An approach to facilitate coherent concept image formation via guided reinvention

Abstract

This chapter presents an approach in mathematical teaching and learning that centers on facilitating student's coherent concept image formation via guided reinvention. The key to forming a coherent concept image lies in the proper understanding of a particular concept. To do this effectively, instead of passively receiving a mathematical notion from a teacher, students take an active role to re-invent the mathematical notion for themselves. There are three general stages in this approach: (1) motivating; (2) investigative and exploring; and (3) reinventing. Three implementations of such an approach are presented in this chapter: (I) areas of closed figures and their formulas; (II) fractions addition and subtraction with different denominators; and (III) the rigorous definition of the limit of a sequence. Details and philosophy of the implementations will be summarized and discussed.