A Modeling Result on Concrete-Pictorial-Abstract Representations

• In Event: 42.084 - Poster Session 8
  In Poster Session: 42.084-5 - Teaching Educational Psychology to Promote Equal Educational Opportunities

Abstract

Using representations to understand mathematical knowledge is popular in teaching. The framework of concrete-pictorial-abstract representations (CPA) for teaching integrates research on learners' cognition and constructivist theories of education, and includes a model on CPA. This paper proposed that a framework on CPA that can best be understood and applied when one considers three fundamental aspects of teaching: a) identification of learners' cognitive situations; b) teacher's scaffolding supporting learners entering into their own zone of proximal development; and c) learners' transferring CPA that must be undertaken through teacher-learner interactions. An example was used to illustrate the application of the framework. This framework was proposed to help teachers understand CPA and allowed for a potential design for guided instruction.

Authors

• Ke Wang, Nicholls State University

• Mary Margaret Capraro, Texas A&M University