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A functional analytic approach to computer-interactive mathematics.

Chris Ninness1, Robin Rumph, Glen McCuller

  • 1School and Behavioral Psychology Program, Department of Human Services, Stephen F. Austin State University, PO Box 13019 SFA Station, Nacogdoches, Texas 75962, USA. cninness@sfasu.edu

Journal of Applied Behavior Analysis
|May 19, 2005
PubMed
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This study shows that computer-based training can teach students to relate mathematical formulas to their graphs, enabling them to identify novel transformations and improving mathematical understanding.

Area of Science:

  • Mathematics Education
  • Cognitive Psychology
  • Computer-Based Learning

Background:

  • Understanding mathematical transformations is crucial for algebraic and trigonometric concepts.
  • Traditional methods may not effectively teach the relationship between mathematical formulas and their graphical representations.
  • Computer-interactive learning offers a novel approach to mathematical concept acquisition.

Purpose of the Study:

  • To investigate the effectiveness of a computer-interactive matching-to-sample procedure in teaching formula-to-graph relations.
  • To assess the transfer of learning to novel and complex mathematical transformations.
  • To examine derived stimulus control in the context of mathematical relations.

Main Methods:

  • 11 naive participants received a lecture on the rectangular coordinate system.

Related Experiment Videos

  • Computer-interactive training involved matching-to-sample procedures for formula-to-formula and formula-to-graph relations (reflections, shifts).
  • Assessment included mutual and combinatorial entailment, followed by a test of novel relations.

    • Main Results:

    • Six out of ten participants demonstrated perfect or near-perfect performance on novel formula-to-graph relations.
    • Participants showed an ability to generalize learned relations to complex variations.
    • Error patterns were analyzed for participants who did not achieve mastery.

    Conclusions:

    • Computer-interactive training effectively facilitates the understanding of mathematical transformations and their graphical representations.
    • Derived transfer of stimulus control is achievable through this training paradigm.
    • This approach shows promise for enhancing mathematical learning and problem-solving skills.