Cognitively Guided Instruction (CGI) is an approach to teaching mathematics that fosters the development of students’ mathematical thinking.

It helps teachers guide students’ understanding of mathematical concepts as they learn about their students’ thinking and the ways in which they solve problems. At the core of this approach is the practice of listening to children’s mathematical thinking and using it as a basis for instruction. Research based frameworks of children’s thinking in the domains of addition and subtraction, multiplication and division, base-ten concepts, multi-digit operations, algebra, geometry and fractions provide guidance to teachers as they listen and work to understand the thinking of their students.

Teachers use a variety of practices to extend children’s mathematical thinking. It’s a tenet of CGI that there is no one way to implement the approach and that teachers’ professional judgment is central to making decisions about how to use information about children’s thinking. Children are able to solve problems without direct instruction by drawing upon informal knowledge of everyday situations.

Teachers and students pose problems that are relevant and that people encounter in their everyday lives. Students solve the problems alone and collaboratively; and the teachers and students facilitate a conversation around selected solutions as a means to understand more deeply the mathematical concepts embedded within the problem.

Novel and diverse approaches deepen mathematical content knowledge of the students and teachers and lead to efficiency in algorithmic thInking and automaticity with facts.

In addition to problem solving aligned to the Common Core State Standards, the teachers also engage the students in a series of warm-ups that foster reasoning, number sense, and fluency with facts. Warm-ups may serve to deepen understanding or they could be used to introduce students to patterns and structures that may assist them in solving the problem for the day.

The beauty of CGI is in its relevance to children’s everyday lives and its ability to strengthen the understanding not only of the students but also of the