Abstract
This paper discusses a series of five studies examining over 800 students' solutions to division-with-remainders story problems. The findings from the studies suggest that students' difficulty in solving these problems is due, in large part, to a failure to engage in situation-based reasoning and sense-making in interpreting computational results obtained when solving the problem. Data from recent studies not only has provided direct evidence to support this hypothesis but also suggested that students' dissociation of sense-making from school mathematics is a major barrier to their engaging in or displaying the reasoning that leads to correct solutions.
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References
Baranes, R., Perry, M., & Stigler, J.: Activation of real-world knowledge in the solution of word problems. Cognition and Instruction 6(4), 287–318 (1989)
Boero, P., Ferrari, P., & Ferrero, E.: Division problems: Meanings and procedures in the transition to a written algorithm. For the Learning of Mathematics, 9(4), 17–25 (1989)
Bransford, J., Hasselbring, T., Barron, B., Kulewicz, S., Littlefield, J., & Goin, L.: Use of macro-contexts to facilitate mathematical thinking. In: The teaching and assessing of mathematical problem solving (R. Charles & E. Silver, eds.), pp. 125–147. Reston, VA: LEA & NCTM, 1989
Brousseau, G.: The crucial role of the didactical contract in the analysis and construction of situations in teaching and learning mathematics (Occasional Paper No. 54). Bielefeld, FRG: Universität Bielefeld, Institut für Didaktik der Mathematik, November 1984
Carpenter, T., Hiebert, J., & Moser, J.: Problem structure and first grade children's initial solution processes for simple addition and subtraction problems. Journal for Research in Mathematics Education 12, 27–39 (1981)
Carpenter, T. P., Fennema, E., Peterson, P. L., Chaing, C, & Loef, M.: Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal 26(4), 499–532 (1989)
Chi, M., Glaser, R., & Rees, E.: Expertise in problem solving. In: Advances in the psychology of human intelligence (R. Sternberg, ed.), pp. 7–75. Hillsdale, NJ: Lawrence Erlbaum Associates 1982
Cobb, P.: The tension between theories of learning and instruction in mathematics education. Educational Psychologist 23(2), 87–103 (1988)
Cobb, P., Wood, T., & Yackel, E.: Constructivist approach to second grade mathematics. In: Constructivism in mathematics education (E. von Glasersfeld ed.). Dordrecht: Kluwer 1991
Lampert, M.: Connecting mathematical teaching and learning. In: Integrating research on teaching and learning mathematics: Papers from the First Wisconsin Symposium for Research on Teaching and Learning Mathematics (E. Fennema, T. Carpenter, & S. Lamon, eds.), pp. 132–165. Madison: University of Wisconsin, Wisconsin Center for Education Research 1988
National Assessment of Educational Progress: The third national mathematics assessment: Results, trends and issues. Denver, CO: Author 1985
National Council of Teachers of Mathematics: Curriculum and evaluation standards for school mathematics. Reston, VA: Author 1989
Schoenfeld, A.: When good teaching leads to bad results: The disasters of “well taught” mathematics courses. Educational Psychologist 23(2), 87–103 (1988)
Silver, E.: Using conceptual and procedural knowledge: A focus on relationships. In: Conceptual and procedural knowledge: The case of mathematics (J. Hiebert, ed.), pp. 181–189. Hillsdale, NJ: Lawrence Erlbaum 1986
Silver, E.: Solving story problems involving division with remainders: The importance of semantic processing and referential mapping. In: Proceedings of the Tenth Annual Meeting of PME-NA (M. Behr, C. Lacampagne & M. Wheeler, eds.), pp. 127–133. DeKalb, IL: Author 1988
Silver, E., Mukhopadhyay, S., & Gabriele, A.: Referential mapping and the solution of division story problems involving remainders. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, March 1989
Silver, E., Smith, M., Lane, S., Salmon-Cox, L., & Stein, M.: QUASAR (Quantitative Understanding: Amplifying Student Achievement and Understanding) project summary. Learning Research and Development Center, University of Pittsburgh, Fall 1990
Silver, E., Shapiro, L., & Deutsch, A.: Sense-making and the solution of division problems involving remainders: An examination of students' solution processes and their interpretations of solutions. Paper presented at the annual meeting of the American Educational Research Association, Chicago, April 1991
Smith, M. & Silver, E.: Examination of middle school students' solutions and interpretations of a division story problem. Paper presented at the annual meeting of the American Educational Research Association, Chicago, April 1991
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© 1992 Springer-Verlag Berlin Heidelberg
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Silver, E.A., Shapiro, L.J. (1992). Examinations of Situation-Based Reasoning and Sense-Making in Students’ Interpretations of Solutions to a Mathematics Story Problem. In: Ponte, J.P., Matos, J.F., Matos, J.M., Fernandes, D. (eds) Mathematical Problem Solving and New Information Technologies. NATO ASI Series, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58142-7_8
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DOI: https://doi.org/10.1007/978-3-642-58142-7_8
Publisher Name: Springer, Berlin, Heidelberg
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