Abstract
When students are given a nonroutine mathematical problem to solve, their reactions often include a lot of emotion. If they work on the problem over an extended period of time, the emotional responses frequently become quite intense. Many students will begin to work on a problem with some enthusiasm, treating it like a puzzle or game. After some time, the reactions become more negative. Students who have a plan to solve the problem may get stuck trying to carry out the plan. They often become quite tense; they may try to implement the same plan repeatedly, getting more frustrated with each unsuccessful attempt. If the students obtain a solution to the problem, they express feelings of satisfaction, even joy. If they do not reach a solution, they may angrily insist on help so that they can reduce their frustration.
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References
Adams, J.L. (1980). Conceptual blockbusting: A guide to better ideas (2nd ed.). New York: Norton.
Armstrong, J.M. (1981). Achievement and participation of women in mathematics: Results of two national surveys. Journal for Research in Mathematics Education, 72, 356–372.
Beck, A.T., & Emery, G. (1985). Anxiety disorders and phobias: A cognitive perspective. New York: Basic Books.
Beckwith, J. (1983). Gender and math performance: Does biology have implications for educational policy? Journal of Education, 165, 158–174.
Bloom, B.S., & Broder, L.J. (1950). Problem-solving processes of college students. Chicago: University of Chicago Press.
Bower, G.H. (1981). Mood and memory. American Psychologist, 36, 129–148.
Brown, A.L., Bransford, J.D., Ferrara, R.A., & Campione, J.C. (1983). Learning, remembering, and understanding. In J. Flavell & E. Markman (Eds.), Mussen’s handbook of child psychology (Vol. 3, pp. 77–166). Somerset, NJ: Wiley.
Brown, S.I., & Walter, M. (1983). The art of problem posing. Philadelphia: Franklin Institute Press.
Burton, L. (1984). Mathematical thinking: The struggle for meaning. Journal for Research in Mathematics Education, 15, 35–49.
Buxton, L. (1981). Do you panic about maths? London: Heinemann.
Charles, R.I., & Lester, F.K., Jr. (1984). An evaluation of a process-oriented instructional program in mathematical problem solving in grades 5 and 7. Journal for Research in Mathematics Education, 15, 15–34.
D’Andrade, R.G. (1981). The cultural part of cognition. Cognitive Science, 5, 179–195.
Fennema, E. (1982, March). The development of variables associated with sex differences in mathematics. Symposium conducted at the annual meeting of the American Educational Research Association, New York.
Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton: Princeton University Press.
Haladyna, T., Shaughnessy, J., & Shaughnessy, J. M. (1983). A causal analysis of attitude toward mathematics. Journal for Research in Mathematics Education, 14, 19–29.
Johnson-Laird, P.N. (1983). Mental models: Towards a cognitive science of language, inference, and consciousness. Cambridge, England: Cambridge University Press.
Kagan, J. (1978). On emotion and its development: A working paper. In M. Lewis & L.A. Rosenblum (Eds.), The development of affect (pp. 11–41). New York: Plenum Press.
Kantowski, M.G. (1977). Processes involved in mathematical problem solving. Journal for Research in Mathematics Education, 8, 163–180.
Kantowski, M.G. (1980). Some thoughts on teaching for problem solving. In S. Krulik (Ed.), Problem solving in school mathematics (pp. 195–203). Reston, VA: National Council of Teachers of Mathematics.
Kilpatrick, J. (1985). Reflection and recursion. Educational Studies in Mathematics, 16, 1–26.
Lawson, M J. (1984). Being executive about metacognition. In J. A. Kirby (Ed.) Cognitive strategies and educational performance (pp. 89–109). Orlando, FL: Academic Press.
Leder, G.C. (1986, April). Gender-linked differences in mathematics learning: Further explorations. Paper presented at the Research Presession for the Annual Meeting of the National Council of Teachers of Mathematics, Washington, DC.
Lester, F.K., Jr. (1983). Trends and issues in mathematical problem-solving research. In R. Lesh & M. Landau, Acquisition of mathematics concepts and processes (pp. 229–261). New York: Academic Press.
