................................................................................................. 8 2. LITERATURE REVIEW .......................................................................................................... 12 Introduction ........................................................................................................................... 12 Rationale for Theoretical Framework ................................................................................... 13 Theoretical Framework for Analysis..................................................................................... 16 Essentialist Perspective ........................................................................................................ 16 Cognitive Social Learning Theory ....................................................................................... 20 Stereotype and Self-assessment .................................................................................... 21 Implicit Bias and Lack of Future Opportunities ........................................................... 22 Social Structural Theory ..................................................................................................... 23 Socialization ................................................................................................................. 23 Family Income .............................................................................................................. 23 Race .............................................................................................................................. 25 Influence of Parents ...................................................................................................... 27 3. RESEARCH DESIGN AND METHODOLOGY ..................................................................... 29 Hypotheses ............................................................................................................................ 29 vi Data Source ........................................................................................................................... 29 Dependent Measure............................................................................................................... 30 Independent Measure ............................................................................................................ 31 Control Variables .................................................................................................................. 32 4. FINDINGS AND INTERPRETATION .................................................................................... 35 5. CONCLUSION AND DISCUSSION ........................................................................................ 46 Directions for Future Research ............................................................................................. 49 Suggestions for Improvement .............................................................................................. 49 Appendix ELS: 2002 Imputation Variables ................................................................................... 50 References...................................................................................................................................... 51 vii LIST OF TABLES Page Table 1 Sample Size for the Total Sample and the Four Ethnic Groups ....................................... 36 Table 2 Descriptive Statistics for IRT - Estimated Math Score for Male and Female Students .... 38 Table 3 Male and Female Students Percentages near the High End of IRT - Estimated Math Score Distributions .................................................................................................. 40 Table 4 Effect of Predictor Variables on Math Scores .................................................................. 42 Table 5 Effect of Predictor Variables on Male and Female Math Scores Separately .................... 45 viii LIST OF FIGURES Page Figure 1 Intent of First-Year College Students to Major in STEM Fields, by Race/Ethnicity and Gender, 2006 ............................................................................................................... 3 Figure 2 NAEP-Long Term Trend (LTT) Mathematics Assessment Average Scores, by Gender, 1978-2004 ............................................................................................................ 6 Figure 3 SAT Mathematics Mean Score by Gender, 1994-2004 ................................................... 14 Figure 4 Main NAEP-Mathematics Average Scores by Family Income Levels, 2007 ................. 24 Figure 5 Main NAEP-Mathematics Assessment Scores for 8th Grade Students, by Gender and Race/Ethnicity, 2007 ................................................................................................. 26 ix 1 Chapter 1 INTRODUCTION In January 14, 2005, Lawrence Summers, president of Harvard University at that time, implied that “the over-representation of men in science and engineering in tenured positions at the elite universities and research institutions may be in part due to innate differences in ability between the sexes” (York, Clark 2007: 7). This instantly sparked the ongoing debate about the discrepancy in the attitude, skills, and scientific/mathematical behaviors between males and females. Why do such debates exist? More importantly, can sociology provide insight into such gender differences? Therefore this study will investigate why there is such a persistent under-representation of women in the field of mathematics and their lack of involvement in this field. This “gender gap” is most visible where male students outscore female students by more than about 3-to-1 at extremely high levels of math ability and scientific reasoning (Wai et al. 2010). A lot has been said, written, and researched about the small number of women found in top positions in science, technology, engineering, and mathematics (Wai et al. 2010). While some researchers such as Lewontin and Levins (1999) like to believe in the intrinsic differences between the sexes’ abilities when it comes to mathematics achievement, organizations like American Association of University Women (AAUW), National Science Foundation (NSF), and National Alliance for Partnerships in Equity (NAPE), consider many social and cultural factors such as self-assessment, stereotypes, and socialization as underlying causes for this gender gap. But in reality there are real 2 differences in the participation of girls compared to boys in the mathematics achievement (Wai et al 2010). Even though the gap has reduced to a ratio of 3 is to 1, there continues to be a persistent underrepresentation of women in mathematics-related fields and this leads to a shortage of competent and skilled women in science-related occupations and presents a model of occupational gender segregation (Penner and Paret 2008). Women now constitute a majority of college students which is evident from the increase in undergraduate degree recipients amongst women. In 2006-2007, 57 percent of the undergraduate degrees awarded were to women, which is a considerable increase from 42 percent (AAUW 2010). But in the STEM fields, women tend to be a step behind men. According to research done by AAUW (2010) as recently as in 2006 women earned only 23 percent of the entire bachelors’ degrees that were granted to engineering majors. In that same year, compared to 29 percent of male freshmen, only 15 percent of female freshmen chose to major in STEM fields. According to another report by National Science Foundation in 2008, the percentage of women earning mathematics and computer science degrees had peaked in 1985 to 26.8 percent. But by 2006 that percentage had fallen to 19.5. Also between 2000 to 2008 there was a 79 percent decrease in the number of incoming female undergraduates who had shown former interest in computer science. The numbers are worse in the case of minority women. In 2008 amongst women computer scientists, African American women comprised 3 percent while Hispanic women only 1 percent (NationalCenter for Women and Information Technology 2009). 3 It is very clear from figure 1 that women are less likely than their male peers to major in a STEM field. 