# Beliefs About Mathematics and Mathematics Learning in the Secondary School: Measurement and Implications for Motivation

## Abstract

Students’ beliefs about mathematics and mathematics learning can have a substantial impact on their interest in mathematics, their enjoyment of mathematics, and their motivation in mathematics classes. This chapter has a dual focus with respect to such beliefs. First, an interview instrument to measure personal and environmental beliefs that influence student motivation in mathematics is discussed. Drawing from the mathematics education as well as psychological literatures, the instrument’s questions focus on topics including feelings about school in general, non-school influences on motivation, self-confidence, perceptions of ability, goal orientation, study habits, mathematics content, assessment practices, and expectations of teachers. Second, findings from the instrument that are specific to beliefs about the nature of mathematics are described in the chapter. Findings include the fact that the nature of mathematics is not something secondary students think about. When pressed, however, most of their comments deal with the procedural rather than conceptual aspects of the subject. Students also tend to feel that memorization is an important part of mathematics even though they feel individuals who do not memorize well can still succeed. Taken as a whole, the chapter documents the importance of considering a wide variety of beliefs when trying to understand individual student interest and motivation in mathematics.

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## References

- Alderman, M. K. (1999).
*Motivation for achievement*. Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Ames, C. (1992). Classrooms: Goals, structures, and student motivation.
*Journal of Educational Psychology*.*84*, 261–271.CrossRefGoogle Scholar - Atkinson, J. W. (1957). Motivational determinants of risk-taking behavior.
*Psychological Review*,*64*, 359–372.Google Scholar - Bandura, A. (1997).
*Self-efficacy: The exercise of control*. New York: Wiley.Google Scholar - Bartsch, K., & Wellman, H. (1989). Young children’s attribution of action to beliefs and desires.
*Child Development*,*60*, 946–964.Google Scholar - Blumenfeld, P. C. (1992). Classroom learning and motivation: Clarifying and expanding goal theory.
*Journal of Educational Psychology*,*84*, 272–281.CrossRefGoogle Scholar - Carl, I. M. (Ed.) (1995).
*Prospects for school mathematics*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Carr. M. (1996). Afterward. In M. Carr (Ed.),
*Motivation in mathematics*(pp. 173–177). Cresskill, NJ: Hampton Press.Google Scholar - Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.),
*Handbook of research design in mathematics and science education*(pp. 547–589). Mahwah, NJ: Lawrence Erlbaum.Google Scholar - Covington, M. V. (1992).
*Making the grade: A self-worth perspective on motivation and school reform*. Cambridge, England: Cambridge University Press.Google Scholar - DeGroot, E. (2000, April).
*In their own words: Adolescents and their teachers talk about learning and schooling*. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.Google Scholar - Eccles, J., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., & Midgley, C. (1985). Self-perceptions, task perceptions, socializing influences, and the decision to enroll in mathematics. In S. F. Chipman, L. R. Brush, & D. M. Wilson (Eds.),
*Women and mathematics: Balancing the equation*(pp. 95–121). Hillsdale NJ: Erlbaum.Google Scholar - Elliott, E. S., & Dweck, C. S. (1988). Goals: An approach to motivation and achievement.
*Journal of Personality and Social Psychology*,*54*, 5–12.CrossRefGoogle Scholar - Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman Mathematics Attitude Scales.
*JSAS: Catalog of Selected Documents in Psychology*,*6*(1). (Ms. No. 1225).Google Scholar - Ford. M. I. (1994). Teachers’ beliefs aboutmathematical problem solving in the elementary school.
*School Science and Mathematics*,*94*, 314–322.CrossRefGoogle Scholar - Graham, S., & Weiner, B. (1996). Theories and principles of motivation. In D. C. Berliner & R. C. Calfee (Eds.),
*Handbook of Educational Psychology*(pp. 63–84). New York: Macmillan.Google Scholar - Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997).
*Making sense: Teaching and learning mathematics with understanding*. Portsmouth, NH: Heinemann.Google Scholar - Huntley, M. A., Rasmussen, C. L., Villarubi, R. S., Sangtong, R. S., Sangtong, J., & Fey, J. T. (2000). Effects of
