Students' images of problem contexts when solving applied problems

Kevin C. Moore, Marilyn Carlson

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This article reports findings from an investigation of precalculus students' approaches to solving novel problems. We characterize the images that students constructed during their solution attempts and describe the degree to which they were successful in imagining how the quantities in a problem's context change together. Our analyses revealed that students who mentally constructed a robust structure of the related quantities were able to produce meaningful and correct solutions. In contrast, students who provided incorrect solutions consistently constructed an image of the problem's context that was misaligned with the intent of the problem. We also observed that students who caught errors in their solutions did so by refining their image of how the quantities in a problem's context are related. These findings suggest that it is critical that students first engage in mental activity to visualize a situation and construct relevant quantitative relationships prior to determining formulas or graphs.

Original languageEnglish (US)
Pages (from-to)48-59
Number of pages12
JournalJournal of Mathematical Behavior
Issue number1
StatePublished - Mar 2012


  • Precalculus
  • Problem solving
  • Quantitative reasoning
  • Student reasoning
  • Word problems

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics


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