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Related Experiment Videos

Transformations of mathematical and stimulus functions.

Chris Ninness1, Dermot Barnes-Holmes, Robin Rumph

  • 1School & Behavioral Psychology Program, Stephen F Austin State University, Nacogdoches, Texas 75962, USA. cninness@sfasu.edu

Journal of Applied Behavior Analysis
|October 6, 2006
PubMed
Summary
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Participants learned to match algebraic formulas to their graphs. Their preference for standard or factored equation forms could be manipulated by contextual rules and financial rewards.

Area of Science:

  • Mathematics Education
  • Cognitive Psychology
  • Behavioral Science

Background:

  • Understanding the relationship between mathematical formulas and their graphical representations is crucial for learning advanced mathematics.
  • Prior research indicates that learning can be influenced by the format of information and external motivators.

Purpose of the Study:

  • To investigate how individuals unfamiliar with algebraic and trigonometric functions learn to associate formulas with their corresponding graphs.
  • To examine the influence of contextual cues, specifically mathematical form preferences (standard vs. factored), on this learning process.
  • To determine if these preferences can be manipulated by explicit instructions and financial incentives.

Main Methods:

  • A computer-interactive matching-to-sample procedure was used to train formula-to-formula and formula-to-graph relations.

Related Experiment Videos

  • Participants underwent novel formula-to-graph and graph-to-formula tests.
  • Contextual cues regarding mathematical preferences (standard vs. factored forms) were manipulated through instructions and financial rewards.

    • Main Results:

    • Seven out of eight participants significantly improved in identifying formula-to-graph relations.
    • Initially, participants favored factored forms when identifying graphs from formulas.
    • Preferences shifted towards standard forms when instructed, and then reversed to favor factored forms when financial rewards were contingent on selecting factored forms.

    Conclusions:

    • Individuals can effectively learn to map algebraic formulas to their graphical representations through interactive training.
    • Mathematical form preferences are malleable and can be influenced by contextual rules and reinforcement contingencies.
    • This study highlights the impact of external factors on mathematical understanding and problem-solving strategies.