Abstract
The current paper introduces a provisional model designed to describe the cognitive processes involved in solving algebraic and more complex mathematical problems. The model contains three major components: (1) the problem task environment, (2) long-term memory, and (3) working memory. Each of the major components consists of major processes and subpro-esses that are described. Questions about the specificity of models are raised in the discussion.
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Bhaskar, R., & Simon, H. A. (1977). Problem solving in semantically rich domains: An example from engineering thermodynamics. Cognitive Science, 1, 193–215.
Briars, D. J. (1983). An information-processing analysis of mathematical ability. In R. F. Dillon & R. R. Schmeck (Eds.), Individual differences in cognition (pp. 181-204). New York: Academic Press.
Clement, F. (1979). Patterns of Joey’s comments on arithmetic problems. Journal of Children’s Mathematical Behavior, 2, 58–68.
Davis, R. B. (1982, March). Representations and judgments in mathematical thought. Paper presented at the meeting of the American Educational Research Association, New York.
Gough, P. G. (1972). One second of reading. In J. F. Kavanagh & I. G. Mattingly (Eds.), Language by eye and ear (pp. 331-358). Cambridge, MA: MIT Press.
Greeno, J. G. (1976). Cognitive objectives of instruction: Theory of knowledge for solving problems and answering questions. In D. Klahr (Ed.), Cognition and Instruction (pp. 123-159). Hillsdale, NJ: Erlbaum.
Greeno, J. G. (1978). Understanding and procedural knowledge in mathematics instruction. Educational Psychologist, 12, 262–283.
Greeno, J. G., Magone, M. E., & Chaiklin, S. (1979). Theory of constructions and set in problem solving. Memory & Cognition, 7, 445–461.
Hayes, J. R., & Flower, L. S. (1980). Identifying the organization of writing processes. In L. W. Gregg & E. R. Steinberg (Eds.), Cognitive processes in writing (pp. 3-30). Hillsdale, NJ: Erlbaum.
Hunt, E. (1978). Mechanics of verbal ability. Psychological Review, 85, 109–130.
Just, M. A., & Carpenter, P. A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87, 329–354.
LaBerge, D., & Samuels, S. J. (1974). Toward a theory of automatic information processing in reading. Cognitive Psychology, 6, 293–323.
Larkin, J. H. (1980, October). Models of skilled and less skilled problem solving in physics. Paper presented to the NIE-LRDC Conference on Thinking and Learning Skills, Pittsburg.
Larkin, J. G., McDermott, J., Simon, D. P., & Simon, H. A. (1980). Models of competence in solving physics problems. Cognitive Science, 4, 317–345.
Mayer, R. E. (1981). Frequency norms and structural analysis of algebra story problems into families, categories, and templates. Instructional Science, 10, 135–175.
Michener, D. R. (1978). Understanding mathematics. Cognitive Science, 2, 361–383.
Newell, A., & Simon, H. A. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.
Resnick, L. B. (1976). Task analysis in instructional design: Some cases from mathematics. In D. Klahr (Ed.), Cognition and instruction (pp. 51-80). Hillsdale, NJ: Erlbaum.
Woods, S. S., Resnick, L. B., & Groen, G. J. (1975). An experimental test of five process models for subtraction. Journal of Educational Psychology, 67, 17–21.
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Dinnel, D., Glover, J.A. & Ronning, R.R. A provisional model of mathematical problem solving. Bull. Psychon. Soc. 22, 459–462 (1984). https://doi.org/10.3758/BF03333877
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DOI: https://doi.org/10.3758/BF03333877