*Standards-based*mathematics education: A study of the Core-Plus Mathematics Project algebra and functions strand.*Journal for Research in Mathematics Education*,*31*, 328–361.Google Scholar - Kelley, H. H. (1973). The process of causal attribution.
*American Psychologist*,*28*, 107–128.Google Scholar - Kloosterman, P. (1988). Self-confidence and motivation in mathematics.
*Journal of Educational Psychology*,*80*, 345–351.CrossRefGoogle Scholar - Kloosterman, P. (1996). Students’ beliefs about knowing and learning mathematics: Implications for motivation. In M. Carr (Ed.),
*Motivation in mathematics*(pp. 131–156). Cresskill, NJ: Hampton.Google Scholar - Kloosterman, P. (1998, April).
*How hard do you work in mathematics? Motivational profiles of six high school students*. Paper presented at the annual meeting of the American Educational Research Association. San Diego. Retrieved May 30, 2002 from: http://www.indiana.edu/~pwkwww/AERA98.html - Kloosterman, P., & Cougan, M. C. (1994). Students’ beliefs about learning school mathematics.
*Elementary School Journal*,*94*, 375–388.CrossRefGoogle Scholar - Kloosterman, P., & Mau, S. T. (1997). Is this really mathematics? Challenging the beliefs of preservice primary teachers. In D. Fernandes, F. Lester, A. Borralho, & I. Vale (Eds.), (1997).
*Resolução de problemas na formacão inicial de professores de matemática: Multiplos contextos e perspectivas (Solving problems in the preparation of mathematics teachers: Multiple contexts and perspectives)*(pp. 217–248). Aveiro, Portugal: Grupo de Investigação em Resolução de Problemas.Google Scholar - Kloosterman, P., & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving.
*School Science and Mathematics*,*92*, 109–115.Google Scholar - Lester, F. K., & Kroll, D. L. (1991). Evaluation: A new vision.
*Mathematics Teacher*,*84*, 276–284.Google Scholar - Maple, S. A., & Stage, F. K. (1991). Influences on the choice of math/sciencemajor by gender and ethnicity.
*American Educational Research Journal*,*28*, 37–60.Google Scholar - Mitchell, J. H., Hawkins, E. F., Jakwerth, P. M., Stancavage, F. B., & Dossey, J. A. (1999). Student work and teacher practices in mathematics.
*Washington, DC: National Center for Education Statistics*.Google Scholar - National Council of Teachers of Mathematics (2000).
*Principles and standards for school mathematics*. Reston, VA: Author.Google Scholar - National Research Council (1989).
*Everybody counts: A report to the nation on the future of mathematics education*. Washington, DC: National Academy Press.Google Scholar - Nicholls, J. G. (1984). Conceptions of ability and achievement motivation. In R. E. Ames & C. Ames (Eds.),
*Research on motivation in education*Vol. 1:*Student motivation*(pp. 39–73). Orlando, Academic Press.Google Scholar - Paris, S. G., Turner, J. C., (1994). Situated motivation. In P. R. Pintrich, D. R. Brown, & C. E. Weinstein (Eds.),
*Student motivation, cognition, and learning: Essays in honor of Wilbert J. McKeachie*(pp. 213–237). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Pintrich, P. R., & Schrauben, B. (1992). Students’ motivational beliefs and their cognitive engagement in classroom academic tasks. In. D. H. Schunk & J. L. Meece (Eds.),
*Student perceptions in the classroom*(pp. 149–183). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar - Reyes, L. H. (1984). Affective variables and mathematics education.
*Elementary School Journal*,*18*, 207–218.Google Scholar - Schunk, D. H. (1991). Self-efficacy and academic motivation.
*Educational Psychologist*,*26*, 207–231.CrossRefGoogle Scholar - Seegers, G., & Boekarts, M. (1993). Task motivation and mathematics achievement in actual task situations.
*Learning and Instruction*,*3*, 133–150.CrossRefGoogle Scholar - Shernoff, D., & Schneider, B. (2000, April).
*Engagement in math and science among high school students: Examining school, individual, and family influences*. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.Google Scholar - Stage, F. K., & Kloosterman, P. (1995). Gender, beliefs, and achievement in remedial college-level mathematics.
*Journal of Higher Education*,*66*, 294–311.Google Scholar - Steen, L. A., & Forman, S. L. (1995). Mathematics for work and life. In I. M. Carl. (Ed.),
*Prospects for school mathematics*(pp. 219–241). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Stipek, D. J., (1996). Motivation and instruction. In D. C. Berliner & R. C. Calfee (Eds.),
*Handbook of Educational*Psychology (pp. 85–113). New York: Macmillan.Google Scholar - Weiner, B. (1984). Principles for a theory of student motivation and their application within an attributional framework. In R. E. Ames & C. Ames (Eds.),
*Research on motivation in education*Vol. 1:*Student motivation*(pp. 15–38). Orlando, FL: Academic Press.Google Scholar