Cognitively Guided Instruction (CGI) is a teacher professional learning program that supports teachers to understand research knowledge of children’s mathematical thinking and how to use students’ mathematical thinking to guide instruction. CGI is a student-centered approach to teaching math with understanding. Teachers start with what their students already know and build on their natural understanding of number and their intuitive approaches to problem solving. CGI is not a curriculum or a teaching program but rather a way of listening to students, asking smart questions, and engaging with their thinking. CGI teachers are constantly working to uncover and expand every students’ mathematical understanding.
Based on the work of Thomas Carpenter and Elizabeth Fennema, this over 30-year research base continues to explore the knowledge of how children’s number sense developments over time. The original research explored grades K-3’s understanding of the single digit operations in addition, subtraction, multiplication and division. That expanded to multidigit base ten development and invented strategies in the four operations (Carpenter et al., 2015), algebraic and relational thinking (Carpenter et al., 2003), and K-5 development of fraction and decimal operations (Empson & Levi, 2011). The most recent publication focuses on early childhood (Carpenter et al., 2017). The research continues across the country through the work of researchers at locations such as UCLA, University of Missouri, UNC Greensboro, UC Davis, Florida State University, and others.