Investigating Mathematics Teachers' Knowledge for Teaching and Their Learning Trajectories

This study investigated three secondary mathematics teachers’ knowledge for teaching and their learning trajectories from their own schooling through their establishment as experienced teachers in their education system. Their current knowledge includes four categories: mathematics content, curriculum, students’ conceptions and misconceptions, and mathematics pedagogy. Three case studies were conducted through semi-structured research instruments and interviews. Other data such as prior and current official curricula and other materials related to teachers’ professional development were also collected. The findings also indicate that the process of teacher professional development is complex. Teachers learned from various formal and informal sources. The sources and motivation for the teachers’ professional development were: the school mathematics curriculum, their students, the content they taught, the school environment for professional development, their interests, and beliefs and value toward mathematics teaching and learning. The content of their teaching, and their students’ questions and challenges, helped them to reflect about their classroom practices and assisted the teachers in following various approaches to upgrade their knowledge. The findings indicate that there are five categories of professional knowledge for teachers: subject matter knowledge, curriculum knowledge, knowledge of students, mathematics pedagogy, and knowledge of professional development. Each has its subcategories. The categories and subcategories have their properties and some levels of bonds among others. Teachers’ knowledge for teaching is not static but is dynamic. The knowledge is shaped with the changes of school curriculum and teachers’ choice of approaches and learning directions for their professional development. Teacher’s subject matter knowledge is aligned with the curriculum, and the students’ prior learning. Mathematics pedagogical content knowledge is developed over many years of teaching. It depends on the approaches and directions of teachers’ professional development, what they teach and who they teach. Mathematics pedagogical content knowledge of secondary school mathematics teachers should include the alignment of elementary, secondary and post-secondary mathematics fundamental ideas, strategies, mathematics thinking and analysis structures of content. Teacher programs also need to provide approaches and directions of professional development. Inservice teacher programs need to entail teachers’ needs for subject matter and pedagogical content knowledge development in their educational system.Ph.D