Innovative Pedagogical Plan to Conceptualize the Axiomatic Concept of Group Theory

Abstract

This innovative plan was thought to address the problem of conceptualization of group theory by undergraduate students. The design-based research was used to design, test, update, and finalize the innovation. The action process, object, and schema (APOS) theory was used to design innovation by following the sequence of inquiry-oriented instruction, a type of inquiry-based learning. The research utilized forms and formats of design-based research. Before starting definition of groups, different properties of a set and an operation are explored. Students create different examples of groups themselves in the given condition and extend the created groups by adding minimal elements. Students test a list of sets and operations to conceptualize group. As a result, students can use their own symbols of group axioms. The finalized plan is a ready to use resource to faculty members in helping students to conceptualize the group theory at undergraduate level. Based on the result of the quiz, classroom observation, interview, it is reflected that the concept by construction strategy is best for conceptual understanding, mathematical thinking, and creativity. The developed innovation plan is a reference resource for teachers who follow inquiry-based learning in their classroom. This plan has served as a best tool for building concept of group theory because students got opportunity to act as mathematicians.