29 percent of all male freshmen compared to 15 percent of all female freshmen planned to major in any STEM field in 2006. But in engineering and computer science, the disparity between men and women is even more significant. Percentage Figure 1: Intent of First-YearCollege Students to Major in STEM Fields, by Race/Ethnicity and Gender, 2006 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Female Male Major Source: American Association of University Women (AAUW), Why So Few?: Women in Science, Technology, Engineering, and Mathematics, Catherine Hill and Christianne Corbett and Andresse St. Rose, 2010, Washington D.C. The number of women in science and engineering are constantly increasing, but they are also continuously being outnumbered by men. In elementary and middle school the participation of boys and girls in math and science courses are roughly equal, yet fewer women pursue these courses as majors compared to men (Hill et al. 2010). So where does the gap emerge? There is no doubt that the participation of girls in math courses have 4 increased since the passage of Title IX in 1972. This educational amendment is significant for gender equity in the United States as it bans sex discrimination in schools – whether academics or athletics (Hill et al. 2010). Before the passage of this amendment, girls did not receive equal opportunities to increase their skills inside or outside of the school (Roche 2007). In a survey conducted by Girl Inc. in 2006, 44 percent of boys and 38 percent of girls agreed that the smartest girl was not the most popular one. In that same survey, 17 percent of the boys and 14 percent of girls felt that the teachers gave the message that it was not important for girls to be good in mathematics (Girls Inc. 2006). So gaps start surfacing in early school life when barriers to girls’ and women’s participation get reinforced through messages received in schools and society. According to the Commission on the Advancement of Women and Minorities in Science, Engineering and Technology (2000), there are four points in a girls’ life when they start losing interest in math and science. They were while entering middle school, late high school, college and graduate school, and in their professional lives. During this time they either receive the wrong messages from society or from individual figures of authority. These messages persuade girls to change their academic interests at a fairly early stage, which then curtails their opportunities and future options because they do not have proper course foundations (Dean 2006). According to the 1969-70 National Assessment of Educational Progress (NAEP), grade school and middle school girls have lagged behind boys in their mathematics achievement scores by an average of 5 points which then increased to 17 points when they reached high school. But more recently girls have started faring a little better. 5 According to the NAEP 2005 High School Transcript, the gap between girls’ and boys’ math assessment in 4th, 8th, and 12th grade were 4 points only (U.S. Department of Education 2007). Despite doing so well, boys still outperform girls in math and science consistently. In 2009, 38 percent of AP physics test takers were girls and only 19 percent in AP computer science (Hill et al. 2010). Even in high school SAT exams there is a huge disparity between girls’ scores and boys’ scores. Though girls do relatively well in their high school tests, they fail to score as well as the boys. In 2008 there was a 33 point difference in the math scores of boys and girls with boys consistently ahead of girls since 1972 (Hill et al. 2010). Figure 2 below, breaks down the NAEP-Mathematics tests into ages 9, 13 and 17 to show how the gender gap increases with age of the students. It shows how over the years giving the tests and also improving, the gender gap is steady and invariable. The gap between the fourth grade boys and girls are evident but this gap increases when the same students reach high school. 6 Figure 2: NAEP-Long Term Trend (LTT) Mathematics Assessment Average Scores, by Gender, 1978-2004 245 Average Score (0-500) 240 235 230 225 Age 9 Male 220 Age 9 Female 215 210 205 200 1978 1982 1986 1990 1992 1994 1996 1999 2004 Year 285 Average Score (0-500) 280 275 270 Age 13 Male 265 Age 13 Female 260 255 250 1978 1982 1986 1990 1992 1994 1996 1999 2004 Year 7 315 Average Score (0-500) 310 305 300 Age 17 Male Age 17 Female 295 290 285 1978 1982 1986 1990 1992 1994 1996 1999 2004 Year Source: American Association of University Women (AAUW), Where the Girls Are: The Facts about Gender Equity in Women, Catherine Hill and Christianne Corbett and Andresse St. Rose, 2008, Washington D.C. So when do the differences begin? Researchers like Levine et al (1999) believe that the main reason there exists a gender gap in mathematics as early as age four is because of the difference of spatial abilities between boys and girls, with the boys having an advantage over the girls. This is because boys use different techniques to process visualspatial information than girls. In a study Levine et al (1999) found that on average preschool boys are more accurate than girls at spatial tasks. Research done by Maccoby and Jacklin (1974), and Halpern (2007) have all shown that disparities in spatial abilities between boys and girls emerge as early as kindergarten. Why is spatial ability important? This is because spatial ability is considered essential to mathematics and scientific thinking such as in organic chemistry and especially for performance on standardized tests, and problem solving ability (Delgado and Prieto 2004). 8 This study will examine the persistent under-representation of women in the field of mathematics and their lack of involvement in this field. Why study the difference in mathematics? Math skills are considered to be essential as well as a gateway to success in STEM fields (Hill et al. 2010). Historically, boys have outperformed girls in math, and this difference has been continual. Secondly, there exists a stereotype that boys are better in math than girls, and this negative stereotype has been one of the most important reasons why girls are lagging behind.Therefore this study uses data from the Educational Longitudinal Study of 2002 to examine the causes for the persistent gender gap in mathematics performance. This dataset was designed to provide trend data about critical transitions experienced by students as they proceed through high school and into the postsecondary education or their careers.More specifically, this research will look into differences in the mathematical achievement of male and female students in the 10th12thand grades and their attitude towards the subject by focusing on questions like: Is there any difference between 10th grader and the 12th grader male and female students’ attitude towards mathematics? How does their level of mathematics achievement differ? And more importantly, is the difference in the mathematics achievement consistent across the ethnic group as well different socio-economic background in the United States? Significance of the Study This research addresses some of the myths associated with the gender gap in STEM fields, in particular math education and performance since math skills are considered to be very essential for the success in STEM fields. But girls not only fall behind in most of the nationalized tests compared to the boys, but they also take less advanced classes like 9 calculus, physics, computer science or chemistry. They persistently have been performing poorly than their male peers in standardized tests like NAEP, SATs, and ACTs. If students are interested in pursuing STEM courses at the college level, it is essential that they be proficient in algebra and pre-calculus (Bryk and Treisman 2010). Some math courses like algebra I are considered to be a gateway to higher levels of study in mathematics, and the completion of these courses leads to improved performance in higher proficiency tests as well as understanding of advanced mathematics. If completed successfully, it increases the rate of enrollment in advanced course work in high school (Matthews and Farmer 2008). Failure to perform well in this class leads to early dropouts and poor performances in standardized tests, and eventual decision to not pursue STEM careers. It is important for women to join the STEM workforce because their contribution in the field of science can maximize the innovation and increase creativity and competitiveness (Hill et al. 2010). Scientists today are doing a lot of work which involves cutting edge technology, medical miracles and discoveries, tackling global warming, building bridges and machineries. Lack of women’s participation in these important activities leads to an exclusion of a true diversity of perspective in addressing needs of women in productive activity. Another implication of the shortage of women in scientific fields is the overall deficiency of American scientists in the U.S. workforce. An estimate of 1.4 million computer specialist jobs will be created by 2018, and if women and minorities do not take part now, there will be shortage in the workforce and most of the jobs will be outsourced. 10 At the given rate, US universities can only produce 29 percent of computer science graduates to fill up those jobs (NationalCenter for Women and Information Technology 2009). There are even fewer women in jobs which require high skills in math related occupations, like engineering. Women comprise no more than 15 percent of any engineering sub discipline, and only 9.5 percent of engineering managers. This research has been inspired by the research conducted by the American Association of University Women’s (AAUW) over a ten-year period (2001-2010) including Why So Few (2010), Where the Girls Are: The Facts about Gender Equity (2008), and Beyond the “Gender Wars”: A Conversation about Girls, Boys, and Education (2001). This research replicates the 1997 study “Gender differences in mathematics achievement: Findings from the National Education Longitudinal Study of 1988.” done by Xitao Fan, Michael Chen, and Audrey R. Matsumoto as a corollary to the research done by AAUW. Consequently the research focuses on the effect of social variables like socio-economic status, parental education and parental expectations on mathematic scores of male and female students. This study focuses on 10th and 12th grade level of students to determine what socio-cultural factors mediate gender differences in the achievement and attitude towards mathematics. Therefore the research questions that will be asked are: Is there any difference between 10th grader and the 12th grader male and female students’ attitude towards mathematics? How does their level of mathematics achievement differ? And more importantly, is the difference in the mathematics achievement consistent across the ethnic groups as well different socioeconomic background in the United States? Do variables like socio-economic status, 11 parental education, school urbanicity, and parental expectations affect the math score of male students differently than female students? This study reviews the existing literature drawn mainly from psychology and sociology to understand the impact of the variables listed above on the gender gap in mathematics performance and achievement in the next chapter (chapter 2). The third chapter reviews the methods used to analyze the NELS data set before providing a discussion and conclusion (chapter 4 and chapter 5). 