Knowledge of curriculum embedded mathematics: exploring a critical domain of teaching

Abstract

This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term knowledge of curriculum embedded mathematics (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and representations in mathematics curriculum materials. The KCEM framework is situated within existing research on content-specific teacher knowledge. Through analysis of elementary mathematics teacher’s guides from the USA, we identified elements of curriculum resources teachers interact with when using them to plan instruction. These findings were complemented by interviews of teachers using curriculum guides to plan lessons, uncovering how they interacted with different elements of their guides. From this analysis, we propose four overlapping dimensions of KCEM: foundational mathematical ideas, representations and connections among these ideas, problem complexity, and mathematical learning pathways. Using an excerpt from one elementary curriculum guide and one of the teacher interviews on using this guide to plan a lesson, we illustrate how these dimensions might be activated as teachers read and use their guides.