GENDER DIFFERENCES IN MATHEMATICS PERFORMANCE IN THE ELEMENTARY GRADES: IMPLICATIONS FOR WOMEN'S PARTICIPATION IN SCIENTIFIC AND TECHNICAL OCCUPATIONS

Seleshi Zeleke *

Abstract: This study was undertaken to examine gender differences in mathematics achievement among fifth and sixth grade students and to identify the factors that account for variations in their performance. The findings indicate a difference in favor of boys among sixth graders. In addition, the regression analysis results suggest three variables as important predictors of boys' and girls' achievement. These are attitudes toward mathematics, the school in which students learn, and peer expectations. Furthermore, parental expectations and frequency of exercise in mathematics account reliably to the prediction of boys' achievement. The implications of these findings for mathematics education as well as for women's participation in scientific and technical occupations are discussed.

1. INTRODUCTION

The marginal participation of women in science and technology in Ethiopia and other developing countries is well recognized (Atsede 1991; Ngau 1999). Women's minimal participation in these areas is often attributed to or explained by their poor performance in such school subjects as science and mathematics. Because of their lower achievement in mathematics and the sciences, most girls avoid the study of these and other related courses when they join higher institutions of learning. Consequently, their advancement into higher paying occupations is blocked. For this reason, some refer to mathematics as a "critical filter" (Sherman, 1982) that bars women from entering scientific and technical occupations.

A look into some local studies confirmed that girls' performance in mathematics (Seleshi 1995) and physics (Yalew 1997) is substantially lower than that of boys at the secondary school level. However, there is hardly any evidence that indicates whether gender differences in science and mathematics first appear in the secondary grades or at the elementary school level. That is to say, there is no evidence to indicate that girls' achievement in mathematics and the sciences begins to be poor at the high school level. Especially, if the differences appear in the elementary grades, as evidenced in some studies (Marshall 1984), any attempt to narrow the gender gap or to boost girls' academic achievement at the secondary school level could not easily be successful. This is so because by the time girls reach the secondary school level, for example, the negative attitudes they have developed toward mathematics over the years could not easily be changed. This implies that any effort to help girls achieve better in school, particularly in mathematics and the sciences, should be made as early as possible. Obviously, any undertaking of this sort needs to be based on some research evidence pertaining to girls' performance at the elementary school level and the factors that have a bearing on their achievement. In this paper, a modest attempt is made to address these matters by focusing on mathematics performance of elementary school students in Addis Ababa.

1.1. Gender Differences in Mathematics Performance

Despite the variations in the explanations they put forward, many investigators (e.g., Fennema and Carpenter 1981; Fennema and Sherman 1977; Hilton and Berglund 1974; Sherman 1980) have presented convincing evidence that boys outshine girls in their mathematics performance at the high school level. Nonetheless, the picture seems to differ when one examines the case for elementary school students. A number of studies (e.g., Burton 1979; Fennema and Carpenter 1981; Fennema and Sherman 1978; Hilton and Berglund 1974) have disclosed no gender difference in mathematics achievement at different levels of the elementary school or at the elementary school level as a whole. A few studies have, however, revealed differences in favor of either boys or girls. For instance, according to some scholars (Fennema 1974; Marshall 1984), girls were better than boys in solving computation items whereas boys were better than girls in solving higher-level cognitive problems such as application items and word problems. Somewhat differently, a longitudinal study (Marshall and Smith 1987) has reported significant differences in favor of girls in almost every mathematics area evaluated in the third grade although the differences converged by the time the students reached the sixth grade.

In general, studies of gender differences in mathematics achievement at the elementary school level have reported divergent findings. For instance, some investigators (Zambo and Follman 1994) have reported a rather rare finding that reveals female superiority in problem solving at the sixth grade level in the United States. Furthermore, though computation is assumed to be a mathematical skill in which girls always outperform boys, some investigators (Lummis and Stevenson 1990) have shown in three cultures (United States, Taiwan, and Japan) that this was not so. More specifically, girls were found to perform as well as boys. Lummis and Stevenson further noted in their cross-cultural study that boys were superior in problem solving as early as the first grade. In sharp contrast, other investigators (Hyde, Fennema, and Lamon 1990) who have conducted a meta-analysis of 100 studies concluded that there were no significant differences in problem solving in the elementary grades while there was a slight female superiority in computations.

