Abstract
Despite the general agreement among researchers today that students’ beliefs have an important influence on mathematical problem solving there is still a lack of clarity from a conceptual viewpoint. In this chapter we present a literature review of available categorizations or models of students’ beliefs related to mathematics learning and problem solving. These reveal that although they all cover a broad spectrum of relevant beliefs, there appears to be no consensus on the structure and the content of the relevant categories of students’ beliefs, A philosophical and psychological analysis of the nature and the structure of beliefs enables us to come to a deeper understanding of the development and the functioning of students’ beliefs and to clarify the relation between beliefs and knowledge. The insights developed through this analysis result in an elaborated and concrete definition of students’ mathematics-related beliefs and allow us to develop a theoretical framework that coherently integrates the major components of prevalent models of students’ beliefs. We differentiate between students’ beliefs about mathematics education, students’ beliefs about the self, and students’ beliefs about the social context, i.e., the class context.
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References
Abelson, R. (1979). Differences between belief systems and knowledge systems. Cognitive Science, 3, 355–366.
Alexander, P. A., Schallert, D. L., & Hare, V. C. (1991). Coming to terms: How researchers in learning and literacy talk about knowledge? Review of Educational Research, 61(3), 315–343.
Ames, C., & Archer, J. (1988). Achievement goals in the classroom: Students’ learning strategies and motivation processes. Journal of Educational Psychology, 80, 260–267.
Bain, A. (1859). The emotions and the will. London: Longmans, Green.
Bereiter, C., & Scardamalia, M. (1993). Surpassing Ourselves: An inquiry into the nature and implications of expertise. Chicago: Open Court.
Bogdan, R. J. (1986). The importance of belief. In R. J. Bogdan (Ed.), Belief: Form, content, and function (pp. 1–16). New York: Oxford University Press.
Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–42.
Carter, C. S., & Yackel, E. (1989). A constructivist perspective on the relationship between mathematical beliefs and emotional acts. Paper presented at the annual meeting of the AERA, San Francisco.
Carter, G., & Norwood, K. S. (1997). The relationship between teacher and student beliefs about mathematics. School Science and Mathematics, 97(2), 62–67.
Cobb, P., & Yackel, E. (1998). A constructivist perspective on the culture of the mathematics classroom. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 158–190).
Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while engaged in mathematical problem solving. In D. B. McLeod, & V. M. Adams (Eds.), Affect and Mathematical Problem Solving: A new perspective. New York: Springer-Verlag.
Connell, J. P., & Wellborn, J. G. (1990). Competence, autonomy, and relatedness: A motivational analysis of self-system processes. In M. Gunnar, & L.A. Sroufe (Eds.), Minnesota Symposium on Child Psychology, Vol. 23. Hillsdale, N.J.: Erlbaum.
de Abreu, G., Bishop, A. J., & Pompeu, G. Jr. (1997). What children and teachers count as mathematics. In T. Nunes, & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 233–264). Hove, UK: Psychology Press Ltd.
De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D.C. Berliner, & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 491–549). New York: Simon & Schuster Macmillan.
De Corte, E., Verschaffel, L., & Op’ t Eynde, P. (2000). Self-regulation: A characteristic and a goal of mathematics learning. In M. Boekaerts, P. R. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation (pp. 687–726). San Diego: Academic Press.
DeBellis, V. A. (1996). Interactions between affect and cognition during mathematical problem solving: A two year case study of four elementary school children. Unpublished doctoral dissertation, Rutgers University: (University Microfilms No. 96-30716).
Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–254). Basingstoke: Falmer Press.
Ernest, P. (1991). The philosphy of mathematics education. London: Falmer.
Fennema, E. (1989). The study of affect and mathematics: A proposed generic model for research. In D. B. McLeod, & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 205–219). New York: Springer-Verlag.
Fenstermacher, G. (1994). The knower and the known: The nature of knowledge in research on teaching. In L. Darling-Hammond (Ed.), Review of research in education, Vol. 20 (pp. 1–54). Itasca, IL: Peacock.
Frank, M. L. (1988). Problem solving and mathematical beliefs. Arithmetic Teacher, 35, 32–35.
Garofalo, J. (1989). Beliefs and their influence on mathematical performance. Mathematics Teacher, 82, 502–505.
Gilbert, D. T. (1991). How mental systems believe. American Psychologist, 46(2), 107–119.
Green, T. (1971). The activities of teaching. New York: McGraw-Hill.
