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Over the years, numerous studies have been conducted to examine students' beliefs and attitudes toward mathematics. Implicit in much of this research is the assumption that positive affect might lead to positive achievement behavior (see McLeod, 1992, for a review). While some psychologists emphasize the role of ability-related self-perceptions in motivating achievement behavior, others attribute equal importance to subjective task values in predicting behavior (see Eccles, Wigfield, Harold, & Blumenfeld, 1993, for a discussion). These subjective task values are defined in terms of interest in and enjoyment of the task, perceived importance of being good at the task, and perceived usefulness of the task. Although considerable research has been conducted on the beliefs and attitudes toward mathematics among middle school and older students, relatively less research has been done on these topics with elementary-level students (however, see Eccles et al., 1993). In part, this may be due to the fact that no gender differences in quantitative performance have been observed in the early elementary years (see Leder,1992, for a review). The existing research on affect in mathematics education at the elementary school level suggests that most children like mathematics and that there are no significant differences in the attitudes of girls and boys (e.g., Rathbone,1989; Suydam,1984). Nonetheless, there is evidence of gender difference in the students' subjective views of their own competence: even at this young age, boys hold more positive beliefs than girls about their competence in mathematics (e.g., Eccles et al., 1993; Rathbone, 1989). At the elementary level, there are few reports on the perceived usefulness and importance of mathematics, gender stereotyping of the field of mathematics, and perceptions about the relation between mathematics and other areas of the curriculum. Little research exists on children's attitudes towards the different strands of mathematics. This information would be useful assuming close links between affect and activity choice (e.g., Bandura,1989; Nicholls,1984; Schunk, 1984). A recent formative program review in a large urban school district provided an opportunity to survey the beliefs and attitudes toward mathematics among third- and fifth-grade students. The survey addressed (a) students' enjoyment of mathematics in general, as well as the various strands of mathematics; (b) perceived competence at mathematics; and (c) the perceived importance, usefulness, and relevance of mathematics. In addition, the survey included items about the process of doing mathematics and the relation of mathematics to other curricular subjects. Responses of girls and boys were analyzed and compared. Method Schools Sixty elementary schools were randomly selected to participate in the review. The average enrollment for elementary schools in the school district is approximately 400 students. The percentage of students whose primary language at home is not English is 43%. The major non-English languages spoken at home include Portuguese, Spanish,

Italian, and Polish. English was the primary language of instruction in all schools involved in the study, and all 60 schools were coeducational. Respondents In each school, one class of Grade 3 students and one class of Grade 5 students was randomly selected to complete the survey conducted in the spring of 1994. A total of 1,344 Grade 3 students (679 girls and 665 boys) and 1,412 Grade 5 students (745 girls and 667 boys) participated. From each grade, a sample of 660 girls and 660 boys was randomly selected for further analyses. Consistent with the ethnocultural diversity of the school district population, 46% of respondents indicated that their parents always spoke English at home, 47% reported sometimes, and 7% indicated never. The vast majority of students (94%) reported that they had lived in Canada for at least 2 years. The majority of students (91%) indicated that they had a calculator at home; only 50% stated that they had a computer at home. Over the years, numerous studies have been conducted to examine students' beliefs and attitudes toward mathematics. Implicit in much of this research is the assumption that positive affect might lead to positive achievement behavior (see McLeod, 1992, for a review). While some psychologists emphasize the role of ability-related self-perceptions in motivating achievement behavior, others attribute equal importance to subjective task values in predicting behavior (see Eccles, Wigfield, Harold, & Blumenfeld, 1993, for a discussion). These subjective task values are defined in terms of interest in and enjoyment of the task, perceived importance of being good at the task, and perceived usefulness of the task. Although considerable research has been conducted on the beliefs and attitudes toward mathematics among middle school and older students, relatively less research has been done on these topics with elementary-level students (however, see Eccles et al., 1993). In part, this may be due to the fact that no gender differences in quantitative performance have been observed in the early elementary years (see Leder,1992, for a review). The existing research on affect in mathematics education at the elementary school level suggests that most children like mathematics and that there are no significant differences in the attitudes of girls and boys (e.g., Rathbone,1989; Suydam,1984). Nonetheless, there is evidence of gender difference in the students' subjective views of their own competence: even at this young age, boys hold more positive beliefs than girls about their competence in mathematics (e.g., Eccles et al., 1993; Rathbone, 1989). At the elementary level, there are few reports on the perceived usefulness and importance of mathematics, gender stereotyping of the field of mathematics, and perceptions about the relation between mathematics and other areas of the curriculum. Little research exists on children's attitudes towards the different strands of mathematics. This information would be useful assuming close links between affect and activity choice (e.g., Bandura,1989; Nicholls,1984; Schunk, 1984).