Mandler, G. (1975). Mind and emotion. New York: Wiley.
Mandler, G. (1984). Mind and body: Psychology of emotion and stress. New York: Norton.
Mandler, G. (1985). Cognitive psychology: An essay in cognitive science. Hillsdale, NJ: Lawrence Erlbaum Associates.
Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. London: Addison-Wesley.
Matthews, W. (1984). Influences on the learning and participation of minorities in mathematics. Journal for Research in Mathematics Education, 15, 84–95.
McLeod, D.B. (1985). Affective issues in research on teaching mathematical problem solving. In E.A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 267–279). Hillsdale, NJ: Lawrence Erlbaum Associates.
Mehan, H. (1978). Structuring school structure. Harvard Educational Review, 48, 32–64.
Meichenbaum, D. (1977). Cognitive behavior modification: An integrative approach. New York: Plenum Press.
National Council of Teachers of Mathematics. (1980). An agenda for action. Reston, VA: Author.
Norman, D.A. (1981). Twelve issues for cognitive science. In D.A. Norman (Ed.), Perspectives on cognitive science (pp. 265–295). Norwood, NJ: Ablex.
Ohio Department of Education. (1980). Problem solving: A basic mathematics goal. Columbus: Author.
Polya, G. (1945). How to solve it. Princeton: Princeton University Press.
Resnick, L.B., & Ford, W.W. (1981). The psychology of mathematics for instruction. Hillsdale, NJ: Lawrence Erlbaum Associates.
Reyes, L.H. (1984). Affective variables and mathematics education. Elementary School Journal, 84, 558–581.
Rigney, J.W. (1980). Cognitive learning strategies and dualities in information processing. In R.E. Snow, P. A. Federico, & W.E. Montague (Eds.), Aptitude, learning, and instruction (Vol. 1, pp. 315–343). Hillsdale, NJ: Lawrence Erlbaum Associates.
Rosamond, F. (1982). Listening to our students. For the Learning of Mathematics, 3, 6–11.
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. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
Shiffrin, R.M., & Dumais, S.T. (1981). The development of automatism. In J.R. Anderson (Ed.), Cognitive skills and their acquisition (pp. 11–140). Hillsdale, NJ: Lawrence Erlbaum Associates.
Shufelt, G. (Ed.). (1983). The agenda in action. Reston, VA: National Council of Teachers of Mathematics.
Silver, E.A. (1982, January). Thinking about problem solving: Toward an understanding of metacognitive aspects of mathematical problem solving. Paper prepared for the Conference on Thinking, Fiji.
Silver, E.A. (1985). Research on teaching mathematical problem solving: Some under-represented themes and needed directions. In E.A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247–266). Hillsdale, NJ: Lawrence Erlbaum Associates.
Simon, H. A. (1982). Comments. In M.S. Clark & S.T. Fiske (Eds.), Affect and cognition. The Seventeenth Annual Carnegie Symposium on Cognition (pp. 333–342). Hillsdale, NJ: Lawrence Erlbaum Associates.
Spielberger, C.D., O’Neil, H.F., & Hansen, D.N. (1972). Anxiety, drive theory, and computer-assisted learning. In B.A. Maher (Ed.), Progress in experimental personality research (Vol. 6, pp. 109–148). New York: Academic Press.
Strongman, K.T. (1978). The psychology of emotion (2nd ed.). New York: Wiley.
Turkle, S. (1984). The second self: Computers and the human spirit. New York: Simon and Schuster.
Wertime, R. (1979). Students, problems, and “courage spans.” In J. Lochhead & J. Clement (Eds.), Cognitive process instruction (pp. 191–199). Philadelphia: Franklin Institute Press.
Whimbey, A., & Lochhead, J. (1982). Problem solving and comprehension (3rd ed.). Philadelphia: Franklin Institute Press.
Wickelgren, W.A. (1974). How to solve problems. San Francisco: W.H. Freeman.
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McLeod, D.B. (1989). The Role of Affect in Mathematical Problem Solving. 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_2
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DOI: https://doi.org/10.1007/978-1-4612-3614-6_2
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