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Finding formulas: Does active search facilitate appropriate generalization?

Nicole R Hallinen1, Lauren N Sprague2, Kristen P Blair3

  • 1Microsoft, 1 Microsoft Way, Redmond, WA, 98052, USA. nicole.hallinen@gmail.com.

Cognitive Research: Principles and Implications
|July 19, 2021
PubMed
Summary
This summary is machine-generated.

Searching for algebraic formulas before instruction helps learners generalize better and avoid errors. This method is more effective than traditional "tell-and-practice" approaches for adaptive learning.

Keywords:
AlgebraInductionMathematics learningSketchingTransfer

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Area of Science:

  • Cognitive Psychology
  • Educational Psychology
  • Learning Sciences

Background:

  • Adaptive learning requires appropriate generalization and avoiding overgeneralization.
  • Generalization involves understanding applicable features and necessary modifications for new contexts.

Purpose of the Study:

  • Investigate if searching for an algebraic formalism before direct instruction improves generalization.
  • Examine the impact of pre-instructional search on adaptive learning outcomes.

Main Methods:

  • Three experiments were conducted to compare learning strategies.
  • Participants engaged in either a search-first activity or a tell-and-practice activity.
  • The effect of sketching as a learning aid was also explored.

Main Results:

  • Searching for an equation before instruction reduced overgeneralization compared to tell-and-practice.
  • The success of creating new adaptations correlated with performance in the search task.
  • Sketching helped mitigate negative effects of tell-and-practice but not enhance searching.

Conclusions:

  • Pre-instructional search for algebraic formulas aids in connecting formulas to referents and preventing overgeneralization.
  • Standard tell-and-practice led to significant overgeneralization errors.
  • Enhanced tell-and-practice with visual connections showed similar or worse results than search-first conditions.