Likewise, many studies (e.g., Aiken 1976; Ernest 1976; Fennema and Sherman 1978; Hilton and Berglund, 1974) have evidenced no variation in attitudes of elementary school boys and girls. Once again, a few studies have indicated that boys have more favorable attitudes toward mathematics than girls while some others have reported just the opposite. For a comprehensive review on attitudes toward mathematics see Aiken 1970, 1976). Overall, one may conclude that most of the studies of sex differences in mathematics achievement and attitudes have revealed no consistent differences in favor of either sex at the elementary school level.

1.2 Factors that Account for Variations in Students' Mathematics Performance

A number of factors do influence students' mathematics achievement positively or negatively. One among these factors that contributes significantly to variations in mathematics achievement is attitude toward mathematics. The direct relationship between mathematics achievement and attitudes, as well as their reciprocal influence are well documented (Aiken 1970; Johnson 1984; Sherman, 1980; Tsai and Walberg 1983). The studies have shown, especially for high school students, that the more favorable students' attitudes are toward mathematics, the better their achievement would be. That is, if students have positive attitudes toward mathematics, it is likely that they will allot a considerable portion of their study time to the subject and strive to master the knowledge and skills necessary at that level and can thus have better achievement scores than students with negative attitudes. Along with favorable attitudes, frequent exercise plays an important role in improving their mathematics achievement.

A related factor is perceived difficulty of mathematics. In general, mathematics is considered by many individuals as a difficult subject to learn (Fennema and Sherman, 1976). Obviously, if students have such a perception from the outset, it is less likely that they would be confident in learning the subject and would thus have poor mathematics achievement. Perceived usefulness or importance of mathematics has also a similar effect. As stressed by Fennema and Sherman, (1976: 14) "Certainly usefulness is a reality factor. Mathematics is not particularly easy to learn for most people. Why learn it if it has no use." This generally indicates that if a student believes that the learning of a certain subject is useful for further education or future occupation, he or she will exert more effort in learning that subject than in learning another subject, which he or she considers unimportant.

Other factors include teacher, peer, and parental expectations. In connection with this, a number of scholars (Burton 1979; Fennema 1974; Fennema & Sherman 1976; Fox 1981; Jacobsen, 1985) have noted that mathematics is perceived as a male domain in various countries and the study of mathematics is conceived to be inconsistent with feminine sex role. Such a stereotyped perception affects not only students' attitudes and achievement but also the attitudes of teachers, peers, and parents toward students, particularly girls, as learners of mathematics. In general, according to some studies (e.g., Fennema 1980; Fox 1981; Jacobsen 1985), teachers, parents, and peers hold lower expectations for girls than for boys in relation to mathematics performance. These interpersonal expectations reportedly influence girls' attitudes toward mathematics negatively (Aiken 1972; Fennema 1974; Fennema and Sherman 1976). This shows, though indirectly, that interpersonal expectations affect girls' mathematics achievement negatively.

The present study focuses on the examination of the contributions of two cognitive factors (how often is mathematics studied, and academic support provided by family members) and six affective variables (attitudes, perceived difficulty and perceived importance of mathematics, teacher, peer, and parental expectations) to variations in mathematics achievement. The selection of these variables is based on previous studies (Fennema and Sherman 1977; Seleshi 1995) that revealed their importance in relation to secondary school students' mathematics achievement.

2. OBJECTIVES

A previous study (Seleshi 1995) that examined gender differences in mathematics among Ethiopian high school students has revealed statistically significant differences in favor of boys in grades eight through eleven. Based on this finding and the dominant attitudes of the public toward the education of girls in general, the author hypothesized that these differences could manifest themselves even at the elementary school level and recommended this for further investigation. The aim of the present study was to examine that hypothesis.

More specifically, the study had the following two major objectives:

(1) to examine differences in mathematics achievement among fifth-and sixth-grade girls and boys, and

(2) to identify the factors that contribute to variations in their mathematics performance.

The examination of gender differences at the elementary school level would be helpful, among other things, to see the trend of gender differences from elementary through secondary grades. In addition, such an investigation would be useful for early detection of the problem as well as for devising measures to overcome the problem before it becomes more serious in the high school grades.

3. METHODOLOGY

3.1 Subjects

Initially, 352 fifth and sixth-grade students were chosen at random from eight elementary schools in Addis Ababa. The schools included four government and four public schools¹, which were randomly selected from a separate list of government and public schools in the city. Because of missing information, the data gathered from 24 students were discarded. The analysis was, thus, done based on data collected from 328 students (169 girls and 159 boys). Some recent studies (e.g., Zambo and Follman 1994) have noticed that the upper elementary grades (particularly grade six) are critical, for it is about this time that gender-related differences first appear. The reason for focusing on fifth and sixth graders in this study was thus to see whether this is the case in the Ethiopian context.