12 Chapter 2 LITERATURE REVIEW Introduction Girls in the United States have made significant strides toward improving their performance in mathematics over the past fifteen years. Girls have been participating more in standardized tests, and sometimes more than the boys (Hill et al. 2010). In researchconducted by AAUW, Where the Girls Are? (2008), it was reported that more and more girls are attending and graduating from high school and college at a higher rate. But there has been no reduction in the gender gap. It has not only been persistent since the last fifteen years, but in some majors like engineering and computer science, the gap has increased. Ongoing research has attempted to peg down actual causes of this gap. Although some researchers justify using essentialist theoriesof biological differences as was invoked by Lawrence Summers in 2005 in his now infamous statement, gender stratification theory is the main socio-cultural factor that researchers in sociology use to understand this gap. This chapter is divided into two sections. The first section discusses the rationale of using gender both as a category of analysis for the theoretical framework as well as an independent variable to be used during the analysis. Despite the increased participation of girls in mathematics education the gender gap has been persistent. It is for this reason that gender is used as a central category of analysis. The second section discussesthe 13 relevance of the two most important theories used in this study – social structural theory and cognitive learning theory. Rationale for Theoretical Framework For the past few decades there has been a growing interest in different educational experiences, success and educational outcomes that prevail for females and males. This has been fuelled by the perceived lack of interest and success of females in a number of schooling areas, particularly mathematics (National Assessment of Educational Progress 2009). The main reason is that mathematics achievement helps the student to decide his or her successive schooling, career choices and professional achievements. Researchers have defined mathematics as a “critical filter for future academic and occupational options” (Crombie et al. 2005). Women are attending and graduating from high school and college at a higher rate than their male peers. They have made more rapid gains in earning college degrees. But despite the tremendous gain, the field of mathematics remains overpoweringly male (Hill et al. 2010). Even though girls and boys take the same amount of math and science courses, somewhere between middle and high school, the pipeline starts leaking, and men end up pursuing more science and engineering majors than women (Hill et al. 2010). According to the NAEP 2005 High School Transcript Study, the largest gap between boys’ and girls’ scores on math assessment in grades 4, 8, and 12 was only four points, and girls’ high school math grades were higher than boys. Despite attaining the same scores and completing equally challenging curricula, boys have persistently outperformed girls in math overall, as well as perform better on standardized tests like NAEP, SATs, and ACTs (National Center for Education 14 Statistics2007). There is a small gender gap on the mathematics section of the SATs and the ACTs, whereas they do better than the boys on the verbal section (AAUW 2001). More boys take the Advanced Placement (AP) exams on STEM subjects than girls who also score lower than the boys (Hill et al. 2010). In figure 3, the average scores on the SATMathematics (M) has improved for both boys and girls, but the gender gap remains constant throughout the years with boys outscoring girls by 34 to 36 points. Figure 3: SAT Mathematics Mean Score by Gender, 1994-2004 550 SAT-M Score (200-800 Scale) 540 530 520 510 Male 500 Female 490 480 470 460 1994 1996 1998 2000 2002 2004 Year Source: American Association of University Women (AAUW), Where the Girls Are: The Facts about Gender Equity in Women, Catherine Hill and Christianne Corbett and Andresse St. Rose, 2008, Washington D.C. The transition from high school to college is a significant phase as most of the girls turn away from STEM- related career paths especially those that are mathematics-related. 15 According to the National Science Foundation (2009), 29 percent of all male college freshmen and only 15 percent of all female college freshmen planned to major in a STEM field. Women who enter these majors are considered to be well qualified and also have equally high grades as males in all of their math classes in high school. Yet, they leave their STEM majors early in their careers than their male counterparts (Hill et al. 2010). The workforce reflects the schooling and the college patterns. Over the years women have increased in the STEM workforce, but they are still underrepresented in many STEM professions. In 1960, women made up only 1 percent of all the engineers, whereas by 2000 they made up 11 percent of the engineering workforce (U.S. Department of Labor Statistics 2009). Though the increase is notable, women still make up only a small minority of working engineers. So where does the difference start?Penner and Paret (2008) observe that most of the differences emerge after high school as boys are better prepared in their mathematics curriculum than their female classmates. These are due to a number of reasons primary of which are socio-cultural factors where the differences in attitude is instilled at a very young age. The two main myths that are popular are that math talent is innate and girls are naturally not good at it (University of Wisconsin-Madison. 2009). These negative convictions discourage girls and young women to pursue skills required to master mathematical sciences. According to a poll taken by the American Society for Quality (2009) of young boys and girls aged 8 to 17, 24 percent of boys, and only 5 percent of girls said that they were interested in engineering career. In another poll, 74 percent of 13-17 year old boys said 16 that they would be interested in majors that involved computing, as opposed to 32 percent girls of the same age (WGBH Education Foundation and Association for Computing Machinery 2009). Interest in a particular occupation can be influenced by many factors (Hill et al. 2010). There have been many debates over the factors(Kurtz-Costes et al 2008). Some think that it is the competence perceptions, values and stereotypes, while others think that the problems like schools, teacher expectations, pressure from parents, and peers are the basis for this gap (Marsh et al 2005). Some of them have also dismissed the differences in the spatial ability argument because they accept the socialization perspective to account for male advantage in mathematics (Casey et al. 2001). Therefore in STEM education, mathematics achievement needs to be analyzed using gender as central category of analysis for the reasons stated above. Theoretical Framework for Analysis Essentialist Perspective “Legislators, priests, philosophers, writers, and scientists have striven to show that the subordinate position of woman is willed in heaven”, wrote Simone de Beauvoir (1989) in ‘The Second Sex’ (York and Clark 2007:7). Biological justifications for gender inequality in every field, whether it is education or work, have been a basis for the modern supporters of socio-biology and evolutionary psychology (York and Clark 2007). Most of the socio-biologists group believes that the biological explanations for gender differences in mathematics achievement fall into three categories: genetic, hormonal and cerebral. The geneticists portray gender differences in mathematics achievement as attributable to intrinsic genetic differences (Plominand Craig 2001). Hormonal 17 considerations, on the other hand, believe that the importance of hormones is paramount in the gender difference of spatial ability (Penner 2008). Finally, theorists who focus on brain lateralization propose that males have more asymmetrically organized brains and greater hemisphere-specific processes (Halpern 2000). The essentialist perspective is no longer considered valid in recent sociological and psychological research because there is no conclusive evidence to show that there are innate biological differences among the genders. In a study conducted by Jane Mertz and her colleagues of University of Wisconsin-Madison (2009), they found out that it is not biological differences which create a gender gap in math but cultural ones. There are other countries where gender disparity in mathematics performance does not exist and in these countries girls perform at the same par as the boys (University of WisconsinMadison 2009). In another study Lynn and Irwing (2004) found that there exists no difference in the IQ between boys and girls. Both genders may have certain cognitive strengths and weaknesses, but one gender is definitely not smarter than the other. Boys outperform girls on tasks such as spatial orientation and visualization whereas girls outperform boys on verbal skills and tests involving memory and perpetual speed (Kimura 2002). The largest gender gap in cognitive skills is seen in the area of spatial skills where boys have consistently outperformed girls (Hill et al. 2010). Some people think that spatial skills are important for success in science and engineering, but there is no connection between these spatial skills and success in STEM fields (Hill et al. 2010). Despite all the debate, research shows that spatial skills can be improved fairly easily with short-term training. 