Cognitively Guided Instruction

Cognitively Guided Instruction, or CGI, is a professional development program built on an integrated program of research into the development of students' mathematical thinking, the instruction that influences that development, teachers' own knowledge and beliefs, and how those beliefs and practices are in turn shaped by teachers' understanding of their students' mathematical thinking. CGI is an approach to teaching mathematics rather than a fixed curriculum program, centered on listening to children's mathematical thinking and using it as the basis for instruction; research-based frameworks describing children's thinking in addition and subtraction, multiplication and division, base-ten concepts, multidigit operations, algebra, geometry and fractions guide teachers in that listening. Its research base shows that children can solve problems, including some involving multiplication, division and multiple steps, without direct instruction, by drawing on informal knowledge of everyday situations through a strategy called direct modeling, in which a child constructs a solution by modeling the action or structure of a story problem. CGI holds that there is no single way to implement the approach, and that teachers' own professional judgment is central to deciding how to use what they learn about their students' thinking.