From the same schools, a sample of 48 mathematics teachers with ages ranging from 23 to 54 participated in the study. The sample comprised all mathematics teachers in grades five and six. But since the number of the teachers in these grades was small, those teaching in grades four, seven, and eight were also included in the study. The samples were chosen from government and public schools to see the differences, if any, in the mathematics achievement of the students from the two types of schools.

3.2 Instruments

Data for the study were gathered using achievement tests, an attitude scale, and student and teacher questionnaires. A brief description of each follows.

Tests. A curriculum-based mathematics test² was constructed for students at each grade level. A table of specifications was prepared for each grade, and items were developed in line with the table. The author and his friend, both of whom had taught mathematics for more than six years, carried out these tasks. At both grade levels, the items stressed the ability to understand mathematical concepts and solve word problems through computations. The tests for grades five and six had internal consistency reliability estimates³ (KR-21) of 0.64 and 0.71, respectively.

Attitude Scale. A Likert scale was employed to obtain data from students regarding their attitudes toward mathematics. The scale comprised 20 statements, which dealt with perceived importance of mathematics, motivation to work hard in the subject, how students see the challenge presented by mathematical problems, and their confidence. The items were written in Amharic (the official language in Ethiopia) and students were asked to indicate their agreement to each statement on a two-point scale (agree or disagree). The scale was adopted from Seleshi (1995) and was found to be moderately reliable (with an internal consistency reliability (KR-21) coefficient of 0.83) for the present sample.

Student and Teacher Questionnaires. The student questionnaire included 31 items most of which were structured. The items were concerned with peer expectation, perceived teacher and parental expectations, perceived difficulty of mathematics, and whether or not students study mathematics often. Peer, teacher, and parental expectations were assessed by one item each. The responses were scored either one or zero. Whereas a score of one was assigned to expectations that are not stereotyped ("girls perform better than boys" or "boys and girls do equally"), zero was assigned to stereotyped expectations ("boys perform better than girls").

Students were also required to rank in order some factors that could influence their mathematics achievement. The teacher questionnaire, on the other hand, included 29 items which were similar to the items of the student questionnaire. The items were designed to secure teachers' opinions of their expectation and treatment of students in mathematics classes, the difficulty of the mathematics textbooks, and students' efforts, if any, in the learning of mathematics. Like the student respondents, teachers were asked to rank in order of importance some factors that could affect students' mathematics performance negatively.

3.3 Procedures for Data Collection and Analysis

The data were collected in two phases. The data pertaining to predictor variables (such as attitudes of students toward mathematics) were gathered through the attitude scale and the student questionnaire in October 1998. Achievement scores were secured after the mathematics tests were administered to students in January 1999. The teacher questionnaire was also administered in the second phase.

In data analysis, a test was employed to examine differences in boys' and girls' mathematics achievement and attitudes. In addition, the bivariate and multivariate relationships of achievement, attitude, and age were explored by Pearson's product-moment correlation and partial correlation coefficients, respectively. Furthermore, multiple regression analysis investigated the contributions of attitude and other selected variables in the prediction of students' mathematics achievement. Achievement scores and categorical data were also examined using analysis of variance and chi-square, respectively.

4. RESULTS

4.1 Differences in Mathematics Achievement and Attitude among Boys and Girls

The means and standard deviations on the mathematics tests and the attitude scale for boys and girls at each grade level are given in table 1 below.

Table 1. Means and standard deviations for mathematics achievement and

attitude by sex and grade

Note: Highest possible scores: Achievement = 25; Attitude = 40

Analysis of the data using t test showed that boys and girls at the fifth-grade level had performed on the mathematics test nearly at the same level (t = 0.91, p >.05). However, sixth-grade boys' performance was significantly better than that of sixth-grade girls (t = 3.04, p =.003).

Unlike the case for mathematics achievement, girls reported a favorable attitude toward mathematics as boys in both grade five (t = 0.36, p >.05) and grade six (t =1.55, p >.05). That is, the data evidenced no reliable difference between girls' and boys' attitudes toward mathematics.

4.2 Relationships of Achievement, Attitude and Age of Students

The bivariate relationships of achievement, attitude, and age as measured by Pearson product-moment correlation were all statistically significant as shown in table 2. The magnitude of the coefficients (or the strength of the relationships) was, however, different for boys and girls.

