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Related Experiment Videos

Characterizing the intuitive representation in problem solving: evidence from evaluating mathematical strategies

J A Dixon1, C F Moore

  • 1University of Wisconsin, Madison, USA. jdixon@trinity.edu

Memory & Cognition
|May 1, 1997
PubMed
Summary

This study reveals that people evaluate math strategies based on underlying principles, not just integrated answers. Intuitive domain understanding influences how instructions affect strategy evaluation.

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Area of Science:

  • Cognitive Science
  • Mathematical Cognition
  • Problem Solving

Background:

  • Evaluating mathematical strategies relies on how individuals represent problems intuitively.
  • Two primary intuitive representations are hypothesized: principle-based and integrated.

Purpose of the Study:

  • To investigate the nature of intuitive problem representation in mathematical strategy evaluation.
  • To determine if intuitive understanding mediates the impact of instruction on problem evaluation.

Main Methods:

  • Experiment 1: Subjects judged math strategies for temperature mixture problems, manipulating answer distance and principle violation.
  • Experiment 2: Subjects received instruction on acid mixture principles, completed an estimation task, and then evaluated strategies.

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Main Results:

  • Results supported the principle representation hypothesis, indicating strategies are evaluated based on underlying rules.
  • Intuitive domain understanding was found to mediate the effect of instruction on strategy evaluation.
  • Evidence suggests subjects map their intuitive understanding to mathematical strategies.

Conclusions:

  • Mathematical strategy evaluation is primarily guided by an intuitive, principle-based representation.
  • Domain-specific intuitive knowledge plays a crucial role in how individuals learn and apply mathematical concepts.
  • A mapping process between intuitive understanding and strategy execution is central to problem-solving.