18 Researchers and social scientists agree that there is a perceptive difference between boys and girls regarding their math achievements, attitudes, and affect. But what are the factors that bring these differences? We have already seen what the essentialist theorists believe and how their theories have been disregarded. Baker and Jones (1993) have argued that the primary reason of girls’ low achievement and poor attitude towards mathematics are socio-cultural factors and gender stratification is a primary reason. This hypothesis is known as the gender stratification theory and it proposes that because of patriarchal society, male students link their achievement to future opportunities, while female students do not perceive such a link and hence do not have the same success rate as boys in the same domain. According to Baker and Jones (1993): Female students, who are faced with less opportunity, may see mathematics as less important for their future and are told so in a number of ways by teachers, parents, and friends. In short, opportunity structures can shape numerous socialization processes that shape performance (pg 92) Thus the gender stratification hypothesis proposes that female students will have a less positive attitude and will perform poorly on mathematics achievement tests than their male peers (Baker and Jones. 1993). Eccles’ expectancy-value theoretical model provides an explanation of the socialization process that can justify the stratification hypothesis. According to Eccles (1994), an individual might not take on any project unless he or she is sure about the accomplishment of the completion of the project. The value of this task is fashioned by the cultural environment for e.g., cultural stereotypes, self-assessment, and occupational segregation by gender, lack of future opportunities, socialization and 19 the individual’s immediate and future plans. And the expectation of success comes from previous triumphant performances like test scores and self-concepts about ability (Aronson and McGlone 2008). Parents, and teachers’ attitudes and expectations are some of the socio-cultural forces, along with stereotypes, that shape self-concepts and attitude towards a subject. In a society where girls are not open to the same career opportunities as boys, gender stratification tends to exist. As a result of these stereotypes, the behavior of the parents, and the teachers change and they in course pass along their anxieties to the young boys and girls (University of Wisconsin-Madison). If a girl believes that the career opportunities that will be available for her does not require her to have mathematical knowledge and skills, she is less likely to develop such skill by taking advanced math classes. She may perceive math as not a useful expertise and more masculine, and may also think that she is incapable of doing math. There are two kinds of theories that support the gender stratification hypothesis: Cognitive Social Learning Theory and Social Structural Theory. This study is therefore located at the intersection of these two theories. By focusing on self-assessment questions (‘As things stand now, how far in school do you think you will get?’ and ‘Do you plan to continue your education right after high school or at some time in the future?’) from the Educational Longitudinal Study of 2002, this study will be able to find out the importance of stereotypes and self-assessment on high school students. This dataset (NELS) was constructed to observe the transition and the changes of a national sample of young people from the 10th grade to the world of work. The 20 NELS is a longitudinal study where the data were collected in four waves – 10th grade, 12th grade, post-secondary education, and the world of work. This research will focus on the 10th grade and the 12th grade specifically to answer some questions like: Is there any difference between 10th grade and 12th grade male and female students’ attitude towards mathematics? How does their level of mathematics achievement differ? And, is the difference in mathematics achievement consistent across the ethnic groups as well as different socio-economic groups in the United States? Cognitive Social Learning Theory A psychological theory that further supports the gender stratification hypothesis is cognitive social learning theory (Bussey and Bandura 1999). According to this theory, reinforcements, modeling and cognitive processes are some of the social factors that contribute to the development of gender-type behaviors. Role models and socializing agents are important factors of this theory because while making academic choices, individuals depend on gender-appropriate behavior from others. This is because girls are observant to the behavior of other women and how they lead their everyday life. If they perceive that women are not choosing careers that are on the same lines as being a scientist or a mathematician or an engineer, they might feel that these careers are unachievable for women. As a result they might not be willing to put in the hard work for those subjects. These feelings then get internalized within the individuals and provide some explanation as to why women make such gendered decisions (Bussey and Bandura 1999). Factors such as stereotypes and self-assessment, and implicit bias further reinforce the gendered behavior. 21 Stereotype and Self-assessment Stereotype and the effects of stereotype threat is one of the most important gendered behaviors and it can provide an explanation as to the differences in mathematics (Reyna 2000). Children are constantly getting messages from everywhere that promotes stereotype threat in all possible fields. Gendered stereotype effects on self-perceptions are strong when these stereotypes are salient (Blanton et al 2002). When a gender stereotype is significant high school students rated themselves as having weaker abilities in science and also reported lower grades in math than when the stereotype is not that relevant. Disparities in the math performance of girls are seen as a biological difference and a lack of talent (Keifer and Shih 2006). Stereotypes also results in loss of confidence as girls progresses through school (Hill et al. 2010). Along with stereotypes, self-assessment is another important factor which either prompts girls to take up advanced math courses or pushes them to drop off from those classes. And most of the time stereotypes give rise to negative self-assessment. Boys assess their mathematical abilities higher than the girls and this encourages them to enroll into advanced mathematical classes (Correll 2001). Negative stereotypes affect the selfassessment of girls. If a girl believes that most people think that boys are better at math, that thought affects her, even if she doesn’t believe it herself (Hill et al. 2010). Stereotype and self-assessment are the most important issues in this research. This study will try to find out whether it affects a female students decision of choosing mathematics for higher education. The self-assessment question from the Educational Longitudinal Study, “As things stand now, how far in school do you think you will get?” and “Do you plan to 22 continue your education right after high school or at some time in the future?” (STEXPECT) will hopefully shed some light on this concern. Implicit Bias and Lack of Future Opportunities The gender stratification that takes place at a national and a societal level manipulates the perception of the youths as well as the adults who are involved in the socialization and academic training of these youths (Riegle-Crumb 2005). The lack of women in the labor force sometimes conveys a negative message about the correlation between gender and opportunities (Oakes 1990). In a gender stratified society, when girls are confronted with the reality of limited opportunities for their future, they may invest less effort in their education, perceive it as less important and become more vulnerable to unpromising stereotypes regarding academic performances (Oakes 1990). Gender segregation has some effect on young people’s perception of future, but not as much as it has on the institutions and other adult individuals who come in contact with these young people. For example schools may reproduce gender inequality through differential treatment of students and teachers may be less inclined to become mentors for young girls and encourage them to become academically strong. Sometimes schools can use gender as one of the characteristics to stratify opportunities (Baker and Jones 1993). Implicit bias is another important factor which is sometimes more harmful than blatantly held beliefs and values because individuals refuse to recognize them, and hence correct it. (Hill et al. 2010). 