Table 2. Intercorrelations of achievement, attitude and age for boys

and girls

Note: The coefficients above the diagonal are for boys (N = 159) whereas those

below it are for girls (N=169). All coefficients are statistically significant at

least at p<0.05. Figures in parentheses are partial correlation coefficients⁴.

The relationship between achievement and attitude is positive for both boys and girls but it is stronger for girls, than for boys. Attitude and age are negatively related for both boys and girls but this is more so for girls than for boys. Somewhat differently, achievement and age are negatively related for girls but positively for boys.

4.3 Contributions of Attitude and other Variables to Variations in Achievement

Because gender difference was found as, shown earlier, a separate multiple regression analysis was employed for girls and boys to identify the variables that account for variations in their mathematics achievement. In each analysis, the eight variables (frequency of exercise, academic support provided at home, attitudes, perceived difficulty, perceived importance, peer expectation, perceived teacher and parental expectations) were included and all were entered simultaneously. Table 3 presents the results for girls.

Table 3. Regression analysis results for predicting mathematics achievement

from attitude and other selected variables (females only)

Note: Only significant predictor variables are shown here.

The analysis revealed three important variables that reliably predict girls' mathematics achievement. The variables were the school in which girls learn, their attitudes toward mathematics, and peer expectations. A similar analysis for boys produced the following results.

Table 4. Regression analysis results for predicting mathematics achievement

from attitude and other variables (males only)

Note: Only significant predictor variables are presented here.

As shown in table 4, the analysis disclosed five variables that make a significant contribution to predicting the mathematics achievement of boys. As was the case for girls, attitude, school, and peer expectation contributed reliably to the prediction of boys' achievement. Besides, parental expectations and frequency of exercise accounted significantly for the variation in boys' achievement.

In both analyses, academic support provided at home, teacher and parental expectations failed to account significantly to variations in performance. Closer examination of the responses revealed that significantly more students (81.7% of the girls and 86.3% of the boys) perceived their teachers as having expectations that are not stereotyped (_²= 45.97, df=1, p<.001). Teachers were also perceived as treating girls in the same way as boys in mathematics classes. Furthermore, the majority (74%) of teachers confirmed that they hold similar expectations for boys and girls.

Likewise, parents were perceived by a substantially larger number of students (86.7% of the girls and 66.9% of the boys) to have expectations that are not stereotyped (_²= 29.38, df=1, p<.001). With regard to academic support provided at home, a good number of the student respondents (62.3% of the girls and 66.2% of the boys) reported that there is some one at home who could give them the academic support they need in general and in mathematics in particular.

5. DISCUSSION

5.1 Boys' and Girls' Mathematics Performance

Examination of the mean scores on the tests irrespective of the sex of subjects showed that the students' performance is generally not satisfactory. Whereas, the maximum possible score on the test was 25, the mean score for the entire subjects was only 11.58 (SD=4.24, N= 328). To put it differently, the majority (63.4%) of the subjects answered more than half of the test items incorrectly. This result is indicative of the presence of a serious problem in the learning of mathematics.

Why did students perform so poorly on the test? A possible explanation is the perceived difficulty of mathematics among students and its association with their achievement. If students perceive mathematics as difficult, it is not difficult to see that this will have a negative effect on their achievement as well as their confidence. In the present study, about 43 percent of the subjects reported that mathematics is more difficult to learn than any other subject. To make things worse, among the entire sample of boys and girls only 30 percent of the boys and 29 percent of the girls reported that they studied mathematics often. It is axiomatic, however, that additional effort on the part of students is essential particularly for challenging subjects like mathematics. But as reported by teachers, students did not often do their mathematics homework, let alone exert additional effort on their own. More than three-quarters (78%) of the teacher respondents identified this as a major problem in the teaching-learning process.

Thus, perceived difficulty of mathematics appeared to be responsible for the students' poor performance. What makes this argument more likely is that perceived difficulty of mathematics was ranked first by both boys and girls among factors that have a negative bearing on mathematics achievement, followed by lack of confidence. Besides, a comparison of the mean scores of those who perceived mathematics as more difficult and those who perceived it as easier than, or as difficult as, any other subject provides further support. The difference in achievement between the two groups was significant and in favor of the latter group (t =2.13, p =.035).

