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Related Experiment Videos

Adding apples and oranges: alignment of semantic and formal knowledge

M Bassok1, V M Chase, S A Martin

  • 1Department of Psychology, University of Washington, Seattle 98195-1525, USA. mbassok@u.washington.edu

Cognitive Psychology
|May 8, 1998
PubMed
Summary

Structural alignment, a key to analogical reasoning, also influences arithmetic word problem interpretation. This semantic alignment guides how people apply mathematical operations based on real-world object relationships, ensuring sensible problem-solving.

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Area of Science:

  • Cognitive Psychology
  • Mathematical Cognition
  • Language and Reasoning

Background:

  • Analogical reasoning relies on structural alignment to map relations between different domains.
  • Arithmetic word problems require understanding both semantic and mathematical relations.
  • Prior research has not fully explored how semantic relations influence mathematical reasoning in word problems.

Purpose of the Study:

  • To investigate the role of structural alignment in arithmetic word problem interpretation.
  • To demonstrate how semantic relations in word problems create "content effects" on mathematical reasoning.
  • To examine the alignment between real-world object semantics and mathematical operation arguments.

Main Methods:

  • Analysis of how college students and textbook authors construct arithmetic word problems.

Related Experiment Videos

  • Examination of the inferred semantic relations between real-world objects (e.g., CONTAIN).
  • Assessment of the correspondence between these semantic relations and mathematical operations (e.g., DIVIDE).

    • Main Results:

    • A systematic correspondence, termed "semantic alignment," exists between inferred semantic relations and mathematical operations.
    • This alignment guides the selective and sensible application of formal mathematical knowledge.
    • Examples include dividing items among containers (apples among baskets) but not vice versa, and adding compatible items (apples and oranges) but not incompatible ones (apples and baskets).

    Conclusions:

    • Structural alignment is a fundamental mechanism underlying both analogical reasoning and arithmetic word problem interpretation.
    • Semantic alignments significantly influence how abstract mathematical concepts are applied to concrete problems.
    • Understanding these alignments is crucial for designing effective educational materials and improving mathematical cognition.