Developing 11-13 year old students’ conceptual understanding of rational numbers : a case study investigating effective teacher pedagogical actions in a mathematics classroom : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education in Mathematics Education at Massey University, Albany, New Zealand
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2024
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Massey University
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Rational numbers, encompassing fractions, percentages, and decimals, are challenging for many students to understand. Research often focuses on the teaching and learning of these topics in isolation, rather than as part of the broader concept of rational numbers. However, there is limited research on the teaching practices that effectively support students’ overall understanding of rational numbers. This study explores the teacher actions that help students develop a conceptual understanding of rational numbers and examines how students demonstrate their growing understanding. A case study and qualitative methods were chosen for this research. The study involved one teacher and a class of 24 Year 7 and 8 students from an urban school in New Zealand. The teacher facilitated eight lessons focused on rational numbers, which included collaborative mathematical discussions. A variety of data were collected and analysed, including interviews, video recorded classroom observations, and examples of student work. The findings revealed that when teachers design lessons around real-world mathematical tasks, promote collaborative discourse, and encourage the use of mathematical practices, students develop a deeper understanding of rational numbers. Additionally, using visual representations and explicitly connecting different forms of rational number representations helped enhance students’ mathematical understanding. This study contributes to the literature on how primary school teachers can effectively support students in developing a strong understanding of rational number concepts. It highlights that teacher content knowledge, combined with purposeful teaching strategies, can provide greater opportunities for students to develop a deeper understanding of rational numbers.