Another problem that could perhaps be associated with the students' lower performance concerns the textbooks. Most teachers raised this as a basic problem. Whereas, 77 percent of the teacher respondents evaluated the mathematics textbooks as difficult relative to students' level of comprehension, no one rated them as easy. In fact, only slightly more than a fifth (21%) of the teachers indicated that the mathematics textbooks are as they should be (that is, they are neither easy nor difficult). The difference between the percentages of teachers who evaluated the textbooks favorably and unfavorably is substantial (_² =32, df = 1, p<.0001).

The respondents further indicated the reasons why the textbooks were too difficult. According to them, the authors of the textbooks had never taught mathematics at these levels (grades 5and 6) and thus had no idea what students could not and cannot do or understand. Besides, according to the same subjects, the authors had never consulted or worked with any mathematics teacher from these grade levels. In other words, the respondents stated that they did not participate in the preparation of the textbooks at all; rather, some high school teachers who fulfilled the selection criteria (such as having a B.Sc. Degree in mathematics and experience of teaching the subject for more than ten years) set by the Addis Ababa City Education Bureau took the responsibility of writing the textbooks.

However, it is well known that textbook preparation requires the collaborative efforts of a subject expert, a curriculum expert, and a subject teacher. This shows the need for some changes in the current practices of the selection of textbook authors; that is, the selection criteria need to be changed. It should be noted, however, that the difficulty of the textbooks appears to be a major concern not only among subject teachers but also among educators with whom the author had discussion on the matter. Unfortunately, only teachers were asked to evaluate the difficulty levels of the textbooks. It was assumed that such an evaluation would be difficult for students involved in this study.

The teacher respondents further reported that the distribution of textbooks was limited and not every student obtained a textbook for each subject. Obviously, textbooks are indispensable for school subjects like mathematics in which students are required to do assignments frequently. Without them, the teaching-learning process could not go on smoothly.

In spite of the poor performance of the entire sample on the mathematics tests, boys received a better mean score than did girls. The difference was, however, statistically significant only at the sixth-grade level. Given this result and that of a previous study (Seleshi 1995), it appears that in the Ethiopian context, boys do better than girls in mathematics beginning from grade six through the high school years. However, it should be noted that the two studies were conducted in two relatively different communities - Seleshi's (1995) study was done in a rural area (North Shoa) whereas the present study was undertaken in an urban setting (Addis Ababa) - and the conclusion drawn should be seen in that light.

On the other hand, the absence of attitude differences between boys and girls at both grade levels is to be expected, for a similar result was found for eighth graders (Seleshi 1995). Other investigators (e.g., Aiken 1976; Ernest 1976; Fennema and Sherman 1978) have also reported no gender differences in attitudes toward mathematics at the elementary school level. Once again, with the above caution in mind, it appears that girls' attitude toward mathematics is comparable to that of boys until they complete the eighth grade.

Apart from grade levels, the study showed that both boys' and girls' attitudes can be reliably predicted from the students' age. Attitude was negatively and reliably related to age for both boys (r = -0.24) and girls (r = -0.36) suggesting that as students get older, their attitudes become less and less favorable, but this was more so for girls than for boys. But since achievement can mediate the relationship of attitude and age, the examination of the partial correlation coefficients could be more informative. Partialling out the effect of achievement, however, resulted only in some minor changes (r = -0.29 for boys and r = -0.31 for girls). That is, even after controlling for the mediating effect of achievement, age and attitude are correlated negatively and significantly. Thus, from the simple and partial correlation coefficients it appears that both boys' and girls' attitudes toward the learning of mathematics become more negative or less favorable as students get older.

A similar examination of the association of age and achievement produced a positive correlation for boys (r=0.18, p=.024) but a negative one for girls (r=-0.24, p=.002). This result suggests that as girls grow older their mathematics achievement gets lower, while this is not the case for boys. A comparison of the mean scores for younger (ages 10-12) and older (ages 13-16) children lends additional support. Younger girls had higher mean scores than older girls, a difference that was statistically significant (t=1.99, p=.049). On the contrary, older boys had higher mean scores than younger boys though the difference was not reliable (t=-1.30, p>.05).

Besides, the correlation coefficients made it clear that girls' achievement is more predictable from their age than is boys' achievement. It is, however, important to control the mediating effect of attitude. For example, unlike the simple correlation coefficients, the partial correlation coefficients (that is, controlling for the effect of attitude) yielded a non-significant association between students' mathematics achievement and their age for girls (r =-0.1491, N=166, p>.05) but still a significant one for boys (r =0.2351, N=156, p=.003). This clearly indicates particularly for girls that the relationship between students' age and their achievement is moderated by their attitude and that it is necessary to examine the partial correlation coefficients before drawing any conclusion on the basis of the simple correlation coefficients.

