Secondary students' attitudes toward mathematics.

Abstract

The purpose of this study was to investigate the attitudes of secondary school students toward mathematics study, to compare the attitudes of students in the USA with eight other countries, and to compare differences in attitudes by gender for students in the USA. The study also analyzed the relationships between these attitudes and other mathematics learning factors and reported their impact on mathematics achievement.

Introduction

Research centering on students' attitudes toward mathematics study has received increasing attention. Studies have shown that factors such as motivation and attitude have impacted student achievement (Cote & Levine, 2000; Singh, Granville & Dika, 2002). Moreover, instructional strategies may also support student needs in order to increase student achievement. For example, Bottge (2001) found that when math problems were interesting and engaging, students with learning disabilities were able to solve problems that emphasized higher level thinking skills. Tymms (2001) investigated 21,000 students' attitudes toward math and suggested that the most important factors were the teacher and students' academic level; while age, gender, and language were weakly associated with attitudes. Webster and Fisher's (2000) study revealed that rural and urban students' attitudes toward math and career aspirations positively affected their performance. Altermatt and colleagues (2002) found that students' attitude changes could be predicted and influenced by types of classmates. Webb, Lubinski, & Benbow (2002) found educational experiences, abilities, and interests predicted undergraduate degree concentrations in math and science. Koller, Baumert, and Schnabel (2001) studied gender differences in mathematics achievement, which favored males in achievement, interest, and placement in advanced math courses. Few studies systematically analyzed attitudes, various mathematics learning factors, and achievement of secondary school students using an international database. Utilizing trends in International Mathematics and Science Study (TIMSS), provides insight into cross-national similarities and differences, and augments the existing literature.

Methods

Sample. A total of 9,072 eighth grade students in the USA were compared with students from eight other countries. These countries included Australia (4,032), Canada (8,770), Chile (5,907), England (2,960), Israel (4,195), Japan (4,745), Russia (4,332), and South Africa (8,146). Australia's sample included both eighth and ninth grade students, and England's sample included only ninth grade students. The sampling design from the TIMSS 1999 study ensured that a representative sample of eighth or ninth grade students was drawn.

Data Sources. The data were derived from the TIMSS 1999 study that included student achievement in mathematics and information obtained through a student questionnaire. A total of 57 items were selected from the student questionnaire. Of these items, 11 reflected students' attitudes toward mathematics study. Questions were centered on three categories: importance (2 items), interest (3 items), and difficulty (6 items). Students rated their level of agreement with each item on a four-point scale: 1=Strongly Disagree, 2=Disagree, 3=Agree, and 4=Strongly Agree. Of the remaining 46 items, questions were centered on additional categories including family factors (4 items), friends/classmates' attitudes and behaviors (4 items), self-expectations (3 items), self-concept of performance in math (4 items), motivation (4 items), teaching approaches (26 items), and gender (1 item).

Data Analysis. Descriptive statistics were employed to analyze the characteristics of eighth grade students, which centered on three categories: importance, interest, and difficulty. Where questionnaire items that were categorized as indicating interest or difficulty were reversed, the items were recoded to reflect the opposite score. For example, one of the three items measuring interest in mathematics stated, "mathematics is boring." If the respondent totally agrees (a value of 4) with this item, it means that they do not have a high interest in mathematics. Since the level of interest is being measured and since the higher the score the less interest is shown by the respondent, the accurate scoring of this item should be reversed. Three separate ANOVAs were used to compare American students' attitudes toward math study with the other countries. A Least Significant Difference (LSD) multiple-comparison test was followed when ANOVA results showed significant differences between the USA and the other countries. Additionally, a t-test was used for making comparisons of American students' attitudes toward mathematics by gender. A Pearson correlation was used to reveal the relationships between students' attitudes toward math study and factors of math learning and achievement.

