Gender nad mathematics achievement parity: Evidence from post-secondary education

This paper examines gender and mathematics performance at the postsecondary education level by using semester grades. The subjects of this experiment are the 479 students in the 24 general math classes taught by the author over the period of 1987-1990. The results of this experiment show no significant gender differences in mathematics achievement. The finding of this experiment support the environmental explanation of gender differences in mathematics performance.

Introduction

Over the last two decades, the gender differences in mathematics performance have been studied intensively, and the findings of these studies have produced controversy regarding educational strategies for teaching mathematics. Some researchers have even examined the possibility of segregated classes for female students, and special teaching and learning styles as congruent with women's "ways of knowing" (Belenky et al., 1986; Marr and Helme, 1992; Kaur, 1992). Gender and Mathematics was the focus of the International Organization of Women and Mathematics Education (IOWME) meetings at the Sixth International Congress on Mathematical Education (ICME6) in Budapest, Hungary, in 1988.

In this study, I have examined the question of gender and mathematics performance at post-secondary education by using the semester grades of 479 students at a two-year community college and four-year state college in Denver, Colorado, in the United States. In the following sections, after a brief survey of the literature, the procedure of evaluating the students' performance, testing method, and the special features of this study are explained. The final section concludes the paper.

Review of the Literature

The general conclusion of the majority of authors of genders and mathematics is that gender differences in learning mathematics do not tend to appear until at least the beginning of the secondary school years; when they appear, they almost always favor boys (Fennema,1974; Fennema and Sherman, 1978; Sherman, 1980; Fennema and Carpenter, 1981;Armstrong,1981; Badger, 1981; Kaminski, 1982; Keys, 1987; Gordon et al.,1990; Kaur,1992, to name a few). However, some recent studies have challenged this general conclusion. Galbraith (1986), for example, studied 334 Australian junior high school pupils (157 boys and 177 girls) and found that girls outperformed boys in mathematics. The same conclusion was reached by Stockard and Wood (1984) for high school students in the U.S. and by Tressou-Milonas (1992) for Greek primary school students.

There are also studies that have found no gender differences in learning mathematics. Swafford (1980) investigated the performance of girls and boys with comparable math backgrounds in first-year algebra classes in high schools across the U.S. and found no significant differences between the genders. Leder (1980) used the data from testing for a high school certificate from the state of Victoria, Australia. She also found no significant gender-related differences in mathematics performance. Kaeley (1988) examined gender and mathematics learning at post-secondary education in a neo-literate society, Papua New Guinea, in the South Pacific. He evaluated the mathematics performance of the students with no significant differences in their math background (through continuous assessment in the form of assignments, test, and the final examination) and found no significant differences in the mathematics achievement of male and female students.

With respect to different aspects of mathematics achievement, the general consensus seems to indicate that females tend to perform better than males in computation, and males tend to perform better than females in problem solving (Hyde et al., 1990). Better verbal ability for girls and spatial ability for boys is also frequent finding (Maccoby and Jacklin, 1974; Werdelin, 1985; Kaur, 1992). Boswell and Katz (1980) argue that better spatial ability of boys and verbal ability of girls are the result of socio-cultural factors. For example parents buy constructional and scientific toys for boys and domestic toys and dolls for girls. However, according to Tartre ( 1990), the nature and extent that spatial ability might influence gender differences in mathematics achievement are largely unknown.

A meta-analysis of the studies that have been done during the period of 1974-1987 on mathematics and gender has produced two general conclusions. First, the average gender gap is very small and statically insignificant. Second, the gender differences have declined over the years (Friedman, 1989). Another metaanalysis of 100 recent studies in gender and mathematics performance has also concluded that the gender gap in mathematics performance is small, insignificant, and has declined over the years (Hyde et al. 1990).

Some researchers have examined the contributing factors for gender-related differences in mathematics. Badger (1981) concludes that social factors, not genetic factors, are responsible for the cases in which girls have performed relatively poorer in math. Fennema (1985) argues that social conditions which influence the educational environment and personal beliefs of females account for gender differences in mathematics. Leder (1990) concludes that gender differences in mathematics learning are complex issues, and in order to eliminate the current existing gender differences in mathematics participation and performance we must examine and modify the variables linked to gender differences in mathematics. Some of the variables which have studied in the literature mentioned by Leder (1990) are the following: 1. Schools' differential treatment of male and female students.

2. Teachers' differential treatment of male and female students.

3. Parents' differential expectation of their sons and daughters, which itself is related to parents' education and occupation.