Consequently, the above statement that, as girls grow older their achievement gets lower should be modified. Put differently, girls' achievement has no relationship with their age if their attitude toward the subject is controlled. This shows that the improvement of girls' achievement is dependent upon the modification of their attitudes. Thus, ways of transforming the predominant attitude, for example through education materials which appeal to girls and which include positive role models need to be developed.

In sum, the hypothesis that gender differences in mathematics performance could appear before students complete their elementary education is confirmed. But why the results of studies that dealt with gender differences in mathematics achievement are so divergent is not clear. The gender difference found in the present study, for instance, is partly consistent and partly inconsistent with Zambo and Follman's (1994) finding. In both studies, gender difference is found at the sixth grade level. Nonetheless, whereas the difference favors boys in the former study, it favors girls in the latter study.

According to some researchers (Lummis and Stevenson 1990), the real cause of the divergent findings remains unknown. One possible cause of the variation, for example, could be the difference in the instruments or tests employed. The tests may be different in the emphasis they place on different skills. The tests could also be different in their contents and the difficulty levels of the items they included. Another cause could be socio-economic status. The difference in the socio-economic status among families could be reflected in their ability to provide their children such things as necessary materials and academic support at home by hiring a tutor, both of which are considered to have an important influence on students' mathematics performance. One can add possibly many factors to the list of variables that might have caused the discrepant findings. Which factors really cause the discrepancy, however, could only be known through further research.

5.2 Factors Contributing to Mathematics Achievement

Results of the regression analysis disclosed three variables that contributed significantly in the prediction of the mathematics achievement of both boys and girls. The school in which students learn was among these variables. How did the school as a variable affect the mathematics achievement of boys and girls? One important factor within the general variable of school is whether it is a government or a public school. A comparison of the mean scores of students from the two types of schools revealed a statistically significant difference in favor of those from government schools (t = 2.76, df = 326, p =.006). One problem usually observed in public schools is large class size. Actually, class size is also a problem of government schools although it is less serious there. Large class size has obviously a negative effect on the teaching-learning process and thus on students' achievement.

Subjects like mathematics require students to do assignments almost daily. The teacher should also correct these assignments frequently to give immediate feedback to students. But when the class size is large, the teacher cannot appraise the students' performance periodically. Consequently, he/she could not provide feedback to students. In such an environment where the guidance of the teacher is minimal, if students feel that they are performing adequately, they will continue in the same way even if they are not on the right track and one can imagine what the performance of these students on mathematics tests would look like.

Added to this, the two school types are different with regard to teachers' qualification (or educational level). Most of the mathematics teachers who teach at the fifth and sixth grade levels in government schools have had a one-year education in Teacher Training Institutes (TTI) and some have even a diploma, currently a requirement to teach at the second cycle (grades 5-8) of the primary school. Notwithstanding this, the educational level of teachers in public schools is not so good.

The second variable that substantially contributed to variation in mathematics achievement among both boys and girls was attitude toward mathematics. The association of attitude and achievement was positive for both boys (r=0.18, p=.02) and girls (r=0.30, p=.0005) though it was stronger for girls than boys. The coefficients for both boys and girls suggest that the more favorable students' attitudes are toward mathematics, the better their achievement. But this is once again more so for girls than boys. That is, girls' achievement scores are more predictable from their attitudes than are boys' scores. This corroborates results found by other investigators (Aiken 1976; Fennema 1974; Sherman, 1979). Nevertheless, partialling out the effect of age, boys' and girls' achievement scores become almost equally predictable from their attitude scores (the partial correlation coefficients were r=0.2390 and r=0.2305 for boys and girls, respectively) indicating the moderating effect of age on the relationship between achievement and attitude.

The importance of positive attitudes in mathematics achievement was further confirmed by a comparison of mean scores for students with favorable and less favorable attitudes. The results revealed a reliable difference in favor of the former group for both boys (t =2.27, p =.025) and girls (t =2.63, p =.009). This is consistent with what Seleshi (1995) found for a high school sample.

