# Subject-matter Knowledge for Teaching Mathematics

Prof. Ruhama Even

I have been studying mathematics teacher knowledge, beliefs and dispositions, and their role in teaching, for more than two decades. I started my research by constructing an analytic framework of subject matter knowledge for teaching a specific topic in mathematics and applied the framework to central concepts and topics in the secondary school mathematics curriculum. The theoretical framework both guided and was refined by, in an iterative dialectic process, my empirical research on different aspects of teacher subject matter knowledge and the nature of the relationships between teacher subject-matter knowledge and practice.

My findings during this period indicated that we cannot assume that advanced university mathematical studies are sufficient mathematical preparation for secondary school teachers, but rather that teacher education and professional development should explicitly refer to topics included in the high-school curriculum. Although teachers have already studied these topics during their own high-school years, their subject-matter knowledge is, in many cases, not sufficiently comprehensive and articulated to enable them to teach for understanding.

A recent study continues the above line of research and examines what might be the relevance of advanced mathematics courses taught by research mathematicians, for developing expertise in secondary school mathematics instruction. It addresses this question by investigating the views on this issue of a group of secondary school mathematics teachers who study in a special master’s program where such courses comprised a sizeable share (the Rothschild-Weizmann Program). Initial findings revealed three features of advanced mathematics courses that are viewed as relevant to the work of teachers: (1) as a resource for teaching secondary school mathematics, (2) for improving understanding about what mathematics is, and (3) for reminding teachers what learning mathematics feels like.

Another study extends this line of research in a different direction. It examines approaches of math educators (school teachers, teacher educators, curriculum developers, researchers in math education, and mathematicians) to deductive reasoning – which is central to work in mathematics. The study also investigates views regarding the commonly stated goal of using mathematics learning to develop deductive reasoning that is usable outside of mathematical contexts. The findings of this study show that different meanings are ascribed to the above stated goal. Three distinct views were identified; each was interrelated with a distinctive approach to deductive reasoning and its nature in and outside mathematics. A follow-up study revealed connections between these views and classroom teaching in regard to shaping students opportunities to engage in argumentative activity.