Results of Research

Descriptive Statistics

Importance of Math Study. Two items centered upon the category denoted as importance: "I think it is important to do well in mathematics at school" and "I think mathematics is important to everyone's life." On a rating scale from l-4, 95.1% of American eighth grade students overall strongly agreed or agreed that math study is very important, where the mean and standard deviation of the total score was 3.52 and 0.54, respectively. The level of agreement ranged from 91.7% in Japan to 99.3% in England for the item, "I think it is important to do well in mathematics at school." Further, the level of agreement ranged from 61.7% in Japan to 96.9% in Chile for the item, "I think mathematics is important to everyone's life." When comparing the percentage of students who strongly agreed or agreed with items categorized as importance, students in the USA indicated higher levels of agreement than those in Israel, Japan, or South Africa.

Interest in Math Study. The interest category consisted of three items: "I like mathematics," "I enjoy learning mathematics," and "Mathematics is boring" (opposite score). For American students, 65.9% of the respondents agreed or strongly agreed with the three items categorized as interest in math study. For students in the USA, the mean score of 2.75 and standard deviation of 0.81 for items measuring interest were lower when compared to the mean scores for importance. Students in the USA indicated higher levels of agreement for items centering on interest than students in Canada, Australia, or Japan.

Difficulty with Math Study. Six items centered upon the difficulty category: "Mathematics is an easy subject" (opposite score), "I would like mathematics much more if it were not so difficult," "Although I do my best, mathematics is more difficult for me than for many of my classmates," "Nobody can be good in every subject, and I am just not talented in mathematics," "When I do not understand a new topic in mathematics initially, I know that I will never really understand it," and "Mathematics is not one of my strengths." Overall, 41.4% of American students strongly agreed or agreed with the items categorized as difficulty with math study. The mean of 2.40 and standard deviation of 0.73 for the total scores of students in the USA measuring difficulty were lower than the mean scores for items on importance or interest. Students in the USA indicated higher levels of agreement for items centering on difficulty than students in Israel, Russia, Australia, and Canada.

Comparison of USA with Other Countries

Results of the analyses of variance revealed significant differences for importance, interest, and difficulty among the nine countries. The F value (1,8) equaled 915.35, therefore the p value was 0.000 for importance; for interest, the F value (1,8) equaled 433.46, and therefore the p value was 0.000; while the F value (1,8) equaled 342.48, and therefore the p value was 0.000 for difficulty. The post hoc analysis (LSD) showed comparison results of the USA and the other countries.

Importance. Students in Chile, Israel, England, and Canada had higher importance scores than American students' scores, but students in Australia, South Africa, and Japan had lower scores. These differences were all statistically significant. Russian students had comparable importance scores to those students in the USA.

Interest. Students in South Africa, England, Israel, Chile, and Russia had significantly higher scores when examining interest in math study than students in America, but students in Japan and Australia had significantly lower scores. When comparing scores from students in America with those in Canada, there were no significant differences.

Difficulty. Students in Japan, Chile, South Africa, Australia, and England had significantly higher scores reflecting items categorized as difficulty than students in the USA. Alternatively, difficulty scores for Canadian students were significantly lower than those reported by students in the USA. American, Russian, and Israeli students had comparable scores regarding items that reflected difficulty with math study.

Relationship between Attitudes by Gender

The results of the t-test indicated that American eighth grade students' attitudes toward math study by gender had significant differences for one of the three categories. More specifically, the mean scores for female students were statistically significantly higher for items categorized as difficulty with math study than mean scores reported for male students.

Relationships between Attitudes and Family Factors

Students responded to an item for which they reported the level of education attained by their father and their mother. There was a slightly positive correlation with students' importance and interest scores, but a stronger negative correlation with their difficulty scores. The item "About how many books are in your home" was positively correlated with importance and interest scores, but negatively correlated with difficulty scores. Reporting their own mothers' perceptions, the item, "My mother thinks it is important for me to ... do well in mathematics at school," had a positive correlation with students' importance scores interest scores of .42 and. 17, respectively, but a negative correlation of -.09 with difficulty scores.