Greeno, J. G. (1991). A view of mathematical problem solving in school. In M. U. Smith (Ed.), Toward a unified theory of problem solving. View from the content domains (pp. 69–98). Hillsdale, NJ: Lawrence Erlbaum Associates.
Greeno, J. G., Collins, A. M., & Resnick, L. B. (1996). Cognition and learning. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 15–46). New York: Simon & Schuster Macmillan.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549.
Hofer, B. K. (1999). Instructional context in the college mathematics classroom: Epistemological beliefs and student motivation. Program and Organization Development, 16(2), 73–82.
Hofer, B. K., & Pintrich, P. R. (1997). The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Research, 67(1), 88–140.
Isoda, M., & Nakagoshi, A. (2000). A case study of student emotional change using changing heart rate in problem posing and solving Japanese classroom in mathematics. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24 th conference of the International Group for the Psychology of Mathematics Education (pp. 3-87–3-94). Hiroshima: Hiroshima University.
Johnson-Laird, P.N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness Cambridge, UK: Cambridge University Press
Klinger, E. (1996). Emotional influences on cognitive processing, with implications for the theories of both. In P. M. Gollwitzer, & J. A. Bargh (Eds.), The psychology of action: Linking cognition and motivation to behavior. New York: The Guilford Press.
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 Press.
Kloosterman, P., & Coughan, M. C. (1994). Students’ beliefs about learning school mathematics. The Elementary School Journal, 94(4), 375–388.
Kloosterman, P., Raymond, A. M., & Emenaker, C. (1996). Students’ beliefs about mathematics: A three-year study. The Elementary School Journal, 97(1), 39–56.
Kouba, V. L., & McDonald, J. L. (1986). Children’s and teachers’ perceptions and beliefs about the domain of elementary mathematics. In D. Lappan, & R. Even (Eds.), Proceedings of the eight annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 250–255). East Lansing: Michigan State University.
Lampert, M. (1990). When the problem in not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29–63.
Lampert, M. (1996). Agreeing to disagree: Developing sociable mathematical discourse. In D. R. Olson, & N. Torrance (Eds.), The handbook of education and human development: New models of learning, teaching and schooling (pp. 731–764). Oxford, UK: Blackwell Publishers, Inc.
McLeod, D. B. (1988). Research on learning and instruction in mathematics: The role of affect. In E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics. Papers from the First Wisconsin Symposium for Research on Teaching and Learning Mathematics (pp. 60–89). Wisconsin: Wisconsin Center for Education Research, University of Wisconsin.
McLeod, D. B. (1992). Research on affect in mathematics education: a reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (pp. 575–596). New York: Macmillan.
Mischel, W., & Shoda, Y. (1995). A cognitive-affective system theory of personality: Reconceptualizing situations, dispositions, dynamics, and invariance in personality structure. Psychological Review, 102(2), 246–268.
Mtetwa, D., & Garofalo, J. (1989). Beliefs about mathematics: An overlooked aspect of student difficulties. Academic Therapy, 24, 611–618.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Nickson, M. (1992). The culture of the mathematics classroom: an unknown quantity? In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (pp. 101–114). New York: Macmillan.
Niemivirta, M. (1996). Intentional and adaptive learning modes: The self at stake. Paper presented at the second European Conference on Education, September 1996, Sevilla, Spain.
Ortony, A., Clore, G. L., & Collins, A. (1988). The cognitive structure of emotions. New York: Cambridge University Press.
Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86(2), 193–203.
Pehkonen, E. (1995). Pupils’ view of mathematics: Initial report for an international comparison project. University of Helsinki, Department of Teacher Education. Research report 152
Pehkonen, E., & Törner, G. (1996). Mathematical beliefs and different aspects of their meaning. Zentralblatt Für Didaktik Der Mathematik, 4, 101–108.
Pekrun, R. (1990). Emotion and motivation in educational psychology. In P. J. D. Drenth, J. A. Sergeant, & R. J. Takens (Eds.), European perspectives in psychology: Theoretical, psychometrics, personality, development, educational, cognitive, gerontological (Vol. 1 pp. 265–295). Chisester, UK: John Whiley & Sons.
Perkins, D. (1995). Outsmarting IQ. The emerging science of learnable intelligence. New York: The Free Press.
Pintrich, P. (1989). The dynamic interplay of student motivation and cognition in the college classroom. In C. Ames, & M. Maehr (Eds.), Advances in motivation and achievement: Motivation-enhancing environments (Vol. 6 pp. 117–160). Greenwich, CT: JAI Press.
