Exploring how understandings from abstract algebra can influence the teaching of structure in early algebra

Nicholas Wasserman

Abstract


Empirical work connecting content knowledge to teaching practice has become increasingly important in discussions around a professional knowledge base for teaching. This paper aims to continue that work, reporting a single exploratory case study of one elementary mathematics teacher. The purpose of the study was to explore how introducing teachers to advanced mathematics, particularly ideas in abstract algebra, might inform and influence their instructional practices for teaching early algebra topics about arithmetic structure. The findings indicate that instructional practices did change, especially in ways that more explicitly incorporated structure in early algebra with students, and fostered increased reasoning and sense-making about these ideas. Implications for mathematics teacher education are discussed.

Keywords


early algebra; mathematical knowledge for teaching; abstract algebra

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