COGNITIVELY GUIDED INSTRUCTION - A KNOWLEDGE-BASE FOR REFORM IN PRIMARY MATHEMATICS INSTRUCTION

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 descri be a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or spontaneous kn owledge about students' mathematical thinking. Our major thesis is tha t children enter school with a great deal of informal or intuitive kno wledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. The develo pment of abstract symbolic procedures is characterized as progressive abstractions of students' attempts to model action and relations depic ted in problems. Although we focus on one facet of teachers' pedagogic al content knowledge, we argue that understanding students' thinking p rovides a basis for teachers to reconceptualize their own knowledge mo re broadly.