The third variable that significantly accounted for the prediction of both boys' and girls' achievement was peer expectation. A closer examination of the means for boys showed that those who thought boys were superior in mathematics received a better score (mean=13.17, SD=4.71) than those who indicated that girls were either superior or performed as well as boys (mean=11.72, SD=4.24). The difference was statistically significant [F (1,155)=3.95, p<0.05]. Likewise, among girls those who believed girls were better in mathematics obtained a higher mean score (mean=11.16, SD=3.96) than those who thought boys were superior (mean=8.00, SD=2.58). Once again, the difference between the means is reliable [F (1,156)=6.19, p<0.05]. From these results, it appears that among both girls and boys, while the better achievers perceive themselves as superior to members of the other sex, the low achievers consider themselves as inferior.

In addition to the above three variables, the regression analysis recognized perceived parental expectations and frequency of exercise in mathematics as reliable predictors of boys' achievement. Other studies (Ernest 1976; Fennema and Sherman 1977) have also shown that parents' expectations or their attitudes toward their child as a learner of mathematics strongly influenced the child's mathematics achievement. It must be noted that mathematics is one of those subjects in which parents' support and encouragement is crucial. But whether or not parents provide the necessary academic support for their child is at least partly dependent upon their expectations. Other things being equal, the higher their expectations in relation to the child's mathematics performance, the more readily they provide the academic support for their child.

Frequency of exercise, on the other hand, is expected to affect boys' achievement negatively given the fact that most students do not study mathematics often. As indicated earlier, mathematics requires frequent exercise. Students must also do homework regularly. However, according to the teachers who participated in the present study, the students do not do their homework most of the time. All in all, this result underscores the importance of exerting effort and frequent exercise in mathematics.

The importance of frequency of exercise and parental expectation in students' mathematics achievement is undeniable. But, why these factors reliably predict mathematics achievement among boys, but not among girls, is difficult to explain from the data at hand.

In this study, teacher expectation was not found to contribute reliably to the prediction of mathematics achievement. Other studies, however, have reported this variable to have an important predictive power. But this was so, mostly in the high school grades where the gender gap is very wide. Because of this teachers develop biased beliefs and hold lower expectations for female students. Data collected from both teachers and students confirmed that the expectation of teachers is not biased. If this is the case, the variable is not expected to account reliably to variations in mathematics achievement.

The other variable that did not account to the variation in mathematics achievement was academic support provided at home. As indicated earlier, the majority (64.3%) of the students reported that they had someone in their family who could provide academic support to them. Given this response and teachers' observations that most of the students did not do their homework, not to mention the low scores they obtained on the test, one can see that even if there is some one in the family who could provide the necessary support, he/she did not actually (or appropriately) offer the support. Otherwise, the support could have resulted in better marks. Students' responses may thus be some what exaggerated, or else the student respondents might have focused only on parents' educational backgrounds when answering this item. Actually, whether or not parents could provide academic support to their children depends on their educational background. However, daily observations show that even if parents have good educational background, most of them are not proficient enough to assist their children in mathematics. Overall, it may be that most students have the same experience in terms of academic support provided at home. That is, if the students' experience is more or less the same, this factor could not account to variations in mathematics achievement.

5.3 Implications

5.3.1 Implications of the Findings for Mathematics Education

The present study confirmed that a positive attitude toward mathematics is associated with better mathematics achievement. This result has an important message to convey to mathematics teachers and perhaps to other teachers as well. If teachers are to work toward better achievement of their students, they should aim at making their lessons attractive to students. They should also avoid discouraging students in mathematics classes. This would minimize negative experiences that students could encounter in such classes.

In general, alongside imparting knowledge and developing students' mathematical skills, teachers need to exert every effort in order that their students develop positive attitudes toward mathematics. The earlier such efforts are made, the better the outcomes would be. In other words, the effort to develop favorable attitudes needs to be made as early as possible (i.e., in the lower grades) for otherwise it would be difficult, if not impossible, to change students' attitudes once they become negative. It must also be noted, however, that a favorable attitude is a necessary but not a sufficient condition for students' optimal mathematics achievement. In addition to possessing positive attitudes toward mathematics, students must do homework and other mathematical exercises regularly.

The poor performance of the majority of the students generally suggests the need for supporting students' endeavor to improve their mathematics achievement. Indeed, more support should be given to girls than to boys. For the support to be fruitful, however, a thorough knowledge of students' problems is essential. It is important, for instance, to pinpoint the specific areas of concern within mathematics. By design, this study did not examine differences between boys and girls in different mathematical skills such as computations and solving word problems. Future research should thus focus on investigating these areas by employing various mathematics subtests such as algebra and geometry, computation and story problems, or using items with varying degrees of difficulty (e.g., knowledge, comprehension, and application items). The present study considered only a few variables. As a result, only a small portion (about one-fifth) of the total variance was accounted for by the variables. Further research that explores and clarifies the importance of other variables, which were not dealt with in this study, is therefore needed.

