Abstract
During the last 15 years, much understanding has been gained about cognitions in mathematics. Starting with the content area of early number concepts, progressing through rational numbers and algebra, and culminating with problem solving by university mathematicians, scholars have been probing cognitions and determining how human beings think with mathematical ideas. This knowledge is beginning to be useful not only in understanding human thought processes, but also in the development of new paradigms for curriculum development (Carpenter, in press). This knowledge has grown and become useful because a relatively consistent research methodology has been used in relation to a fairly concise theoretical model of cognitive processing. Usually this cognitive science research methodology started with an explicit definition of some specific mathematics content; questions relating to this definition have been formulated; subjects were asked to think aloud (or self-report) as they answered the questions; their responses were studied for patterns of thinking; and, finally, the identified patterns were compared with the overall theory to see if the theory was supported or needed modification.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bloom, B.S. (Ed.). (1956). Taxonomy of educational objectives: Handbook 1. Cognitive domain. New York: David McKay.
Carpenter, T.P. (in press). Teaching as problem solving. In R.I. Charles & E.A. Silver, The teaching and assessing of mathematical problem solving. Reston, VA: National Council of Teachers of Mathematics and Hillsdale, NJ: Lawrence Erlbaum Associates.
Crosswhite, F.J. (1972). Correlates of attitudes toward mathematics (National Longitudinal Study of Mathematical Abilities, Report No. 20). Palo Alto, CA: Stanford University Press.
Dornbusch, S.M. (1974). To try or not to try. The Stanford Magazine, 2, 50–54.
Dowling, D.M. (1978). The development of a mathematics confidence scale and its application in the study of confidence in women college students. Unpublished doctoral dissertation, Columbus: Ohio State University.
Eccles, J.S. (1983). Expectancies, values, and academic choice: Origins and change. In J. Spence (Ed.), Achievement and achievement motivation (pp. 75–146). San Francisco: W.H. Freeman.
Eccles, J.S. (1986, March). Gender roles and vocational decisions. The presidential address delivered to the American Psychological Association, Washington, DC.
Elliott, J.C. (1987). Causal attribution, confidence, perceived usefulness, and mathematics achievement of nontraditional female and male college students. Unpublished doctoral dissertation, University of Wisconsin, Madison.
Fennema, E., Carpenter, T.P, & Peterson, P.L. (1986). Teachers’ decision making and cognitively guided instruction: A new paradigm for curriculum development. Paper presented at the Seventh Annual Psychology of Mathematics Education Conference, London, England.
Fennema, E., & Peterson, PL. (1985). Autonomous learning behavior: A possible explanation of gender-related differences in mathematics. In L.C. Wilkinson & C.B. Marrett (Eds.), Gender-related differences in classroom interactions (pp. 17–35). New York: Academic Press.
Fennema, E., & Peterson, PL. (1986). Teacher-student interactions and sex-related differences in learning mathematics. Teaching and Teacher Education, 2(1), 19–42.
Fennema E., & Peterson, PL. (1987). Effective teaching for girls and boys: The same or different? In D.C. Berliner & B.V. Rosenshine (Eds.), Talks to teachers (pp. 111–125). New York: Random House.
Fennema, E., Peterson, PL., & Carpenter, T.P. (1987). Teachers’beliefs about girls, boys and mathematics. Manuscript in progress.
Fennema, E., & Sherman, J. (1976). Fennema-Sherman mathematics attitude scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. Journal for Research in Mathematics Education, 7(5), 324–326.
Fennema, E., & Sherman, J. (1978). Sex-related differences in mathematics achievement and related factors: A further study. Journal for Research in Mathematics Education, 9(3), 189–203.
Fennema, E., Wolleat, P., Pedro, J., & Becker, A. (1981). Increasing women’s participation in mathematics: An intervention study. Journal for Research in Mathematics Education, 72(1), 3–14.
Frieze, I.H., Fisher, J., Hansua, B., McHugh, M.C., & Valle, V.A. (1978). Attributions of the causes of success and failure as internal and external barriers to achievement in women. In J. Sherman & F. Denmark (Eds.), Psychology of women: Future directions of research (pp. 519–552). New York: Psychological Dimensions.
Glennon, V.J., & Callahan, L.G. (1968). A guide to current research: Elementary school mathematics. Washington, DC: Association for Supervision and Curriculum Development.
Grieb, H., & Easley, J. (1984). A primary school impediment to mathematical equity: Case studies in role-dependent socialization. In M. Steinkamp & M.L. Maehr (Eds.), Women in science: Vol. 2. Advances in motivation and achievement (pp. 317–362). Greenwich, CT: JAI Press.
Gustin, W. (1982). Learning to become a mathematician: The development of independence. Paper presented at the annual meeting of the American Educational Research Association, New York.
Helson, R. (1980). The creative woman mathematician. In L.H. Fox, L. Brody, & D. Tobin (Eds.), Women and the mathematical mystique (pp. 23–54). Baltimore, MD: Johns Hopkins University Press.
Kloosterman, P.W. (1984). Attribution theory, learned helplessness, and achievement in ninth-grade mathematics. Unpublished doctoral dissertation, University of Wisconsin, Madison.
Krathwohl, D.R., Bloom, B.S., & Masia, B.B. (1964). Taxonomy of educational objectives: Handbook 2. Affective domain. New York: David McKay.
Leder, G.C. (1987). Attitudes toward mathematics. In T.A. Romberg & D.M. Stewart (Eds.), The monitoring of school mathematics (pp. 261–277). Madison, WI: Wisconsin Center for Education Research.
McCombs, B.L. (1986, April). The role of the self esteem in self-regulated learning. Paper delivered at the annual meeting of the American Educational Research Association, San Francisco.
Meyer, M.R. (1985). The prediction of mathematics achievement and participation for females and males: A longitudinal study of affective variables. Unpublished doctoral dissertation, University of Wisconsin, Madison.
Meyer, M.R., & Fennema, E. (1988). Girls, boys, and mathematics. In T.R. Post (Ed.), Teaching mathematics in grades K-8: Research-based methods (pp. 406–425). Newton, MA: Allyn & Bacon.
National Council of Teachers of Mathematics. (1988). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Pederson, K., Elmore, P., & Bleyer, D. (1985). Affective and cognitive mathematics-related variables: A longitudinal study. Carbondale, IL: Southern Illinois University.
Peterson, P.L., & Fennema, E. (1985). Effective teaching, student engagement in classroom activities, and sex-related differences in learning mathematics. American Educational Research Journal, 22(3), 309–335.
Sandman, R. (1973). The development, validation, and application of a multidimensional mathematics attitude instrument (Doctoral dissertation, University of Minnesota). Dissertation Abstracts International, 34.
Shavelson, R.J., Hubner, J.J., & Stanton, G.C. (1976). Self-concept: Validation of construct interpretations. Review of Educational Research, 46(3), 407–441.
Wolleat, PL., Pedro, J.D., Becker, A.D., & Fennema, E. (1980). Sex differences in high school students’ causal attributions of performance in mathematics. Journal for Research in Mathematics Education, 11(5), 356–366.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Fennema, E. (1989). The Study of Affect and Mathematics: A Proposed Generic Model for Research. In: McLeod, D.B., Adams, V.M. (eds) Affect and Mathematical Problem Solving. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3614-6_14
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3614-6_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8178-8
Online ISBN: 978-1-4612-3614-6
eBook Packages: Springer Book Archive