4. Peer expectation influences on preparing for their future roles as men and women, such as for women mothering may be considered more important that career.

5. Learners' internal beliefs and conformance to cultural values, such as women mathematicians are not feminine and boys have more natural abilities in math than girls.

Leder (1990) argues that examination of the biological factors is nonconstructive because we can not modify those factors. Fennema (1990) suggest that by modifying the environmental factors that influence existing gender differences in mathematics participation and achievement we can provide justice and equity in mathematics education. She explains that providing equity includes equal opportunity to learn mathematics, equal educational treatment, and equal educational outcome.

Hanna et al. (1990), based on data from the Second International Mathematics Study (SIMS) for male and female students in the last grade of secondary school from 15 countries, conclude that mathematics-achievement means for girls were significantly lower than the means for boys except for Thailand, British Columbia, and England in which the data showed high level of home support for both genders. They found that strong parental support for participation in mathematics by both boys and girls was the only variable linked to the mathematics achievement of boys and girls. Moreover, since the results of gender differences vary from country to country, while biological factor do not, their findings do not support the biological theory that attempt to explain boys superiority in mathematics.

The majority of studies on gender and mathematics have focused on non-classroom measures of mathematics performance, usually standardized tests. Most of the studies that have used classroom grades have found either female superiority or no differences in mathematics performance of male and female students for junior high through university mathematics courses (Kimball, 1989). There are some arguments against using classroom grades:

1. Since the participation rate of females in math classes, particularly advanced math courses, is small, they are a selective sample of the female student population. Therefore classroom grades could be biased in favor of females. The question of sample selectivity does not apply to this study since the sample includes 219 males and 260 female students in the 24 general math classes thought by the author.

2. The girl-friendly classroom literature suggests that female students often receive higher grades than males in classes because of their better behavior. In this study, as explained in the next section, the students have been graded based on three written exams, and their grades were not influenced by good or bad behavior.

There are also some arguments in favor of using classroom grades:

1. Males and females taking the standardized tests usually have different math backgrounds. For this reason grades from classes where students are grouped by similar math backgrounds (for example, prerequisites for the current course) offer a better way for comparing male and female students' achievements in mathematics. Moreover, because only classroom learning is tested, experiences in other math and science courses or math-related experiences outside the classroom potentially do not influence the results as much as when standardized test scores are compared (Kimball, 1989). More importantly, in my study, as explained in the next section, the students in the 24 general math classes had selected their courses based on their placement test scores.

2. Grades are an important measure of achievement. Doing well in math courses is ultimately more important for training in scientific careers than the scores on standardized tests (Kimball, 1989).

Methodology

Populations: The populations of this study are the male and female students of Metropolitan State College of Denver (MSCD) and Community College of Denver (CCD) both on the Auraria campus. The Auraria campus is an urban campus located in down town Denver, Colorado, in the United States providing educational opportunities to over 30,000 diverse college students. The characteristic of interest in this study is their performance in general math courses over the 17-week learning process which is measured by their overall semester grades scaled from zero (F) to four (A). General math courses on this campus include: beginning algebra, intermediate algebra, college algebra, principles of statistics, and finite math. In both colleges, students enter these courses, generally, based on the scores of their placement tests.

Samples: The samples are the overall semester grades of 219 male and 260 female students in the 24 general math classes taught by the author over the four-year period 1987-1990 (see Table 1 for details). On average in each class 20 students continued to the end of the semester and received a grade ranging from F to A. Students in all classes have been graded based on three written exams with essay questions. Each exam included a combination of computation, conceptual questions, and problem solving. Identical grading procedures and criteria have been used for all students. To reduce the grading bias and subjectivity which may influence the students's grades, the author evaluated one question at a time for the entire class without paying attention to the students' name. The samples include both day and evening classes, 2-year college (CCD) and 4-year college (MSCD), and from very young to quite mature students. The students selected their classes without knowing the instructor since the name "staff" appeared on the class schedule. I believe that, because of students' diversity, the standard grading method, and the procedure that the students used to select their class and instructor, these samples are reasonable representations, though not random, of the two populations of this study.