Pintrich, P. R., & Schrauben, B. (1992). Students’ motivational beliefs and their cognitive engagement in academic tasks. In D. Schunk, & J. Meece (Eds.), Students’ perceptions in the classroom: Causes and consequences (pp. 149–183). Hillsdale, NJ: Lawrence Erlbaum Associates.
Pintrich, P. R., Smith, D. A. F., Garcia, T., & McKeachie, W. J. (1993). Reliability and predictive validity of the Motivated Strategies for Learning Questionnaire (MSLQ). Educational and Psychological Measurement, 53, 801–813.
Power, M., & Dalgleish, T. (1997). Cognition and emotion: Form order to disorder. Sussex, UK: Erlbaum Taylor & Francis LTD.
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (second ed., pp. 102–119). New York: Simon & Schuster Macmillan.
Salomon, G., & Perkins, D. N. (1998). Individual and social aspects of learning. In P. D. Pearson, & A. Iran-Nejad (Eds.), Review of Research on Education Vol. 23 (pp. 1–25). Washington, DC: AERA.
Scheffler, I. (1965). Conditions of knowledge: An introduction to epistemology and education. Chicago: Scott Foresman.
Schiefele, U., & Csikszentmihalyi, M. (1995). Motivation and ability as factors in mathematics experience and achievement. Journal for Research in Mathematics Education, 26(2), 163–181.
Schoenfeld, A. H. (1983). Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive Science, 7, 329–363.
Schoenfeld, A. H. (1985a). Mathematical problem solving. Orlando, Florida: Academic Press.
Schoenfeld, A. H. (1985b). Students’ beliefs about mathematics and their effects on mathematical performance: A questionnaire analysis. Paper presented at the Annual Meeting of the American Educational Research Association, March 31–April 4, 1985, Chicago, Illinois.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.
Schommer, M., Crouse, A., & Rhodes, N. (1992). Epistemological beliefs and mathematical text comprehension: Believing it is simple does not make it so. Journal of Educational Psychology, 84(4), 435–443.
Seegers, G., & Boekaerts, M. (1993). Task motivation and mathematics in actual task situations. Learning and Instruction, 3, 133–150.
Snow, R. E., Corno, L., & Jackson III, D. (1996). Individual differences in affective and conative functions. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of Educational Psychology (pp. 243–310). New York: Simon & Schuster Macmillan.
Spangler, D. A. (1992). Assessing students’ beliefs about mathematics. Arithmetic Teacher, 40(3), 148–152.
Spinoza, B. (1982). The etics and selected letters. (S. Feldman, Ed., and S. Shirley, Trans.) Indianapolis, IN: Hackett.
Stipek, D. J., & Gralinski, H. (1991). Gender differences in children’s achievement-related beliefs and emotional responses to succes and failure in mathematics. Journal of Educational Psychology, 83(3), 361–371.
Stodolsky, S. S., Salk, S., & Glaessner, B. (1991). Student views about learning math and social studies. American Educational Research Journal, 28, 89–116.
Teasdale, J., & Barnard, P. (1993). Affect, cognition and change. Hove, UK: Lawrence Erlbaum Associates, LTD.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (pp. 127–146). New York: Macmillan.
Törner, G., & Pehkonen, E. (1996). On the structure of mathematical belief systems. Zentralblatt Für Didaktik Der Mathematik, 4, 109–112.
Tymoczko, T. (1986). (Ed.), New directions in the philosophy of mathematics. Boston: Birkhauser.
Underhill, R. (1988). Mathematics learners’ beliefs: A review. Focus on Learning Problems in Mathematics, 10, 55–69.
Vanayan, M., White, N., Yuen, P., & Teper, M. (1997). Beliefs and attitudes toward mathematics among third-and fifth-grade students: A descriptive study. School Science and Mathematics, 97(7), 345–351.
Vermeer, H. J. (1997). Sixth-grade students’ mathematical problem-solving behavior: Motivational variables and gender differences. Leiden: UFB, Leiden University.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.
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Op’t Eynde, P., De Corte, E., Verschaffel, L. (2002). Framing Students’ Mathematics-Related Beliefs. In: Leder, G.C., Pehkonen, E., Törner, G. (eds) Beliefs: A Hidden Variable in Mathematics Education?. Mathematics Education Library, vol 31. Springer, Dordrecht. https://doi.org/10.1007/0-306-47958-3_2
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