MISCONCEPTION AND DEVELOPMENT OF CONCEPTUAL REASONING OF PROSPECTIVE TEACHER STUDENTS TOWARDS THE NON-COMMUTATIVE PROPERTY OF COMPOSITION FUNCTIONS THROUGH PEER TEACHING-BASED DISCOVERY LEARNING

Abstract

Conceptual understanding of function composition, particularly its non commutative property, is a challenge for prospective mathematics teachers. This difficulty is often indicated by the emergence of miscoceptions stemming from inappropriate generalizations of arithmetic operations of intuitive judgments of results without a clear relational basis. This study aims to describe the initial misconceptions and the development of prospective teachers' conceptual reasoning regarding the non commutative property of function composition through the implementation of contextualized discovery learning within a peer teaching framework. The study employed a qualitative approach with a descriptive-exploratory design. The research participants were graduate students enrolled in a masters program in mathematics education who were directly involved in peer teaching activities. Data were collected through video recordings of instructional practices, student worksheets, prediction sticky notes, and field notes. Data analysis was conducted using qualitative procedures involving data reduction, thematic coding, and interpretative analysis. The findings indicate that, at the initial stage, students tended to exhibit misconceptions based on cross concept analogies and intuitive reasoning that had not yet developed into conceptual understanding. Through presentation and discussion activities in the discovery learning process, students demonstrated a shift in reasoning from a focus on final results toward relational understanding related to the order of function mappings. These findings suggest that discovery learning supported by peer teaching facilitates cognitive conflict and meaning negotiation, thus contributing to the development of prospective mathematics teachers conceptual understanding of the non commutative property of function composition.