Koedinger & Nathan (2004)

The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning

• Authors: Kenneth Koedinger and Mitchell Nathan
• Journal: Journal of the Learning Sciences
• Year: 2004
• Source: http://www.tandfonline.com/doi/abs/10.1207/s15327809jls1302_1

Abstract

This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than solving mathematically equivalent equations. Contrary to some views of situated cognition, this result is not simply a consequence of situated world knowledge facilitating problem-solving performance, but rather a consequence of student difficulties with comprehending the formal symbolic representation of quantitative relations. We draw on analyses of students' strategies and errors as the basis for a cognitive process explanation of when, why, and how differences in problem representation affect problem solving. We conclude that differences in external representations can affect performance and learning when one representation is easier to comprehend than another or when one representation elicits more reliable and meaningful solution strategies than another.

Outline of Headings

• Why Are Story Problems Difficult?
• Story Problems Can Be Easier
• Hypotheses and Experimental Design
• Difficulty Factors Assessments: Studies 1 and 2
  • Methods for DFA1 and DFA2
    • Participants
    • Form design
    • Procedure
  • Results for DFA1 and DFA2
    • DFA1 results
    • DFA2 results
• Strategy and Error Analyses of Learners
  • Qualitative Strategy Analysis—Stories Can Be Solved Without Equations
  • Quantitative Strategy Analysis—Words Elicit More Effective Strategies
  • Error Analysis—Comprehending Equations Is Harder Than Comprehending Words
    • Explaining situation facilitation
• Discussion
  • Assessing the Symbolic, Situation, and Verbal Facilitation Hypotheses
    • Two reasons why story and word problems can be easier
  • Logical Task-Structure Versus Experience-Based Reasons for Difficulty Differences
  • Instructional Implications
• Conclusion

Also

APA

Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. Journal of the Learning Sciences, 13(2), 129–164. doi:10.1207/s15327809jls1302_1

BibTeX

@article{Koedinger2004a,
author = {Koedinger, Kenneth R. and Nathan, Mitchell J.},
doi = {10.1207/s15327809jls1302\_1},
journal = {Journal of the Learning Sciences},
number = {2},
pages = {129--164},
title = {{The real story behind story problems: Effects of representations on quantitative reasoning}},
volume = {13},
year = {2004}
}