23 Social Structural Theory Social structural theory is a robust sociological theory that complements gender stratification theory. This theory maintains that psychological gender differences are rooted in socio-cultural factors, for example the division of labor (Eagly and Wood 1999). The division of labor fosters restrictions and opportunities to males and females based on their social roles and hence promote gender differences in society (Eagly and Wood 1999). If a woman’s cultural and social role is to prepare meals and take care of children but does not involve learning math, they may face structural and social obstacles which might obstruct their mathematics achievement. Factors such as socialization, influence of family members and peers, family income and school characteristics strengthen and highlight gender stratification within the field of mathematics. Socialization The effects of societal beliefs and the learning environment on girls’ achievement and interest in math are considerable. When teachers and parents tell girls that their intelligence can grow with constant learning and experience, they do better on math tests. They are also more likely to continue it in future (Hill et al. 2010). Research on socialization processes has demonstrated that boys are typically expected to do better and be more successful than girls in mathematics (Martinort and Desert 2007). Family Income Socio-economic status is one of the most important factors in student academic performance (Gershoff 2003). Poverty has negative educational, psychological and physical effects on children (Roeper Review 2003). Socio-economic status accounts for a 24 substantial amount of difference in mathematics achievement (NSF 2000). As reported by NSF (2000), students who were in grades 4, 8 and 12 and whose parents had less than high school education scored lower in mathematics compared to students whose parents had a higher education. According to the U.S. Department of Education 2007, students from lower-income families are less likely to score at the proficient level in math and reading. Figure 4: Main NAEP-Mathematics Average Scores by Family Income Levels, 2007 350 Average Score (0-500 Scale) 300 250 200 Higher Income 150 Lower Income 100 50 0 4th grade math 8th grade math 12th grade math Grade Level Source: American Association of University Women (AAUW), Where the Girls Are: The Facts about Gender Equity in Women, Catherine Hill and Christianne Corbett and Andresse St. Rose, 2008, Washington D.C. In figure 4, a majority of 12th graders from lower-income families (61 percent) performed belowa basic level of proficiency on the NAEP math assessment in 2005, while a majority of students from higher-income families (66 percent) performed at or 25 abovea basic level of proficiency. But trends are on the positive side. Fourth and eighth graders from lower income families scored at or above a basic, proficient and advanced levels in math at 2007 than 1996 (U.S.Department of Education 2007). In this study the socio-economic (SES) variable will be taken into account. The variable family income (INCOME) is taken into account for the analysis to see whether the gender gap is less in families of higher income. Race Race/ethnicity is closely associated with the academic performance because African American and Hispanic children score lower on average than white and Asian American children. The minority students have higher drop-out rates and are more likely to not complete high school or college.According to the U.S. Department of Education (2007), while 95 percent of white women had completed high school, only 67 percent of Hispanic women had done so, resulting in a gap of 28 percent between them. According to the NationalCenter for Women and Information Technology (2009), in 2008, only 27 percent of the computer scientists were women and out of that, only 1 percent was Hispanic women. 26 Figure 5: Main NAEP-Mathematics Assessment Scores for 8th Grade Students, by Gender and Race/Ethnicity, 2007 Average Score (0-500 Scale) 300 290 280 270 Male Female 260 250 240 All African American Hispanic White Race/Ethnicity Source: American Association of University Women (AAUW), Where the Girls Are: The Facts about Gender Equity in Women, Catherine Hill and Christianne Corbett and Andresse St. Rose, 2008, Washington D.C. Over the last twenty years according to the National Assessment of Educational Progress (NAEP), mathematics scores have increased for all students. Despite general gains, there continues to be a significant gap between white and African-American students, Hispanic students and Asian-Pacific students (Hambrick 2005). In 2008, there was no substantial change in the White and Black or White and Hispanic score gaps compared to 2004 (NAEP 2009). According to a 2000 NAEP Test, a Hispanic 13 year old student scored lower in mathematics than a white 9 year old student, while an African American and a Hispanic 12th grader failed to score anything at an advanced level in mathematics (Hambrick 2005). Figure 5 breaks down the main NAEP eighth grade math 27 assessment score into race/ethnicity. African-American and Hispanic students score well below the White students. There is a small but statistically significant gender gap which was leaning more towards boys. Amongst African American students there is a significant gap that favored girls, unlike the other racial groups. This study will specifically break down the race/ethnicity variable into gender to find out gender gap within the each racial group. The variable RACE is taken for the analysis to find out the pattern of gender differences in math achievement across the various ethnic groups. Influence of Parents Families play an important role in gender socialization which has led to a considerable interest on the impact of parental factors on students’ mathematics achievement. Family economy perspectives view educational attainment as a rational product of family decision making. If parents are faced with a labor market that privileges males, the first priority becomes the education of the son (Buchmann and Di Prete 2006). A parent’s belief that a daughter’s achievement is due to efforts and a son’s due to talents is closely related to a student’s mathematics related self-concepts and past performances (Penner 2008). Parental encouragement is also very necessary for young students’ career choice. In a study by Jon Miller of Michigan State University (2010), it was seen that only 4 percent of the students with low parental encouragement chose a college major in STEM fields compared to 41 percent of students whose parents strongly encouraged them to attend college (Hill et al. 2010). They also found that parental education had some effect as well as parents encourage their sons more than their daughters. In this research the variable parents’ educational qualification (PARED) and 28 their socio-economic status (SES) are taken to examine whether these variables have any effect on the gender gap. It is a well-known fact that mathematics is considered a gateway course to higher levels of study, especially STEM courses (Walker and Senger 2007). If students are successful in completing the coursework as well as understanding it properly during the middle school, a whole new level of future opportunities open up for them (Wang and Goldschmidt 2003). Therefore, it is very important to understand how differential educational and individual variables may be related to mathematics achievement. It is significant to recognize these variables not only because it may guide future studies, but also to consider potential causal relationships that may allow educators to promote these valuable outcomes. It is thus essential that we consider a number of variables like selfassessment issues (‘As things stand now, how far in school do you think you will get?’ and ‘Do you plan to continue your education right after high school or at some time in the future?’), and parental expectations (‘How far in school does the parent want their tenth grader to go?’) to investigate whether they affect the performance of girls. Another important variable that lacks proper research is the effect of geographical region of the schools. There has been insufficient research done and hence this study will also take this variable into consideration to find out whether the gender gap is greater in certain geographical areas than others. The next chapter will discuss why and how the variables were selected for the study and explore how the hypotheses contribute to a greater understanding of the gender gap in math performance and education. 