Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction

TLDR

Children bring informal mathematical knowledge to school, which can underpin formal curriculum development and help teachers reconceptualize their own knowledge. The article proposes that a research‑based model of children’s thinking can unify teachers’ pedagogical content knowledge and subject‑matter expertise, enabling them to interpret and transform their informal knowledge of students’ mathematics. The authors present a model that interprets children’s thinking as progressive abstractions of action and relational modeling, allowing teachers to transform informal knowledge into formal symbolic procedures.

Abstract

In this article we propose that an understanding of students' thinking can provide coherence to teachers' pedagogical content knowledge and their knowledge of subject matter, curriculum, and pedagogy. We describe a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or spontaneous knowledge about students' mathematical thinking. Our major thesis is that children enter school with a great deal of informal or intuitive knowledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. The development of abstract symbolic procedures is characterized as progressive abstractions of students' attempts to model action and relations depicted in problems. Although we focus on one facet of teachers' pedagogical content knowledge, we argue that understanding students' thinking provides a basis for teachers to reconceptualize their own knowledge more broadly.