CGI: Cognitively Guided Instruction for math
Andrew Woodley, the new Director of Curriculum and Instructional Technology and for PUSD, has been speaking about the value of Cognitively Guided Instruction. Often referred to as CGI, this method is used to enhance math instruction in elementary school. It's a philosophy of math that says students come to school with an innate ability to solve math problems even if they don't know the standard algorithms.
When using CGI students are solving problems in a way that makes sense to them. The student's job is to talk and to try out different solutions. The role of the teacher changes to being a listener who asks questions.
CGI helps students identify the parts of math that are easy for them and those that are more difficult. It also provides a way to deal with the common errors they make when learning. Students are less nervous about wrong answers and more willing to risk because this program emphasizes what students can do, rather than on what they can't. Teachers using the CGI approach focus on what students know and help them build on their current knowledge to create future understanding. The goal of the program is to improve student math skills by increasing teachers' knowledge of their thinking. Workshops help change teachers' perceptions about how their students learn, and this changes their teaching practices.
CGI originated in primary classes about thirty years ago, but moved into the upper grades to help teachers integrate algebra into math instruction. The program is based on the idea that elementary students are capable of learning how to talk through problem-solving issues which gives them a better understanding of arithmetic and helps them learn algebra.
Dan Finkel's Ted Talk, Five Principles of Extraordinary Math Teaching, declared that math should not be about passive rule following. First, he thinks good math teachers start with a question not the answers from the homework or the steps of how to do long division. Like CGI, he feels that math is more fun when engaging students in an inquiry problem.
Next, thinking happens when students have time to struggle so he advises giving them time to problem solve because that is what teaches perseverance. Struggling with a genuine question deepens student's curiosity as well as their powers of observation.
Another feature of a quality math teacher is not to be the answer key. To increase students' inquisitiveness teachers can answer a question with another question. It's okay to tell children that you don't know and then find out answers together. Not knowing is not failure. Instead it's the first step to understanding.
When teachers refuse to be the answer key, it creates space in the classroom for debate to happen. When students think out loud, others can doubt, affirm and deny their thinking. Teachers can say yes to student's ideas rather than immediately correcting wrong answers. It doesn't mean they're right but they're more likely to continue participating in the discussion.
Finkel thinks it's more powerful for students to be shown they're wrong by their peers then to be told they're wrong by their teacher. To have an idea dismissed out of hand is disempowering. To have it accepted, studied and disproven is a mark of respect.
Cognitively Guided Instruction (CGI) is a student-centered approach to teaching math. Students start with what they know and are encouraged to be intuitive about problem solving. CGI is not a math program or curriculum, but rather a way of listening to students, asking questions, and engaging their minds to uncover their own mathematical understanding.
Children are able to solve problems without direct instruction because they figure out the steps to solving story problems using models, drawings and manipulatives. When teachers foster this innate ability by learning to listen to student's thinking, they approach their instruction differently.