Skip to main content

Examinations of Situation-Based Reasoning and Sense-Making in Students’ Interpretations of Solutions to a Mathematics Story Problem

  • Conference paper
Mathematical Problem Solving and New Information Technologies

Part of the book series: NATO ASI Series ((NATO ASI F,volume 89))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)

    Article  Google Scholar 

  2. 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)

    Google Scholar 

  3. 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

    Google Scholar 

  4. 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

    Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Google Scholar 

  7. 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

    Google Scholar 

  8. Cobb, P.: The tension between theories of learning and instruction in mathematics education. Educational Psychologist 23(2), 87–103 (1988)

    Article  Google Scholar 

  9. Cobb, P., Wood, T., & Yackel, E.: Constructivist approach to second grade mathematics. In: Constructivism in mathematics education (E. von Glasersfeld ed.). Dordrecht: Kluwer 1991

    Google Scholar 

  10. 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

    Google Scholar 

  11. National Assessment of Educational Progress: The third national mathematics assessment: Results, trends and issues. Denver, CO: Author 1985

    Google Scholar 

  12. National Council of Teachers of Mathematics: Curriculum and evaluation standards for school mathematics. Reston, VA: Author 1989

    Google Scholar 

  13. Schoenfeld, A.: When good teaching leads to bad results: The disasters of “well taught” mathematics courses. Educational Psychologist 23(2), 87–103 (1988)

    Article  Google Scholar 

  14. 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

    Google Scholar 

  15. 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

    Google Scholar 

  16. 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

    Google Scholar 

  17. 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

    Google Scholar 

  18. 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

    Google Scholar 

  19. 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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-58142-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63483-3

  • Online ISBN: 978-3-642-58142-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics