Mathematical beliefs and knowledge : a case study of a teacher’s communication using representations

Ash, Andy and Boyd, Pete and Jackson, Alison (2023) Mathematical beliefs and knowledge : a case study of a teacher’s communication using representations. PhD thesis, Lancaster University.

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Abstract

Within education, the subject domain of mathematics is recontextualised, through a combination of teachers’ practice and curriculum development, to become what I term ‘school maths’. Currently, in English schools, there is a drive to reform school maths through introducing an approach that is known as ‘teaching for mastery’, which includes a strong emphasis on teachers using multiple representations. Despite this, it can be seen in the literature that effective use of representations in mathematics education is complex and requires a significant amount of teacher expertise. It is likely that teacher beliefs and knowledge will influence the way in which they use representations, however this is an area in need of further research. This study aims to contribute to better understanding the recontexualisation process by examining the relationship between teacher beliefs and knowledge, and their use of representations to teach fractions. Utilising a case study approach, a single teacher, Gillian, is the focus of this research. The aim being not to make generalised claims to knowledge, but instead contribute to theory development by adopting a critical realist methodology and using an innovative approach to analysis in applying Legitimation Code Theory (LCT). Data was collected from four interviews (two of which utilised a stimulated recall approach), two observed and video recorded lessons, and a textbook analysis. Findings show that studying beliefs and knowledge together, as a belief and knowledge system, is an effective way of understanding how teachers influence the recontextualisation process. Specifically, this study showed that believing in the importance of mathematical knowledge acquisition alongside the development of social learning, including learner dispositions, led to an effective use of representations, where dialogue was carefully used to negotiate the meaning of fractions. It was also found that LCT presents a useful way of explaining the organising principles of teacher beliefs, knowledge and practices and is an avenue for further research. Finally, the study found that the specific textbook used can play a key role in the recontextualization process.