The study of teachers’ professional knowledge base for teaching has grown substantially since Shulman (1986) put forward an initial categorization of types of knowledge of a teacher of any subject, namely Subject Matter Knowledge and Pedagogical Content Knowledge. Building on and refining Shulman's work, Ball, Thames and Phelps (2008) advanced a mathematics specific framework which lays the foundation for a practice-based theory for Mathematical Knowledge for Teaching (MKT). Within this model, Shulman’s category of Subject Matter Knowledge is subdivided into Common Content Knowledge (CCK), Specialized Content Knowledge (SCK), and Horizon Content Knowledge (HCK), while more recently researchers (e.g., Zaskis & Leikin 2010) proposed positioning advanced mathematical knowledge (knowledge of maths that goes beyond that of the school curriculum) as an important aspect of MKT. According to Ball et. Al (2008), Specialised Content Knowledge (SCK) encompasses knowledge of mathematics needed by teachers, but not necessarily used by others, such as a knowledge of a particular mathematical model or representation useful for teaching a certain concept. SCK could be thus be conceptualized as a bridge, which starts from a teacher’s understanding of the mathematics content and which enables the teacher to accurately represent mathematical ideas, provide mathematical explanations of rules and procedures, examine and understand a variety of solutions, and aims to reach to students and support their learning. If SCK is not built on a conceptually sound understanding of the underlying mathematics, teachers will fall short of providing their students with those learning experiences that promote conceptual understanding. Even when teachers have a deep understanding of a particular maths content, their SCK only has pedagogical potential, but is not necessarily powerful pedagogically. Prospective teachers generally begin to learn and acquire pedagogically powerful SCK in teacher education programmes, albeit limited to a few maths topics. This paper considers how teacher education could empower teachers develop (beyond the completion of their training) a personal understanding of maths that is pedagogically powerful. We argue that knowledge of more advanced mathematics could serve as pedagogically powerful understanding of the school maths that teachers teach. The pedagogical power might consist of a teacher’s awareness of how school maths topics are instances of more advanced maths ideas; such an awareness would empower teachers in supporting students’ learning in ways that allow for creating a solid foundation for development of more advanced ideas of the discipline of mathematics.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263-281.