Cooperative learning: Differences between group and individual processes of construction of the concept of inverse function

Draga Vidakovic, Purdue University

Abstract

This study was conducted with five individual students and five groups of students who were assigned to work together in the first course of the experimental Calculus classes at Purdue University during the Fall of 1992. The study investigated the differences between group and individual mental constructions of the concept of inverse function. Based on the researcher's understanding of the concept, the general theory, and the observation of students, a description of a construction processes for the developing schema (genetic decomposition) of the inverse function was obtained. After data analysis, it was concluded that there was no difference between genetic decomposition of the concept for the groups and for individuals, but there was a difference between the processes involved in learning the concept. Four main characteristics (disequilibrium, diversity of approaches, building mathematical language, taking different roles) were found to differentiate the study groups from the individual mode of problem-solving. An instructional treatment was developed on the basis of the genetic decomposition for the concept of inverse function. It consists of computer activities designed to stimulate the students to go through the steps of cognitive constructions for developing the schema of inverse function. Based on the results of the study the use of groups is recommended in implementing the instructional treatment.

Degree

Ph.D.

Advisors

Dubinsky, Purdue University.

Subject Area

Mathematics education|Curricula|Teaching

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