29 Chapter 3 RESEARCH DESIGN AND METHODOLOGY Hypotheses Hypothesis I – Mathematics achievement score of female students are lower than the male students and the gap increases from 10th grade to the 12th grade. Hypothesis II – The gender gap in mathematics achievement score increases amongst African American and Hispanic students. Hypothesis III – After controlling for all other variables, self-expectations will be the variable to have the highest effect on the mathematics score of students, and also affect female math scores more than male math scores. Hypothesis IV – Variables like SES, parents’ education, school urbanicity, parental expectations and self-expectations affect female mathematics score more than male mathematics score. Data Source The data source for this study is the Educational Longitudinal Study of 2002 (ELS:2002). The ELS was conducted on behalf of the National Center for Education Statistics (NCES) when it was decreed by the United States Department of Education to “collect and disseminate statistics and other data related to education in the United States” (Ingels et al. 2007:2 codebook). The Educational Longitudinal Study is designed to follow the transition of a national sample of young people as they progress from the tenth grade through 12th grade to post-secondary education to their work life. The ELS: 2002 has two very distinct features, one it being a longitudinal study, and second, it being 30 a multi-level study. The same individuals are surveyed more than once over a certain period of time and the information that is collected are from multiple respondent populations consisting of students, parents, teachers, librarians and their schools. The first year of data collection was 2002 where the students were in the tenth grade. They were tested on their achievements and performance in mathematics and reading. The second wave of data collection was in 2004 when the same students were in the twelfth grade. The third wave was in 2006. For the purpose of this study, only the first wave (base year), and the second wave (first follow up) is required, because this study focuses on the gender gap in the mathematics achievement of the tenth grade students and the twelfth grade students. The students who took the achievement tests in the tenth grade and completed the questionnaire were eligible for the first follow-up mathematics and reading assessment. The questionnaire was predominantly self-administered through inschool survey sessions and for some students they were done through Computer Assisted Telephone interviews, or occasionally through mails or field interviews. The final round of data collection will be done in 2012 to judge the cohorts’ outcomes such as the persistence and attainment of higher education, or transition into the labor market. Dependent Measure The dependent variable is the math IRT estimated number right for the base year (BYTXMIRR), and the first follow up year (F1TXM1IR). According to the ELS:2002 codebook, the base year variable is described as: The estimated number right score for math is an estimate of the number of items students would have answered correctly had they responded to all 72 items in the ELS:2002 math itempool. The ability estimates and item parameters derived from the IRT calibration can be used to calculate each 31 student’s probability of a correct answer for each of the items in the pool. These probabilities are summed to produce the IRT estimated number right score (P. G-17) For the math IRT estimated number right, the scores range from a minimum of 12.52 to a maximum of 69.719, and a standard deviation of 11.87 (N = 16,252). The F1 Math IRT estimated number right for F1 scores is described in the ELS:2002 codebook as: First follow-up Math Item-response theory (IRT) estimated number right. The estimated number right score for math is an estimate of the number of items students would have answered correctly had they responded to all 85 items in the ELS:2002 base year and first follow up math item pool. The ability estimates and item parameters derived from the IRT calibration can be used to calculate each student’s probability of a correct answer for each of the items in the pool. These probabilities are summed to produce the IRT estimated number right score (P. G-36). For the F1 math IRT estimated number right, the scores range from a minimum of -8 to a maximum of 82.54, and a standard deviation of 25.21 (N = 16,252). Independent Measure Gender and race/ethnicity are the two independent variables that are used for the analysis for both the base year and the first follow up year. According to the codebook, BYSEX: For this variable the 10th grade students were asked “What is your sex?” The response categories consisted of: male (=1), female (=2). F1SEX: For this variable the 12th grade students were asked “What is your sex?” The response categories consisted of: male (=1), female (=2). For the purpose of the analyses a dummy variable for female will be created with male as the reference point. Male is coded as (=0) and female as (=1) (N=16,252). In the codebook, BYRACE and F1RACE were defined as: 32 The variable is a composite of a few questions. The students were asked “Are you Hispanic or Latina/Latino?”, “If you are Hispanic or Latina/Latino, which one of the following are you?”, and “Please select one or more of the following choices to best describe your race.” The response categories to the race/ethnicity composite consisted of: American Indian/ Alaska Native, non-Hispanic (=1), Asian, Hawaii/ Pacific Islander, non-Hispanic (=2), Black or African American, non-Hispanic (=3), Hispanic, no race specified (=4), Hispanic, race specified (=5), Multiracial, non-Hispanic (=6), and White, non-Hispanic (=7). But for the purpose of analysis in this study, both the variables, BYRACE and F1RACE were recoded to: Asian (=1), Hispanic (=2), African-American (=3), and White (=4).Dummy variables of Asian, African American and Hispanic for BYRACE will be created with White as the reference category. White is coded as (=0) (N = 16,252). Control Variables For the control variables, a number of items are taken into consideration. Socioeconomic status, parents’ education, geographic region of the school, students’ own expectations from themselves, and parental expectations. In the codebook SES is a combination of income, parental education levels and parental occupation. There are four kinds of SES variables in the codebook, Socioeconomic status composite, v.1 (SES1), quartile coding of SES1 variable (SES1QU), socio-economic status composite, v.2 (SES2), and quartile coding of SES2 variable (SES2QU). For this study, the quartile coding of SES2 variable will be used. According to the codebook, the SES variable is an “NLS-72/HS&B/NELS:88-comparable composite 33 variable constructed from parent questionnaire data when available and student substitutions when not: (Ingels et al 2005: 12). The codebook offers two SEs composite variable one slightly different than the other. One SES variable is based on the Duncan Socioeconomic Index (SEI) scale where the occupational codes are taken from the 1961 Duncan SEI occupational prestige scores. The other composite variable is based on the 1989 NORC / General Social Survey (GSS) Occupational Prestige Scale and the occupational codes are taken from there (Ingels et al 2005). Since the SES composite score which is based on the NORC/GSS is a newer version, the quartile coding of that variable (BYSES2QU) will be used for the purposes of analysis in this study. Parental education (PARED) is the highest level of education achieved by the parent. It is derived from the parent questionnaire when available and if missing, it is achieved from the student questionnaire. PARED is a composite variable of mother’s education (MOTHED, and father’s education (FATHED), and since “MOTHED and FATHED were imputed if otherwise missing, PARED is non-missing for all student respondent cases”. (Ingels et al 2005: 8). In the codebook, the question asked was “What is the highest level of education you and your spouse/partner has reached?” The response categories are: Did not finish High School (=1), Graduated from High School or GED (=2), Attended 2-yr school, no degree (=3), Graduated from 2-yr school (=4), Attended college, no 4-yr degree (=5), Graduated from college (=6), Completed Master’s degree or equivalent (=7), Completed PhD, MD, and other advanced courses (=8). BYSTEXP: 10th grade students were asked “How far student thinks he/she will get in school?” The response categories are: Don’t Know (= -1), Less than High School 34 Graduation (=1), High School Graduation or GED only (=2), Attend or complete 2-year college/school (=3), Attend college, 4-year degree incomplete (=4), Graduate from college (=5), Obtain masters’ degree or equivalent (=6), Obtain PhD, MD, or other advanced courses (=7). BYPARASP: Parents were asked “How far in school do you want your tenth grader to go?” The response categories are: Don’t Know (= -1), Less than High School Graduation (=1), High School Graduation or GED only (=2), Attend or complete 2-year college/school (=3), Attend college, 4-year degree incomplete (=4), Graduate from college (=5), Obtain masters’ degree or equivalent (=6), Obtain PhD, MD, or other advanced courses (=7). BYURBAN: Urbanicity of school locale as indicated in the source data for sampling: the Common Core of Data (CCD) 1999-2000 and the Private School Survey (PSS) 1999-2000. It was coded as Urban (=1), Suburban (=2), and Rural (=3). 35 Chapter 4 FINDINGS AND INTERPRETATION This chapter will contain all the tables that were obtained by running statistical analyses using the Educational Longitudinal study: 2002. The tables are followed by the interpretation of the results. The tables have both the tenth grade and the twelfth grade statistics for easy comparison. Table 1 contains the total sample as well as the students for each ethnic group who took the math test. It is seen that the students taking the math test becomes smaller in the twelfth grade. This can be a function of dropouts, early graduation, or their non-response to the cognitive tests. 