Testing for Equality of Learning Capability by Gender in Mathematics

When the sample size is large the appropriate test for the differences between the two population means is the z-test.' In this study, the author have executed a two-tailed z-test at two different levels of aggregation: first, for all levels of algebra, 16 classes comprised of 147 male and 163 female students, and second, for all general math courses, 24 classes including 219 males and 260 females. If mu^sub 1^, and ^mu sub 2^ are the means of the semester grades of male and female students, respectively, we want to detect a difference between mu^sub 1^ and mu^sub 2^, if such a difference exists. Therefore, it is necessary to test the null hypothesis H^sub 0^: (mu^sub 1^ - mu^sub 2^) = 0 against the alternative hypothesis H^sub a^: (mu^sub 1^ - mu^sub 2^ ) = 0 (i.e. either mu^sub 1^ > mu^sub 2^ or mu^sub 1^

Table 1 shows sample size, sample mean, and sample standard deviation for each subject and each group, and Table 2 presents the calculated z-values for the two aggregated levels of mathematics courses (t-values are also reported).

Comparison of the sample means in columns 5 and 6 of Table 1 shows that the mean semester grades of females is slightly higher than the mean of males in every math subject except finite math. However, the small z-values (or t-values), for both levels of aggregation, will not lead to rejection of the hypothesis of equality (H^sub 0^) when compared to the z distribution (or t distribution), even if the level of significance chosen is as large as 10 percent. Therefore, one might conclude that there is insufficient evidence to infer a difference in the means of semester grades of male and female students in either algebra courses or overall general math courses.

Special Features Of This Study Could Explain The Results

In this study some of the factors which might influence the performance of females in mathematics negatively either do not exist, or their impact has been minimized:

1. All participants in this study are adults college students, and the courses consist of a variety of general math courses which either were required or were necessary for their majors and, consequently, for their success in their careers. Therefore, the female students had the same incentive to learn mathematics that their male counterpart, and did not perceive their math courses as gender-inappropriate or irrelevant to their future careers as suggested by Dwyer (1974), Sherman (1980), and Ormerod (1981).

2. Some researchers suggest that if male and female students with comparable math backgrounds begin a math course and spend the same amount of time learning, the gender-related differences in mathematics performance will disappear substantially (Fennema,1979; Badger, 1981). Since students in this study chose their math courses based on their scores in placement tests, they had, relative to the standardized tests, comparable math backgrounds at the beginning of the semesters, and as may be expected, they performed equally.

Since the author have taught all the classes and evaluated the performance of all students in this study, the students have gone through the same 17-week learning experience and evaluation process. Therefore, the effects of different instructors and the gap between what is taught and what is tested have been eliminated.

4. In this experiment, the gap that usually exists between the real world and a laboratorytype experiment did not exist, because the learning and evaluation processes have been accomplished over 17-week semester of real classroom learning process of college courses for credit.

5. Finally, on this campus there are equal educational opportunities for both men and women. Graphics omitted

Conclusions

The review of the literature reveals that gender differences in mathematics performance are affected by the host of many social and cultural factors and may require many intervention strategies to influence the outcome.

In this experiment, as explained, some of the factors that influence the gender differences in mathematics performance have been controlled or modified. Then performance of 219 male and 260 female students, based on their semester grades, have been used for comparison in two levels of aggregation: aggregation of 16 algebra classes and aggregation of all 24 math classes. Testing results from both levels of aggregation show that there is no significant gender differences in mathematics performance. Therefore, the findings of this experiment support the environmental explanation and do not support the biological theory of gender differences in mathematics achievement.

This experiment also indicates implicitly that the lower level of contribution from women in the field of mathematics can be, at least partially, attributed to the historical treatment of women, lack of opportunity for women, and attitude of societies towards women's roles. Even today, there are many obstacles on the road to equity for men and women=, particularly in some of developing countries, such as the unfavorable attitude of parents towards the education of their daughters (Pollitt et al., 1987) and unfavorable of societies towards the scope of available careers for women. Finally, we may expect that as the social and economic roles of women change3, levels of mathematics participation and performance of women change accordingly (Friedman, 1989; Hude et al., 1990). Table 1

Graphics omttted Table 2

Graphics omitted 2.98 -.876 3.06 -1.212

Notes

Although a z-test is appropriate for a largesample, some researchers use a small-sample t-test which is based on assumptions that are not necessary for the large-sample z-test. However, when the sample is very large, as in the is case, the numerical value of the t- and z-statistics are almost the same, as seen in Table 2, and lead to the same result.

2. Worldwide, 85 millions more boys go to elementary schools than girls (ABC News, January 30,1994).

3. For example, between 1962 and 1993, participation of women in the work force in the U.S. has increased from 24 to 57 millions. (NBC News, February 5,1993), or, 1950 to 1992, the labor force participation rate for women in the U.S. has risen from 35% to 58% (Statistical Abstract of the United States 1992).

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