Carpenter, Thomas, P., Fennema, Elizabeth and Franke, Megan L.
Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction
Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction, The Elementary School Journal, 97 (1), 3-20.
Teachers need to understand students’ thinking to provide coherence to their (the teachers’) pedagogical content knowledge and their knowledge of subject matter, curriculum and pedagogy. Children do, according to the writers, have a great deal of informal or intuitive knowledge of mathematics when they enter school. This can serve as the basis for developing much of the formal mathematics for the primary school curriculum.
The writers describe how the knowledge base in a teacher development programme called Cognitively Guided Instruction (CGI), which focuses on children’s understanding of specific mathematical concepts, can provide a basis for teachers to develop their knowledge more broadly. Addition and subtraction, multiplication and division and multi-digit number concepts and procedures are examined to demonstrate how children think, learn and solve problems. CGI analysis focuses on students’ thinking and forces teachers to confront their own understanding of numerical properties from a new perspective. This leads to the teacher understanding how students develop problem-solving strategies and thus to developing their own teaching strategies.