A recent formative program review in a large urban school district provided an opportunity to survey the beliefs and attitudes toward mathematics among third- and fifth-grade students. The survey addressed (a) students' enjoyment of mathematics in general, as well as the various strands of mathematics; (b) perceived competence at mathematics; and (c) the perceived importance, usefulness, and relevance of mathematics. In addition, the survey included items about the process of doing mathematics and the relation of mathematics to other curricular subjects. Responses of girls and boys were analyzed and compared. Method Schools Sixty elementary schools were randomly selected to participate in the review. The average enrollment for elementary schools in the school district is approximately 400 students. The percentage of students whose primary language at home is not English is 43%. The major non-English languages spoken at home include Portuguese, Spanish, Italian, and Polish. English was the primary language of instruction in all schools involved in the study, and all 60 schools were coeducational. Respondents In each school, one class of Grade 3 students and one class of Grade 5 students was randomly selected to complete the survey conducted in the spring of 1994. A total of 1,344 Grade 3 students (679 girls and 665 boys) and 1,412 Grade 5 students (745 girls and 667 boys) participated. From each grade, a sample of 660 girls and 660 boys was randomly selected for further analyses. Consistent with the ethnocultural diversity of the school district population, 46% of respondents indicated that their parents always spoke English at home, 47% reported sometimes, and 7% indicated never. The vast majority of students (94%) reported that they had lived in Canada for at least 2 years. The majority of students (91%) indicated that they had a calculator at home; only 50% stated that they had a computer at home. The Survey The survey was adapted from an Ontario Ministry of Education (1989) survey entitled Student Questionnaire: Mathematics, part of the 1988-1989 provincial reviews of mathematics and reading for Grade 6. Items in the survey were consistent with curriculum planning guidelines used in the school district. Students were told that they would be asked questions about school activities related to mathematics and their feelings toward them. They were informed that there were no right or wrong answers to the questions on the survey, and that their answers may be different from their classmates. Students were instructed not to write their name on the survey. The entire survey was read out loud to Grade 3 students; students responded as the items were read out. Students in Grade 5 worked on the survey independently. Items on the survey were presented in multiple-choice format, and students were required to circle the response that best applied to them. Related Results

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The survey contained 22 items that addressed students' attitudes and perceptions regarding mathematics. Other information that was collected concerned demographics, classroom practices, parental involvement, and activities at home, all of which were of interest to educators at the school district. For the majority of items, students were required to circle the appropriate response from a set of three alternatives: "1 " (Yes) if they agreed, "2" (No) if they disagreed, and "3" if they were unsure. For a few items, students were required to choose from a different set of response alternatives. Results Eighteen of the 22 items are shown in Table 1. These items have been categorized into three sections: (a) Liking Mathematics, (b) Perceived Mathematics Competence, and (c) Beliefs Regarding Mathematics Relevance. For these items, students were required to select one response from a set of three alternatives: "1" (Yes) if they agreed, "2" (No) if they disagreed and "3" if they were unsure. For purposes of conducting reliability calculations, the latter two categories (i.e., "2" and "3") were grouped together. Cronbach's alpha values were .75, .45, and .53 for each of the three sections respectively. For each of the 18 items, the percentages of "yes" responses among girls and boys in Grades 3 and 5 are shown in Table 1. The remaining four items related primarily to students' beliefs about the process of learning mathematics; responses to these items are summarized in Table 2. Liking Mathematics Ten items were included in the Liking Mathematics section (see Table 1). Chi-square tests for independence between gender and grade were conducted to determine if the proportions of male and female respondents who agreed (i.e., selected the "yes" option) with questionnaire items were different in Grade 3 and Grade 5. These tests revealed statistically significant differences only for Item 19, Chi^sub 2^(1) = 4.73, p The remaining nine items in the Liking Mathematics category were subsequently examined using separate chi-square goodness-of-fit tests for grade (collapsed across gender) and gender (collapsed across grade). A statistically significant difference was obtained for Item 20 with respect to both gender and grade level; fewer girls than boys indicated that they liked solving mathematics problems that made them think a lot, Chi^sub 2^(1) = 7.24, p

Students differed in their reports of liking measurement and geometry. In both grades, more boys than girls stated that they liked measurement, Chi^sub 2^(1) = 5.33, p

