The Complexities of Mathematical Knowledge and Beliefs within Initial Teacher Education: An Analysis of Three Cases

This study arose from a desire to investigate initial teacher education for primary school mathematics teachers in Hong Kong. A conceptual framework for analyzing pre-service teachers' mathematical knowledge and beliefs informed this qualitative investigation. The purpose of the study was to scrutinize both the cognitive and affective domains in mathematics teaching of pre-service primary teachers within the analytical framework. This paper seeks to capture three cases of Hong Kong pre-service primary teachers holding different views about mathematics teaching and learning as revealed by a beliefs survey. Their mathematical knowledge was examined along with a questionnaire, individual interviews, and an analysis of the lesson plans they provided. Through triangulation, it was found that these pre-service teachers' beliefs about mathematics teaching and learning correspond to their pedagogical content knowledge to some extent. The results of lesson plan analysis were mostly consistent with those in the questionnaire and interviews although some of the interview data were inconsistent with the questionnaire results. Such inconsistency seemed to suggest that pre-service teachers' reform-oriented mathematical beliefs were impacted by some traditional values such as Confucianism. Implications are discussed regarding the relationship between knowledge and beliefs in mathematics education as well as the theory of teacher competencies.