5.3.2 Implications for Women's Participation in Scientific and Technical Occupations

In most countries including Ethiopia, women constitute roughly half of the population. However, compared to men, they have limited access to education for several reasons. This is reflected in their low school enrollment rate. In addition to their disappointing enrollment, female students achieve poorly in school especially in mathematics. If girls start to lag behind in their mathematics learning as early as the sixth grade, as found in the present study, they would certainly face a number of problems not only in school but also in their occupations later in life.

In Ethiopia, many more girls than boys learn mathematics in the high school grades simply because taking the course is compulsory. However, as evidenced in other countries like the US where advanced mathematics courses are optional at the high school level and beyond, far fewer girls than boys register for the courses (Ernest 1976). Had mathematics been likewise optional in Ethiopia, we could have observed the same problem.

Girls' poor mathematics performance both in elementary and high school grades generally narrow their career options since they thus avoid the study of not only mathematics but also mathematics-related fields such as physics, chemistry, and engineering in their tertiary education. A study (Atsede 1991) has clearly documented the marginal enrollment of female students in these departments at Addis Ababa University in Ethiopia. The same study has also reported a very small number of female degree graduates from the Faculty of Science and Faculty of Technology.

Generally, many studies (e.g., Ernest 1976; Sherman 1982) have confirmed the hypothesis that mathematics is a "critical filter" that tends to eliminate women from many fields: chemistry, physics, engineering, architecture and the like. In today's world, which is characterized by a rapid rate of scientific and technological development, the learning and understanding of mathematics is becoming more and more important in almost every area of human endeavor. If women are to participate equally with men in solving problems of the society of which they are members through science and technology, they should be encouraged to work hard and pursue the study of mathematics. In this regard, teachers, counselors, as well as parents have a major role to play in widening the career options of girls by boosting girls' morale and confidence in mathematics as early as the elementary grades. It is also useful to sensitize girls about the importance of mathematics for further education and future career. Especially if girls aspire to enter into scientific and technical occupations, they need to be proficient in mathematics and they should be aware of this in the early years of their schooling.

6. CONCLUSION

The results revealed a reliable difference in favor of boys at the sixth grade level. The study has thus confirmed that girls begin to lag behind in mathematics at the elementary school level rather than in the secondary grades at least in the Ethiopian context. Among the variables that accounted significantly for variations in mathematics performance of both boys and girls, two variables (attitudes toward mathematics and the school in which students learn) emerged with greater weight. The study further found peer expectations to be an important predictor. It appears that measures that may be devised to alleviate the mathematics problems of girls and boys need to focus, among other things, on changing students' attitudes as early as possible, improving school-related factors such as class size and teacher competence, and modifying peer expectations. Primarily, however, attention should be directed toward the evaluation and improvement of the mathematics textbooks.

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Notes

¹ Public and government schools are local community- and government-owned institutions, respectively. In public schools, while the Ministry of Education (MOE) assigns the director, other employees including teachers are hired by the School Management Committee, which comprises parents, the director, and teachers. Since the major source of the budget for public schools is students' tuition and registration fee, the number of students they enroll is far beyond their capacity. In contrast, all employees in government schools including teachers and the director are assigned by MOE. The budget and textbooks for these schools are provided by MOE. All activities in government schools are carried out under the close supervision and support of MOE

² Curriculum-based tests are considered generally better than standardized commercial tests in evaluating students' achievement. The former are more flexible in that they could be constructed to fit closely the objectives of a certain subject matter in a certain country or locality.

³ The reliability coefficients for the tests are not high enough. It must be noted, however, that the coefficient of reliability of any test is a function of the number of items included in the test or simply the length of the test. Other things being equal, the longer the test, the larger the coefficient of reliability. The tests that were employed in the present study comprised only 25 items and this could be one reason why the tests had low reliability estimates.

⁴ For example, the partial correlation coefficient of achievement and attitude refers to the association of the two variables when the third variable, in this case age, is kept constant. Among the partial correlation coefficients, the association between achievement and age for girls is the only one that is not statistically significant; that is, p>.05.

* Seleshi Zeleke - Department of Psychology, Addis Ababa University, P. O. Box 150339, Addis Ababa, Ethiopia.