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A microgenetic study of the multiplication and division inversion concept.

Katherine M Robinson1, Adam K Dubé

  • 1Campion College at the University of Regina, Regina, Saskatchewan, Canada S4S 0A2. katherine.robinson@uregina.ca

Canadian Journal of Experimental Psychology = Revue Canadienne De Psychologie Experimentale
|September 11, 2009
PubMed
Summary

This study on multiplication and division concepts found that many 6th graders struggled to discover or appropriately generalize the inversion shortcut, indicating complexities in multiplicative understanding.

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Area of Science:

  • Cognitive psychology
  • Mathematics education
  • Developmental psychology

Background:

  • Limited understanding of multiplicative concepts compared to additive concepts.
  • The inversion concept in multiplication and division is not well-documented.
  • Prior research suggests difficulties in grasping advanced mathematical principles.

Purpose of the Study:

  • To investigate the discovery and development of the multiplication-division inversion concept.
  • To examine how 6th-grade students learn and apply the inversion shortcut.
  • To assess the generalization of the inversion concept and its transferability.

Main Methods:

  • A microgenetic study design was employed over several weeks.
  • Participants (6th graders) solved multiplication and division inversion problems.
  • Transfer of knowledge was assessed using inversion, modified inversion, and lure problems.

Main Results:

  • Over a third of participants did not discover the inversion shortcut.
  • Another third exclusively used the inversion shortcut.
  • Most participants struggled with generalizing the inversion concept appropriately.

Conclusions:

  • Developmental complexities exist in multiplicative concepts, including inversion.
  • Current theories of mathematical understanding may require modification.
  • Further research is needed on the acquisition of multiplicative concepts.