Although mathematics does not appear to be the favorite subject of many students (see Item 44), the percentage of students who indicated that they "liked mathematics" was generally high (70 to 79%). As noted earlier, a relatively lower percentage of students (43 to 55%) said that they liked the mathematics they did in school (cf. Items 19 and 39). The reason for this difference is not readily apparent. Perceived Mathematics Competence Three items were included in the Perceived Mathematics Competence section (see Table 1). In only one instance was there a significant difference in the pattern of responding across genders at the two grade levels: Item 41, Chi^sub 2^(1) = 4.51, p Perhaps the most critical finding was obtained when students were asked if they were good at mathematics (Item 37). In both Grades 3 and 5, more boys than girls indicated that they were good at mathematics, Chi^sub 2^(1) = 14.67, p Beliefs Regarding Mathematics Relevance Four items were included in the section Beliefs Regarding Mathematics Relevance (see Table 1). We found no differences associated with gender but remarkable differences between the two grades. Significantly more students in Grade 5 than in Grade 3 indicated that mathematics helps them outside of school, Chi^sub 2^(1) = 33.95, p Mathematics The data pertaining to students' perceptions about the process of mathematics learning are shown in Table 2. There were no significant differences in responding associated with gender. About half the students in both grades (51 to 64%) agreed that learning mathematics is mostly memorizing, whereas, the remainder either disagreed or were unsure. This result is consistent with reports of secondary students (e.g., Schoenfeld, 1989). Nonetheless, in both grades, between 70 to 85% of students thought that there are usually many ways to solve a mathematics problem. Students in both grades appeared to recognize that there was a relation between learning mathematics and learning other subjects, supporting an integrated view of learning. Although nearly one third of the students in both grades were unsure about the relation of learning mathematics and other subjects, between 10 and 20% of students indicated that learning mathematics was mostly like learning either language or art, and more than 30% indicated that mathematics was mostly like learning science. Finally, responses to Item 45 suggested that students in both grades held a "gender-free" view of mathematics. An overwhelming majority of students (between 88 and 97%) indicated that both girls and boys should learn mathematics. Discussion

One of the most important findings presented in this paper is that more boys than girls consider themselves to be "good" at mathematics, even though no gender differences were observed on many other variables including "liking mathematics." Apparently, even as early as Grade 3, a higher proportion of boys than girls report feeling competent in mathematics, and this pattern is repeated in Grade 5. Most research on gender differences in student attitudes regarding mathematics has focused on the attitudes of older students. For example, in the Fourth NAEP Mathematics Assessment, males were more likely to report being good at mathematics, even though both genders were equally likely to report enjoying mathematics (in Steinback & Gwizdala, 1995). These authors also reported significant gender differences in attitudes towards mathematics, self-confidence, and perceived usefulness, in favor of males. Similar results were reported by Fennema and Sherman (1978), who found that among students in Grades 6 through 11, males were consistently more confident in their ability to learn mathematics than females and thought that males were more adapted to mathematics than females. In the high school grades, males were more likely than females to perceive that mathematics was useful. •

The few studies conducted with younger children also support the observation that boys perceive themselves to be better at mathematics than girls. As part of a comprehensive longitudinal study (Grades 1 to 4), Eccles et al. (1993) found that younger children's perceptions of competence and subjective task values were more positive than those of older children. Secondly, they reported that girls and boys valued mathematics equally, but boys were more likely to believe that they were more competent than girls. Rathbone (1989) observed a similar pattern with Grade 5 students. Our results concur with those reported by these authors. Based on decades of research on gender differences in mathematics learning, investigators have put forth a large number of possible explanations to account for their observations. Much of the emphasis in the proposed explanatory models involve "environmental" variables and "learner-related" variables (Leder, 1992). Environmental variables include the influence of teachers, parents, peer groups, and society in general. Collectively, these variables are thought to reinforce gender-stereotyped expectations and behaviors in the learner. Some of the learner-related variables that have been identified include confidence, fear of success, attributions of success and failure, and persistence. It is believed that these variables affect males and females in ways that result in attitudes and behaviors that are differentiated by gender. The results reported in this paper will be discussed in light of some of the proposed explanations reviewed by Leder (1992), although it must be emphasized that, given the nature of the present study, these explanations are purely speculative. No gender or grade differences emerged when students were asked whether they like mathematics. However, even though between 70 to 80% of students reported that they like mathematics (Item 39), the percentage of students who indicated that they liked the

