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This qualitative case study investigated how lesson study influenced teachers’ pedagogical strategies and content knowledge by leveraging the interplay between conceptual understanding and procedural fluency, with conceptual knowledge forming the foundation for procedural fluency in the planning and implementation of fraction-based mathematics tasks. The study aimed to address two research questions: (1) How does the engagement of teachers in the creation and analysis of fraction-based mathematics tasks in lesson study influence their instructional decision-making processes? and (2) How do teachers construct pedagogical strategies that integrate procedural and conceptual knowledge through lesson study? The sample size consisted of seven elementary school teachers who worked collaboratively to modify fraction tasks. Triangulated data from observations and interviews revealed two key findings. First, the study’s findings highlight the transformative power of collaborative professional growth among teachers and their subsequent shift towards engaging in more conceptual, student-centered mathematics instruction, addressing the first research question. Second, the findings suggest that lesson study can be a valuable tool for enhancing teachers’ pedagogical content knowledge and improving fraction instruction when utilized consistently, thus answering the second research question. Implications for future teacher education are discussed, emphasizing the importance of sustained, collaborative learning opportunities to support conceptual understanding in mathematics education.

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The study’s purpose was to explore the components of pedagogical content knowledge (PCK) for teaching quadratic function in Grade 10 mathematics classrooms in Mogalakwena district, Limpopo. The study was mainly guided by Shulman’s PCK and it was categorised as content knowledge, knowledge of the curriculum, knowledge of learners and knowledge of teaching strategies. The researcher employed a qualitative case study research design to explore the teaching of three purposefully selected Grade 10 mathematics teachers regarding their knowledge of quadratic function, strategies employed to teach quadratic function and knowledge of Grade 10 mathematics learners in quadratic function. In this study the researcher argued that PCK strands are interwoven, and in order to teach mathematical concepts, such as quadratic function, effectively teachers should employ components of PCK to complement one another. Data were gathered by lesson observation and interviews. Findings revealed that concepts of quadratic function are inefficiently addressed in Grade 10 due to teachers’ lack or inadequacy in some aspects of PCK. Therefore, there is need to develop mathematics teachers’ PCK in the Mogalakwena district to enhance their teaching of Grade 10 quadratic function. / Mathematics Education / M. Ed. (Mathematics Education)