Abstract
Soon after their introduction to formal arithmetic, children are confronted with simple arithmetic story problems. The main question of this article is: how do children develop skill in the solving of these simple problems. And furthermore: is it possible to construct simulation models that adequately describe the varied behavior of children at different levels of skill. One of the main problems with the models presented thus far is that they are only capable of describing a limited part of children's behavior that can be observed in daily life. The models presented in this study are an attempt to overcome this difficulty. Use has been made of the notion of “repair” to enhance the range of performance patterns of the different models. The output of five models has been compared to data gathered in an empirical study with 5-, 6-, 7-, and 8-year-olds. The results indicate that the five models do give a fairly adequate description of the behavior under study. The repair notion has been found to be useful in enlarging the scale of possible performance patterns and, consequently, the models are capable of describing a wide variety of empirical data.
Similar content being viewed by others
References
Brown, J. S. and VanLehn, K. (1980). “Repair theory: a generative theory of bugs in procedural skills”, Cognitive Science 4: 379–426.
Brown, J. S. and VanLehn, K. (1982). “Towards a generative theory of bugs”, in P., Carpenter, J. M., Moser, and T. A., Romberg (Eds.), Addition and Subtraction. Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 117–135.
Carpenter, T. P. and Moser, J. M. (1982). “The development of addition and subtraction problem solving skills”, in T. P., Carpenter, J., Moser and T., Romberg (Eds.), Addition and Subtraction: A Cognitive Perspective. Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 9–24.
Clark, H. H. and Clark, E. V. (1979). Psychology and Language; An Introduction to Psycholinguistics. New York: Harcourt Brace Javanovich.
Gelman, R. and Gallistel, C. R. (1978). The Child's Understanding of Number. Cambridge, MA: Harvard University Press.
McGhee, P. E. (1979). Humor. San Francisco: W. H. Freeman and Company.
Greeno, J. G. (1978). “A study of problem solving”, in R., Glaser (Ed.), Advances in Instructional Psychology (Vol. 1). Hillsdale, NJ: Lawrence Erlbaum Associates.
Lindvall, C. M. and Ibarra, C. G. (1980). “A Clinical Investigation of the Difficulties Evidenced by Kindergarten Children in Developing ‘Models’ for the Solution of Arithmetic Story Problems”. Paper presented at the annual meeting of the American Educational Research Association, Boston, April, 1980.
Nesher, P. (1976). “Three determinants of difficulty in verbal arithmetic problems”, Educational Studies in Mathematics 7: 369–388.
Nesher, P. and Teubal, E. (1975). “Verbal cues as an interfering factor in verbal problem solving”, Educational Studies in Mathematics 6: 41–51.
Riley, S., Greeno, J. G. and Heller, J. I. (1983). “Development of problem solving abilities in arithmetic”, in H., Ginsburg (Ed.), The Development of Mathematical Thinking. New York: Academic Press, pp. 153–196.
Rosenthal, D. J. A. and Resnick, L. B. (1974). “Children's solution processes in arithmetic world problems”, Journal of Educational Psychology 6: 817–825.
Schultz, T. R. and Pilon, R. (1973). “Development of the ability to detect linguistic ambiguity”, Child Development 44: 728–733.
VanLehn, K. (1983). “On the representation of procedures in repair theory”, in H., Ginsburg (Ed.), The Development of Mathematical Thinking. New York: Academic Press, pp. 197–252.
Author information
Authors and Affiliations
Additional information
We thank Prof. J. J. Elshout and Dr. Ch. Hamaker for their commentary on the first draft.
Rights and permissions
About this article
Cite this article
Sandberg, J.A.C., De Ruiter, H. The solving of simple arithmetic story problems. Instr Sci 14, 75–86 (1985). https://doi.org/10.1007/BF00052438
Issue Date:
DOI: https://doi.org/10.1007/BF00052438