Relationships between Attitudes and Friends/Classmates

Students were asked to respond to an item that inquired into their friends' perceptions regarding their mathematics performance. "It is important to do well in mathematics at school" had a moderately positive correlation of .34 and .23 with students' importance and interest scores, respectively, but a weakly negative correlation of-.05 with difficulty scores.

Relationships between Attitudes and Self Expectations

Students indicated their expectations for completing their educational level. A positive correlation existed between students' importance and interest scores with their perceived educational level, along with other items such as "Do well in math" and "To get a job that involved using mathematics." Alternatively, students' difficulty scores had a negative correlation of -.61 and -.43 with "Do well in math" and "To get a job that involved using mathematics", respectively.

Relationships between Attitudes and Self-Concept of Performance in Math

Students responded to items that measured their self-concept of performance in math. In response to the prompt, "To do well in mathematics at school

you need," the choices were "Lots of natural talent/ability," "Good luck," "Lots of hard work studying at home," and "To memorize the textbook or notes." Students who had lower importance and interest scores indicated a higher level of agreement with the items "Lots of natural talent/ability" and "Good luck." Similarly, students with higher difficulty scores indicated higher levels of agreement with the same items. Students' perceptions of math importance had a positive correlation of .34 with the item "Lots of hard work studying at home".

Relationships between Attitudes and Motivation

On the student questionnaire, there were four items related to motivation. In response to the prompt, "I need to do well in mathematics," the choices were "To get the job I want," "To please my parent(s)," "To get into the school or university I prefer," and "To please myself." The results indicated that students' importance and interest scores were positively correlated with items of "To get the job I want," "To get into the school or university I prefer," and "To please myself," while students' difficulty scores were negatively correlated, ranging from -.19 to -.13.

Relationships between Attitudes and Teaching Approaches

There was a list of twenty different teaching approaches to which students were asked to indicate the frequency of occurrence on a 4-point scale with 4=Almost always, 3=Pretty often, 2=Once in a while, and l=Never. The results indicated that approaches to teaching mathematics in the classroom had varying degrees of relationships with students' difficulty levels, while some approaches were more closely correlated with students' importance and interest scores. Moreover, 15, 19, and 8 of the correlations were statistically significant for importance, interest, and difficulty categories and teaching approaches, respectfully. The scores of "The teacher shows us how to do mathematics problems" and "We use things from everyday life in solving mathematics problems" had a positive correlation of .20 with students' importance and. 19 with students' interest scores.

Cross-National Comparisons of Attitudes and Achievement

The Pearson correlation examining the relationship between students' attitudes toward math study with achievement among the nine countries resulted in seven out of nine correlation coefficients that were statistically significant. The coefficients were less than or equal to .24 when examining importance and achievement. The coefficients were statistically significant for interest and achievement, and the values ranged from. 10 for England and Israel to .33 for Japan. In contrast, the values for the relationship between difficulty and achievement ranged from -.22 for South Africa to -.57 for Canada.

Conclusions

The conceptual framework supporting the present study is based on research conducted in the areas of attitudes and achievement. When comparing the attitudes towards mathematics of secondary school students among the nine countries, some interesting patterns emerge. Student attitudes were strongest for importance of math study, then interest in math study, and lastly, difficulty with math study, with the exception of Japan. For respondents in Japan, the levels of agreement pertaining to difficulty exceeded those attributed to interest. Additionally, Japan was the only country for which a moderate relationship was indicated between interest in studying math and achievement. Moreover, an inverse relationship existed among eighth grade students between perceptions of those who rated math as being difficult and achievement scores. When comparing the nine countries, student attitudes in the USA ranked sixth for items centering on importance and interest and fifth for items focusing on difficulty. Research suggests that negative perceptions may be formed early in the learning process, beginning in the elementary grades, and continuing through to high school and beyond. Poor academic performance, parent attitudes, and teacher attitudes may reinforce negative attitudes toward mathematics (Bobis & Cusworth, 1994). Strategies focusing on changing perceptions of students' attitudes represent the preliminary step toward improving students' math achievement. Gender differences existed between American males and females with the three constructs of importance, interest, and difficulty. For example, American male students were more interested in studying math than females. Alternatively, female students perceived math as more important than males. Of particular interest, the mean scores for female students pertaining to items categorized as difficulty exceeded those scores for males and were statistically significant. Research conducted by Stipek & Granlinski (1991) indicated that girls have lower expectations and self-concepts with regard to their ability in mathematics. These attitudes commence in elementary school and persist through junior high school. Strategies that were recommended by the researchers to ameliorate these negative attitudes include encouragement and examination of mathematics performance with positive responses.

