A proposal for the study of mathematics teachers’ beliefs through the analysis of their practices

In recent years, research on mathematics teachers’ beliefs has increasingly shifted its focus toward understanding their connection with instructional practices. This article introduces a model designed to explore mathematics teachers’ beliefs through a comprehensive analysis of their practices. The contributions of models that study the relationship between beliefs and practices of teachers, such as those from Schoenfeld (Journal of Mathematical Behavior, 18(3), 243–261, 2000) and Cobb and Yackel (Educational Psychologist, 31(3), 175–190, 1996), were reviewed and considered. Additionally, it includes methodological considerations from Leatham and Speer for studying beliefs. These approaches are integrated by utilizing the notions of practice, types of didactic-mathematical practices and norms, derived from the onto-semiotic approach, as the central organizing axis. Furthermore, we demonstrate the application of these stages of analysis for exploring teachers’ beliefs by analyzing the beliefs of a prospective mathematics teacher. The findings enable us to identify the beliefs held by this prospective teacher regarding the use of introductory activities characterized by a high motivational level but a low mathematical level. Additionally, these results provide insights into potential avenues for developing training programs aimed at instigating a shift in these beliefs, thereby fostering an enhancement in teaching practices. These outcomes show the feasibility of the analytical model proposed in this article.