Using Children’s Mathematical Knowledge in Instruction

This article describes how knowledge of children’s thinking in mathematics, derived by using a cognitive science research paradigm, was used by a first-grade teacher to make instructional decisions. Children in the classroom learned mathematics to a level that exceeds what is recommended by the NCTM Standards ( NCTM, 1989 ). The study is situated in the Cognitively Guided Instruction (CGI) project chain of inquiry. We describe the teacher’s knowledge, beliefs, and method for using research-based knowledge of children’s thinking in addition and subtraction in her classroom. We describe her mathematics curriculum, the expectations she had of children, and the way her classroom was structured to enable her to continually assess children’s thinking and knowledge. The article includes statements of the teacher that indicate the importance of the research-based knowledge to her as she taught. The article ends with some speculation about how knowledge of children’s thinking can influence curriculum reform.