mathematics that they do in school (Item 19) was lower and the difference more pronounced for girls in Grade 5 (43%) than for boys (52%). Leder (1992) suggests that there has traditionally been a difference between males and females in the areas in which they are expected to work for success: men value achievement in intellectual and leadership areas, whereas women value work requiring well-developed social skills. Similarly, other research indicates that males prefer leisure activities focused on skills and mastery of objects, whereas females prefer activities that emphasize interpersonal relationships. Some researchers have argued that these expectations form part of the "gender stereotypes" that are reinforced through teacher and parent behavior and through the media. These preferences develop with age and may become more differentiated between Grades 3 and 5. They might also explain why fewer girls, relative to boys, indicated that they liked solving mathematics problems that make them think. More boys than girls in both grades reported liking measurement. This strand of mathematics typically involves much classroom activity and demonstration. Some of these activities include estimation, comparison, and investigation in measuring distance, capacity, mass, temperature, money, and time. Thus, based on the gender differences described above, one might expect measurement to be an area that would be more popular among boys than girls. It is therefore possible that measurement is characteristically introduced through traditionally male activities. If so, it may be useful to teach measurement using a variety of methods that include activities that typically appeal to boys, as well as activities that typically appeal to girls. Some developmental differences are apparent in students' attitudes toward specific strands of mathematics. Generally, third graders appear to favor subtraction less than fifth graders do; fifth graders favor measurement, geometry, and problem solving less than third graders do. The reasons for this are not readily apparent, although possibly these are the strands that students in the respective grades find most challenging. Although further analysis is necessary, the variability in students' responses suggests that students in both grades are able to identify their attitudes toward the different strands of mathematics. In addition, students' conceptualization of the field seems largely dominated by basic arithmetic, and addition, in particular (cf., McDonald & Kouba, 1986). Between 70 and 80% of students indicated that they like mathematics and that they like addition; the percentages of students who stated that they liked the other strands were lower. These results are consistent with anecdotal evidence suggesting that subtraction is less popular than addition, and division less popular than multiplication. As discussed earlier, more boys than girls reported feeling competent in mathematics. Although a relatively low percentage of girls and boys indicated that mathematics was hard for them, this percentage dropped for boys from 14% in Grade 3 to 9% in Grade 5 but remained constant at about 12% in both years for girls. These observations are consistent with the view that gender-stereotyped beliefs become internalized with age. Whether the confidence expressed by boys is unique to the area of mathematics or whether this is reflective of generally higher levels of confidence cannot be evaluated

using the present data. Further study using appropriate control questions would be needed to assess this possibility. We found no gender differences in students' perceptions concerning the relevance of mathematics, a finding which is not consistent with reports from older students (see Leder, 1992). However, a developmental pattern was clearly evident. More students in Grade 5 seemed to be aware of the usefulness and relevance of mathematics outside of school. Because perceived usefulness is thought to be an important determinant of activity choice (e.g., Feather, 1988; Wigfield & Eccles, 1992), it may therefore be valuable to make mathematics seem relevant in the early grades, perhaps by providing students with real-life applications more frequently (e.g., simulating a shopping transaction).

More boys than girls in both grades reported liking measurement. This strand of mathematics typically involves much classroom activity and demonstration. Some of these activities include estimation, comparison, and investigation in measuring distance, capacity, mass, temperature, money, and time. Thus, based on the gender differences described above, one might expect measurement to be an area that would be more popular among boys than girls. It is therefore possible that measurement is characteristically introduced through traditionally male activities. If so, it may be useful to teach measurement using a variety of methods that include activities that typically appeal to boys, as well as activities that typically appeal to girls. Some developmental differences are apparent in students' attitudes toward specific strands of mathematics. Generally, third graders appear to favor subtraction less than fifth graders do; fifth graders favor measurement, geometry, and problem solving less than third graders do. The reasons for this are not readily apparent, although possibly these are the strands that students in the respective grades find most challenging. Although further analysis is necessary, the variability in students' responses suggests that students in both grades are able to identify their attitudes toward the different strands of mathematics. In addition, students' conceptualization of the field seems largely dominated by basic arithmetic, and addition, in particular (cf., McDonald & Kouba, 1986). Between 70 and 80% of students indicated that they like mathematics and that they like addition; the percentages of students who stated that they liked the other strands were lower. These results are consistent with anecdotal evidence suggesting that subtraction is less popular than addition, and division less popular than multiplication. As discussed earlier, more boys than girls reported feeling competent in mathematics. Although a relatively low percentage of girls and boys indicated that mathematics was hard for them, this percentage dropped for boys from 14% in Grade 3 to 9% in Grade 5 but remained constant at about 12% in both years for girls. These observations are consistent with the view that gender-stereotyped beliefs become internalized with age. Whether the confidence expressed by boys is unique to the area of mathematics or