This study indicated a particularly low correlation between attitudes and parent education levels and resources. However, a moderate relationship existed between the students' mothers' perception for doing well in mathematics and students who perceived math as important. When comparing the relationship of friends' or classmates' attitudes with the three constructs, importance, interest, and difficulty, a moderate relationship existed with students' importance and interest scores. There was a negative relationship between students' difficulty scores and self-expectations. Students with higher difficulty scores had lower self-expectations in terms of doing well in math or getting a job that involved using mathematics. Moreover, a positive relationship existed between importance of math study and the item "Lots of hard work studying at home." The correlations of motivation with the constructs of importance and interest tend to be moderate and were significant. In general, the results suggest those students with high importance scores perceived that it was necessary to do well in mathematics in order to meet educational goals, career goals, or fulfill their personal goals. Grouws & Cebulla (2000) summarized research supporting the use of particular teaching strategies or methods. The results indicated an increased understanding of mathematical concepts, along with improved student achievement and attitudes. This study, however, did not yield significant relationships between teaching methods and attitudes of importance, interest or difficulty.

References

Altermatt, E. R., Pomerantz, E. M., Ruble, D. N., Frey, K. S., & Greulich, F. K. (2002). Predicting changes in children's self-perceptions of academic competence: A naturalistic examination of evaluative discourse among classmates. Developmental Psychology, 38(6), 903-917.

Bobis, J. & Cusworth, R. (1994). Teacher Education: an agent of change for attitudes towards mathematics and science/technology. Retrieved May 13, 2004 from http://www.aare.edu.au/94pap/bob94072.txt

Bottge, B. A. (2001). Using intriguing problem to improve math skills. Educational Leadership, 58(6), 68-72.

Cote, J.E. & Levine, C.G. (2000). Attitude versus aptitude: Is intelligence or motivation more important for positive higher-educational outcomes? Journal of Adolescent Research, 15(1), 58-80.

Grouws, D. & Cebulla, K. (2000). Improving student achievement in mathematics, part h Research findings. ERIC Digest No. ED463952. Retrieved May 14, 2004 from http://www.ericfacility.net/databases/ ERIC_Digests/ed463952.html

Koller, O., Baumert, J., & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education, 32(5), 448-470.

Singh, K., Granville, M., & Dika, S. (2002). Mathematics and science achievement: Effects of motivation, interest, and academic engagement. Journal of Educational Research, 95(6), 323-332.

Stipek, D. & Granlinski, H. (1991). Gender differences in children's achievement-related beliefs and emotional responses to success and failure in mathematics. Journal of Educational Psychology, 83(3), 361-371.

Tymms, P. (2001). A test of the big fish in a little pond hypothesis: An investigation into the feelings of seven-year-old pupils in school. School Effectiveness and School Improvement, 12(2), 161-181.

Webb, R. M., Lubinski, D., & Benbow, C. (2002). Mathematically facile adolescents with math-science aspirations: New perspectives on their educational and vocational development. Journal of Educational Psychology, 94(4), 785-794.

Webster, B. J., & Fisher, D. L. (2000). Accounting for variation in science and mathematics achievement: A multilevel analysis of Australian data. School Effectiveness and School Improvement, 11(3), 339-360.

Kathryn Sanchez, Houston Independent School District 

Laurie Zimmerman, Houston Independent School District

Renmin Ye, Houston Independent School District

Sanchez, Ed.D. is Assistant Superintendent, Zimmerman, Ph.D. is Research Specialist, and Ye, Ed.D. is Application Specialist, in the Department of Research and Accountability.