36 Table 1: Sample Size for the Total Sample and the Four Ethnic Groups Group Total sample [a] Male Female Asian Male Female Hispanic Male Female African American Male Female White 10th Grade 12th Grade 7626 7699 6800 6902 741 724 730 709 1105 1122 940 975 1009 1018 823 906 Male Female 4326 4409 3940 3958 Note: In this table and the following tables, the total sample includes everybody – students with no ethnicity indicators, those of American Indian or Alaska Native origins, and Multi-racial nonHispanic origins. And for this reason, the total sample is larger than the sum of the four ethnic groups. Hypothesis I – Mathematics achievement score of female students are lower than the male students and the gap increases from 10th grade to the 12th grade. Table 2 contains the descriptive statistics for the IRT- estimated math test scores of male and female students of the 10th grade and the 12th grade. Cross sectional weights have been used to get an accurate evaluation of the mathematic achievement of the students. Since the study is a cross-cohort comparison, using weights gives us the most precise way to calculate the math achievement for U.S. national populations at the two grade level. So the items in the Table2 are weighted means and standard deviations for the 10th graders (2002), and the 12th graders (2004). 37 In the table Effect Size (ES) was used to show that the difference in the mathematics score between each ethnic sub-group is statistically significant. The Effect Size was calculated using this formula (Fan and Chen and Matsumoto 1997). ES = (Meanmale- Meanfemale) / Standard Deviationpooled From the table it is seen that male students had a slight advantage over the female students with the ES varying from .10 to .14. After separating the sample according to ethnic groups, slight differences can be seen. The ES increases when the students are in the 12th grade, with African American students having the highest ES of .19, followed by Hispanic students (.15), and White students (.14). Asian students showed a pattern opposite to that of the other students. The negative ES means that the female students had a slight advantage over the male students. 38 Table 2: Descriptive Statistics for IRT - Estimated Math Score for Male and Female Students 10th Grade Total Sample Male Female Asian Male Female Hispanic Male Female African American Male Female White Male Female 12th Grade Mean Standard Deviation Effect size Mean Standard Deviation Effect size 38.20 37.03 12.25 11.50 .10 49.8 47.73 15.42 14.48 .14 41.76 42 12.42 12.15 -.02 54.16 54.92 16.14 15.20 -.05 32.13 30.91 11.34 10.49 .11 42.85 40.77 14.21 13.20 .15 30.28 29.18 9.71 9.31 .12 40.27 37.49 12.51 11.89 .19 41.34 40.13 11.61 10.68 .11 53.19 51.22 14.82 13.57 .14 Hypothesis II – The gender gap in mathematics achievement score increases amongst African American and Hispanic students. In table 3, the students were analyzed in three extreme end of score distribution – those who scored within the first quartile (at or above the 75th percentile), those who scored at the first decile (at or above the 90th percentile), and those who scored at or above the 95th percentile. It is clear from table 3 that male students outnumber the female students in each of the extreme score distributions. Another notable pattern is that female students who score within those distributions decrease drastically at each grade level. As the grade level 39 increases the percentage of female student decreases. In the 10th grade there were 23% of female students that scored within the first quartile. While the percentage of male students coring within the first quartile increases from 27.6% to 28.2%, the percentage of female students decrease from 23% to 21.9%. As the extreme score distribution increases, the percentage of female students keep falling. When they are in the 10th grade, the percentage of female students who score within the first quartile are 23%, it decreases to 8% in the first decile, and 3.6% at or above the 95th percentile. The same pattern that is seen in the total sample can also be seen when it is broken down into ethnic group samples. Only Asian students show a pattern where the percentage of students increase from the 10th grade to the 12th grade in each end of the score distribution – in the first quartile (10th grade) there was 37% of male students and 34.7% of female students. This percentage increases to 40.2% male students and 37.3% female students in the 12th grade. But in the other ethnic group sample (African American, Hispanic, and White), the same configuration is seen. The number of male and female students decreases within each score distribution as well as grade level. There is a radical decrease in Hispanic and African American female students in the extreme score distribution. In the 10th grade there are 10.3% Hispanic and 5.3% African American female students in the first quartile. This decreases to 2.9% Hispanic and 1.1% African American female students in the first decile, and 1% Hispanic and .4% African American female students at the 95th percentile. The numbers become worse when they advance to the 12th grade. 40 Table 3: Male and Female Students Percentages near the High End of IRT - Estimated Math Score Distributions Group In the 1st quartile Total Sample Asian Hispanic African American White In the st 1 decile Total Sample Asian Hispanic African American White At or above 95th percentile Total Sample Asian Hispanic African American White 10th Grade Male Female N % N % 12th Grade Male Female N % N % 2121 27.6 1779 23 1872 28.2 1484 21.9 274 137 37 12.4 251 116 34.7 10.3 287 119 40.2 13.1 258 95 37.3 10.2 68 6.7 54 5.3 57 7.2 49 5.6 1532 35.4 1285 29.1 1323 34 1027 26.2 946 12.3 623 8 831 12.5 512 7.6 159 46 21.5 4.2 130 32 18 2.9 161 35 22.5 3.9 138 20 20 2.1 15 1.5 11 1.1 17 2.2 10 1.1 683 15.8 434 9.8 586 15.1 327 8.3 504 6.6 280 3.6 449 6.8 223 3.3 106 27 14.3 2.4 74 11 10.2 1 106 20 14.8 2.2 77 6 11.1 0.6 7 .7 4 .4 7 .9 1 .1 337 7.8 183 4.2 298 7.7 133 3.4 Note: N is the number of students, both male and female, within each of the three extreme score ratings. 41 Hypothesis III – After controlling for all other variables, self-expectations will be the variable to have the highest effect on the mathematics score of students, and also affect female math scores more than male math scores. Table 4 shows the effect of various control variables on the mathematics score. From table 3 it is quite clear that being a female reduces the math score than being a male, after controlling for race, school urbanicity, parental education, socio-economic status, selfexpectations and parental expectations. Compared to a male student, being a female student reduces the math score on an average, by 1.969 points. Amongst the dummy variables, the pattern seen is quite similar to the hypothesis stated above, as well as the previous tables in the beginning of this chapter. Compared to White students, Hispanic students, and African American students have a lower mathematics scores. Compared to a White student, being a Hispanic student reduces the math score by an average of 5.358 points, and being an African American student reduces it by 7.671 points. Amongst the positive correlations are the parental education, socio-economic status, self-expectations and parental expectations. All these variables show that with one point increase the math score of the student increases. For example, if a student has high expectations, his or her math score increases by 1.792 points. Parental expectation also increases the mathematics score of the students. If parents have higher expectations from their child, the mathematics score increases by 1.094. Every 1 year increase in the parental education increases the math score of the child by .207. 42 Table 4: Effect of Predictor Variables on Math Scores Variable Sex (Female = 1) Race (Asian = 1) Race (Hispanic = 1) Race (African American =1) School Urbanicity (Urban =1) School Urbanicity (Rural =1) Parental Education Socio-economic Status Self-expectations Parental expectation Constant R2 B -1.969*** (.143) .500* (.247) -5.358*** (.217) -7.671*** (.219) -.453** (.162) -.061 (.197) .207*** (.055) 1.573*** (.105) 1.791*** (.056) 1.094*** (.064) 33.853 .339 Beta -.099 .015 -.192 -.270 -.022 -.002 .044 .180 .258 .136 Note: N = 16,252; b = unstandardized regression coefficient with standard error in parentheses; Beta = standardized regression coefficient. *p < 0.05; **p < 0.01; ***p < 0.001 (two-tailed tests) Hypothesis IV – Variables like SES, parents’ education, school urbanicity, parental expectations and self-achievement expectations affect female mathematics score more than male mathematics score. Table 5 was created to see whether the individual predictor variables affect the male and female mathematics score differently. In this table Z score was calculated to test the statistical significance and also help to decide whether or not to reject the null hypothesis. Here the Z score was calculated using this formula: 43 Z = b1 – b2 SEb12 + SEb22 where Z = z score; b1 = female unstandardized regression coefficient; b2 = male unstandardized regression coefficient; SEb1 = female standard error; SEb2 = male standard error (Clogg et al. 1995). From the table below, it is quite clear that most of the z-scores do not approach -/+ 1.96. The critical z-score values when using a 95% confidence level are -1.96 and +1.96 