whether this is reflective of generally higher levels of confidence cannot be evaluated using the present data. Further study using appropriate control questions would be needed to assess this possibility. We found no gender differences in students' perceptions concerning the relevance of mathematics, a finding which is not consistent with reports from older students (see Leder, 1992). However, a developmental pattern was clearly evident. More students in Grade 5 seemed to be aware of the usefulness and relevance of mathematics outside of school. Because perceived usefulness is thought to be an important determinant of activity choice (e.g., Feather, 1988; Wigfield & Eccles, 1992), it may therefore be valuable to make mathematics seem relevant in the early grades, perhaps by providing students with real-life applications more frequently (e.g., simulating a shopping transaction). We found a few noteworthy results about students' perceptions of the mathematical processes. Students' responses suggest a recognition of the relation between mathematics and other curricular areas, a finding that is encouraging to practitioners (although there is room for improvement). Interestingly, the vast majority of students indicated that children of both sexes should learn mathematics (Item 45), even though, consistent with cultural stereotypes, males perceive themselves as more competent. In addition, girls and boys were equally likely to state that their parents really wanted them to learn mathematics (Item 42), contrary to what might be predicted on the basis of gender-stereotyped expectations. •

This paper makes two important contributions. First, the differences in the responses that were observed between students in Grades 3 and 5 and the analyses of gender differences in the respective grades strongly suggest the need for more research during elementary years. Although the reasons forthe observed differences discussed above are highly speculative, they clearly highlight the merits of conducting grade-by-grade analyses even in the early elementary years. Second, the results regarding gender differences in perceived competence in mathematics support those of Eccles et al. (1993). Assuming the close link between abilityrelated perceptions and achievement motivation that is proposed by various psychologists (e.g.,Bandura, 1989; Nicholls, 1984; Schunk, 1984), both sets of data suggest that intervention may be beneficial in the early elementary years. Author Note: We thank the principals, teachers, and students for their cooperation and participation. We are also grateful to James Feeney, our department head, and to the Mathematics Review Committee, especially Brian McCudden and Anne Cirillo, for their support and assistance in conducting this research. Opinions expressed in this article are those of the authors and do not necessarily reflect the opinions or policy of the Metropolitan Separate School Board. References

Bandura, A. (1989). Human agency in social cognitive theory. American Psychologist, 44, 1175-1184. Eccles, J., Wigfield, A., Harold, R. D., & Blumenfeld, P. (1993). Age and gender differences in children's self and task perceptions during elementary school. Child Development, 64, 830-847. Feather,N. T. (1988). Values, valences, and course enrollment: Testing the role of personal values within an expectancy-value framework. Journal of Educational Psychology, 80, 381-391. Fennema, E. H., & Sherman, J. A. (1978). Sexrelated differences in mathematics achievement and related factors: A further study. Journal of Research in Mathematics Education, 9, 189-203. Leder, G. C. (1992). Mathematics and gender: Changing perspectives. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 697-633). New York: McMillan Publishing Company. McDonald, J. L., & Kouba, V. L. (1986). Kindergarten through sixth grade students' concepts of the domain of mathematics. Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbookof research on mathematics teaching and learning (pp.575-596). New York: McMillan Publishing Company. Nicholls, J. G. (1984). Achievement motivation: Conceptions of ability, subjective experience, task choice, and performance. Psychological Review, 91, 328-346. Ontario Ministry of Education. (1989). Mathematics and reading, Grade 6: Review instruments. Ministry of Education, Ontario, Canada. Rathbone, S. A. (1989). Gender differences in attitudes toward mathematics between lowachieving and high-achieving fifth grade elementary students. Paper presented at the annual meeting of the Eastern Educational Research Association, Savannah, GA. •

Schoenfeld, A. H. (1989). Explorations of students' mathematical beliefs and behavior. Journal of Research in Mathematics Education, 20, 338-355. Schunk, D. H. (1984). Self-efficacy perspective on achievement behavior. Educational Psychologist, 19, 48-58. Steinback, M., & Gwizdala, J. (1995). Gender differences in mathematics attitudes of secondary students. School Science and Mathematics, 95, 36-41. Suydam, M. N. (1984). Research report: Attitudes toward mathematics. Arithmetic Teacher, 32, 12. Wigfield, A., & Eccles, J. S. (1992). The development of achievement task values: A theoretical analysis. Developmental Review, 12, 265-310.

Marina Vanayan, Nicholas White, Patricia Yuen, and Maria Teper Metropolitan Separate School Board, Toronto Correspondence concerning this article may be sent to Marina Vanayan, Research Department, Metropolitan Separate School Board, 80 Sheppard Ave. E., Toronto/Willowdale, Ontario, M2N 6E8, CANADA.