Agents of Change in Promoting Reflective Abstraction: A Quasi-Experimental, Study on Limits in College Calculus

• Cappetta, Robert W. ^[1] ; Zollman, Alan ^[2]
  1. [1] College of DuPage

     College of DuPage

     Township of Milton, Estados Unidos

     
  2. [2] Northern Illinois University

     Northern Illinois University

     Township of DeKalb, Estados Unidos

     
• Localización: REDIMAT, ISSN-e 2014-3621, Vol. 2, Nº. 3, 2013, págs. 343-357
• Idioma: inglés
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• Resumen

  • We measured student performance on the concept of limit by promoting reflection through four agents of change: instructor, peer, curriculum and individual. It is based on Piaget’s four constructs of reflective abstraction: interiorization, coordination, encapsulation, and generalization, and includes the notion of reversal, as refined into a construct by Dubinsky. Our quasi-experimental study examined the performance of two sections of first-semester calculus students at a midwestern community college. Scores by students in the experimental section were significantly higher than scores by students in the control traditional section on a posttest of limits. A deeper examination of a three-tiered subgroup showed the reflective abstraction section had moderate effect size on mathematical knowledge and strategic knowledge and a large effect size on explanation.