standard deviations. Only the predictor variables Asian and self-expectations have z scores above +/- 1.96. As none of the other variables are close to the desired z-score value, there is no significant difference and we fail to reject the null hypothesis. The predictor variables do not affect the female mathematics score any differently than it does to the male mathematics score and has no differing impact. The two relationships, Asian - female and self-expectations – female, have a z-score which is higher than +/- 1.96. This means that the variables Asian and self-expectations affect females differently than the males. The z-score for Asian is 2.025 (p< .043. This means that being an Asian female student increases the chances of having a higher mathematics score compared to a White female student.Being an Asian female student increases the math score by .973 points whereas being an Asian male student decreases the math score by .029 points. Table 2 also had a result quite consistent with table 5. In table 2 it was seen that the Asian female students had a slight advantage over Asian male students in terms of mathematics score. Also seen in table 3, the percentage of Asian female students increased from the 10th grade to the 12th grade. This pattern was quite 44 different compared to the other students whose percentage decreased as they progressed from the 10th grade to the 12th grade. The self-expectations variable had a z score of -2.669(p< .007).This means the effect that the self-expectation variable has on male and female students is significantly different. A 1-unit increase in self-expectation increases the math score of female students by 1.634 points compared to 1.936 points in a male student. Self-expectation has a larger impact on male math score than female math score. This means that female students had a lower self-expectation from themselves. As discussed earlier, female students compared to male do have a very low expectations from themselves. They tend to believe that boys are better at mathematics than they are, and as a result it affects their math scores (Hill et al 2010). In table 4, it was seen that self-expectations had the highest correlation with a students’ mathematics scores. If a student has high expectations, his or her math score increases by 1.792 points. Table 5 shows that this variable affects the female students differently than male students. 45 Table 5: Effect of Predictor Variables on Male and Female Math Scores Separately Variable Constant Asian Hispanic African American Urban Rural Parents’ Education Socio-Economic Status Self- Expectations Parental Expectations Female b1 Std Error 1 32.247*** .54 .973** .335 -5.199*** .295 -7.542*** .297 -.508* .219 .034 .266 .194** .075 Male b2 Std Error2 33.645*** .524 -.029 .364 -5.538*** .318 -7.806*** .322 -.399 .239 -.143 .290 .220** .082 -1.858 2.025* .782 .603 -.336 .450 -.234 1.703*** .141 1.422*** .155 1.341 1.634*** .080 1.936*** .080 -2.669** 1.116*** .089 1.079*** .092 .289 N= 16,252; b= unstandardized regression coefficient. *p < 0.05; **p < 0.01; ***p < 0.001 (two-tailed tests). Z 46 Chapter 5 CONCLUSION AND DISCUSSION There has been a constant debate whether gap in mathematics achievement still exists after so many years. This thesis was a replication of Fan, Chen, and Matsumoto’s study (1997). The study found a substantial gender gap in mathematics achievement of students of eighth, tenth and twelfth grade. This thesis analyzed data from the Educational Longitudinal Study of 2002, and found a significant gender gap as well. Even after ten years the gender gap has been the same in the field of mathematics, and even though more and more girls are participating in math classes, the gap has not closed enough. In Fan, Chen and Matsumoto’s study “Gender differences in mathematics achievement: Findings from the National Education Longitudinal Study of 1988”, the gender gap was quite significant. In the first quartile the percentage of 10th grade female students were 47.3 percent compared to 52.70 percent male students. This decreased further when they were in the 12th standard becoming 44.82 percent female students compared to 55.18 percent male students. The numbers decreased further in the first decile and the 95th percentile. Using the ELS: 2002 dataset, this thesis had a comparable result. The percentage of 10th grade female students who were in the first quartile was 45.62 percent compared to 54.38 percent. In the 12th grade it decreased further to 44.22 percent female students compared to 55.78 percent male students. And similar to Fan, Chen, and Matsumoto’s study, the percentage decreases in the first decile and the 95th percentile. 47 So why are so few girls and women in mathematics? The key to unlocking this question lies in society’s ability to identify the stereotypes, bias and cultural beliefs that exist about gender in mathematics and science. Half of the work is done if those stereotypes are isolated, because that means the societal institutions can work systematically at undoing them. According to AAUW (2010), promoting girls’ achievements and interest in mathematics, creating a friendly environment in schools and colleges that support more and more women in this field, and finally neutralizing the bias are the three most important points to keep in mind while encouraging women to join the field of mathematics. The main purpose of the study was to discover some nuances to the gender gap in schools. To that end it was to uncover whether a gender gap exists in the tenth and twelfth grade, and whether this gap increases when students progress from the tenth grade to the twelfth grade. To provide a more precise explanation the study isolated predictor variables that affected female mathematics performance differently than male mathematics performance. The results were not very different from those obtained by Fan, Chen and Matsumoto (1997). Even after ten years the gender gap is the same. Compared to a male student, being a female student reduced the math score on an average, by 1.969 points. When the high end of math score distribution was observed (Table 3), substantial gender differences were revealed. Female students were constantly outnumbered by the male students and this gap increased from the tenth grade to the twelfth grade. 48 Race had a significant correlation to the mathematics score of the students. Compared to White students being African American, and Hispanic decreased a student’s math score by 7.671 points and 5.358 points respectively. And if the student was a female, the chances of having a lower math score were also high. Self-expectation variable also had a very high correlation with the math score of the students. This variable also affected female students differently than the male students. The selfexpectations variable had a z score of -2.669. This means that female students had a lower self-expectation of themselves. What was surprising is that parental expectation variable was not statistically significant and neither was the geographical location of the school. The dataset Educational Longitudinal Study: 2002 had certain advantages and disadvantages. Amongst the advantages, the most important one is the fact that the source of the dataset is reliable and reputable. The ELS: 2002 is conducted on behalf of NationalCenter for Education Statistics (NCES). Secondly, the dataset was readily available which made it easier for the researcher to analyze it. The total sample of the data was 16,252 which were large enough for the researcher to generalize the results to the entire population. The main disadvantage of this data source was the fact that it did not contain any data for eighth grade students. The ELS (2002) collected data for only tenth and twelfth grade students. Availability of the eighth grade student data would have given the researcher another comparison point. 49 Directions for Future Research Future research should focus on the determinants of the gender difference. It has already been proven that gender difference exists. Emphasis should be put on predictors like attitude changes toward math learning, social expectancies, social stereotyping and career options. Researchers can follow the same students to college, and discover whether more female students have opted out of mathematics courses, and also how many of these female students have chosen STEM careers. More research should be done to see whether geographical location has a positive impact on the student’s mathematics achievement or not. Suggestions for Improvement Parents and educators can do a great amount of work to encourage more girls and women to enter mathematics and also increase their interest. But unfortunately stereotypes, myths and incorrect beliefs that boys are better in math and can handle STEM careers better persists in society. Research has already shown that such negative stereotypes are harmful for girls’ self-assessment and math test performance because girls can show that they can excel in mathematics. These stereotypes influence their decision to pursue further advanced courses in mathematics and science. Counteracting these negativities can help improve their participation rates as well as their mathematics achievements. 50 APPENDIX ELS: 2002 Imputation Variables The number of missing cases as shown in the table below range from .05 percent for gender to 22.4 percent for family income. 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