An Introduction to Teaching Cognitively Guided Instruction Math to Your Students

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What is CGI Math?

Cognitively Guided Instruction (also referred to as CGI math) is an approach to teaching mathematics that uses a student’s own mathematical thinking as the basis for instruction. The method is the result of research conducted by Elizabeth Fennema and Thomas P. Carpenter from the University of Wisconsin - Madison in the late 80’s and early 90’s.

Its premise is based on the underlying assumption that students already posses an informal knowledge of mathematics. The teacher’s role, is to build from this prior knowledge so that students can eventually make connections between situational experiences and the abstract symbols typically found to represent them in mathematical equations (+, -, x and so forth.) This approach is quite different from the traditional method of teaching the symbolic computation first, and then expecting students to apply the concepts to problem solving situations.

For CGI math to be successful, teachers must have a thorough understanding of the grade-level curriculum and the distinctions between different problem types within that curriculum. They must also have a working knowledge of the processes that are typically used to solve these problems, and the various stages that students go through in developing their own concrete knowledge.

Story Problems

Children in a CGI math classroom spend most of their time solving story problems. A typical problem might look something like this:

Megan has 5 bags of cookies. There are 7 cookies in each bag. How many cookies are there altogether?

Students are encouraged to use and develop a variety of self-selected strategies and models to solve the problems. They are also held accountable for explaining exactly how they solved the problem. The teacher then uses this information to guide the student learning and identify any breakdown in understanding that might occur.

Engaging in this type of ongoing student assessment provides teachers with the opportunity to:

  • identify what base knowledge a child has.

  • understand different strategies employed for solving problems.

  • understand what those strategies tell us about the child’s thinking.

  • understand and demonstrate the ways that this thinking evolves.

Moving Ahead

In the next article about Cognitively Guided Instruction, we will take a closer look at different types of CGI math problems, and how they can be classified.


  • Information offered in this article is based on the author’s extensive experience as a classroom teacher.

This post is part of the series: CGI Math In Your Classroom

Learn more about the Cognitively Guided Instruction approach and how it can be used in your classroom to effectively further student learning. This series will explore the principles behind CGI math, identify related concepts, and offer a multitude of problems you can use in your own classroom.

  1. CGI - An Approach to Teaching Mathematics
  2. Teaching Different Types of Math Story Problems
  3. Using Cognitively Guided Instruction for Teaching and Assessment
  4. Math Skills Assessment for Division Problems Using Cognitively Guided Instruction
  5. Elementary Math - Assessment of Strategies for Solving Math Problems