EXPLORING EXPLICIT MULTIPLE REPRESENTATIONS IN THE TEACHING OF FRACTIONS IN JUNIOR SECONDARY CLASSROOMS: A CASE OF THREE MATHEMATICS TEACHERS
B. Banjo1, K. Luneta2
Introduction:
The use of multiple representations (MR) in mathematics instruction has been widely recognised as a key strategy for improving students' understanding of complex concepts, particularly fractions. However, research highlights a lack of explicit integration and systematic approaches to employing MR in teaching practices. This gap is especially significant in resource-constrained contexts such as South Africa, where curriculum guidelines often focus on procedural techniques rather than conceptual understanding. This study investigates how three junior secondary mathematics teachers in the Tshwane region of South Africa employ and integrate MR to teach fraction concepts. This study aims to explore MR employed in teaching fractions in junior secondary mathematics classrooms, and how these representations are integrated to provide learning opportunities for students.
The research questions are:
I. What multiple representations did junior secondary mathematics teachers use to teach fraction concepts to their students?
II. How did the explicitness of multiple representations vary across the selected teachers?
Methods:
A qualitative case study methodology was adopted, involving classroom observations of three teachers teaching Grade 8 mathematics. Data were collected through audio recordings, field notes, and visual documentation of teaching materials. A thematic analysis was conducted using a deductive coding approach based on Post and Prediger's (2024) framework, which categorizes the explicitness of MR into juxtaposition, implicit transition, conscious translation, and explicit connection.
Results:
The findings reveal significant variability in the teachers' integration and explicitness of MR. While all teachers predominantly relied on symbolic and technical representations, their use of visual, contextual, and meaning-related representations varied. Mala demonstrated the highest level of explicit integration, effectively linking symbolic, visual, and contextual representations with clear explanations. In contrast, Bash and Kamo exhibited more implicit transitions and limited visual connections, focusing on procedural fluency.
Conclusion and Implications:
The study suggests the need for targeted professional development to enhance teachers’ ability to integrate MR explicitly. Experienced teachers like Bash could benefit from workshops on visual and contextual representations, while novice teachers like Kamo require mentoring to build confidence in using diverse instructional strategies. Revising curriculum guidelines to include explicit directives on MR integration and fostering reflective practices could bridge the gap between procedural and conceptual teaching, thereby improving student mathematical knowledge.
Keywords: Multiple representations, fractions, mathematics teaching, explicit integration, conceptual understanding.