Fractions speak louder than words: Investigating preservice primary teachers’ knowledge and understanding for teaching fractions with representations

Mathematics presents specific challenges for primary preservice teachers and fractions is among the most problematic of topics. This thesis investigates preservice primary teachers’ understanding and use of fractions and fraction representations. Preservice teachers have particular difficulty explaining the rationale behind fraction operations, often only demonstrating superficial knowledge of symbolic procedures. This level of knowledge is insufficient for teaching and, thus, initial teacher education presents a crucial opportunity to deepen teachers’ knowledge before they begin their teaching careers. The study addresses the crucial need for further research into the initial teacher education of preservice teachers at a time where there is a national agenda for improving education in Australia. However, despite the potential to redress preservice teachers’ knowledge of fractions, there is a dearth of studies elucidating how fraction knowledge develops over a program in initial teacher education, particularly in an Australian context. To address this gap, the current study aimed to investigate the development of preservice primary teachers’ knowledge about teaching fractions during a Graduate Diploma of Education (GradDipEd) program with a focus on their understanding and use of fraction representations. To focus the study, the following research questions were posed: RQ1. How do preservice teachers’ understandings of fractions and fraction representations develop over a teacher education program? RQ2. How and why do preservice teachers use fraction representations for learning and teaching tasks over the course of a teacher education program

Building conceptual knowledge of fraction operations among pre-service teachers: Effect of a representation-based teaching approach within a teacher education program

A deep understanding of fraction concepts and operations is necessary if pre-service teachers (PSTs) are to present the concepts in multiple forms to learners. Such an understanding needs to be grounded in rich conceptual knowledge. In the present study, we explore the development of this understanding by supporting a cohort of 103 PSTs, who had previously demonstrated poor conceptual understanding of fraction concepts and operations, with a Representational Reasoning in Teaching and Learning (RRTL) approach aimed at strengthening their conceptual knowledge. A comparison of pre- and post-test results indicated that participants showed a significant improvement in shifting the balance of their fraction knowledge to the conceptual end of the procedural-conceptual spectrum. Insights into how this approach assisted in developing PSTs\u27 conceptual understanding were explored through interviews with four participants and an analysis of their pre- and post-test responses. We suggest that the use of teaching strategies such as RRTL are necessary in order to assist PSTs develop strong conceptual knowledge of fractions

Developments in Pre-service Teachers\u27 Mathematics for Teaching of Fractions

The mathematics required for teaching is increasingly becoming an important issue for research (Ball, Thames & Phelps, 2008). This study examines the development and quality of the mathematical content knowledge of a cohort of pre-service primary teachers. We commenced the study of the impact of a Model-Based Teaching and Learning (MBTL) approach on the development of pre-service teachers\u27 conceptual knowledge in the domain of fractions (Forrester & Chinnappan, 2011). In this present study we found further evidence for the robustness of MBTL as an effective instructional strategy in promoting conceptual knowledge