Supportive and problematic conceptions in making sense of multiplication: A case study

This study aims to exemplify a framework based on an empirical study and the empirical study is to explore how a mathematics expert teacher makes sense of multiplication. The study was conducted through interviewing a secondary school mathematics expert teacher with over 30 years of mathematics teaching experience. The theoretical framework used in this paper is proposed by Chin and Tall (2012) and further developed by Chin (2013) and Chin (2014). The collected data are anaylsed qualitatively using this framework in order to find out what are the supportive and problematic conceptions involved in making sense of multiplication and consequently investigate how do these conceptions affect the sense-making of multiplication across different contexts. The findings suggested that when changes of meaning occur, supportive or problematic conceptions might arise and these either support or inhibit learners from building a coherent understanding. This study also showed that supportive conceptions might contain problematic aspects and problematic conceptions might contain supportive aspects. The respondent strived to build a coherent understanding by removing the problematic aspect, however when the problematic aspect cannot be removed then he had no choice but to accept the new meaning of multiplication. It is the teachers' responsibility to guide students in realising their existing knowledge which may not be appropriate in a new context. Thus, this study offers a foundation for teachers to sense where, when and how the changes of meaning of multiplication take place which in turn can help them to facilitate students effectively in making sense of multiplication.