Cognitively Guided Instruction (CGI) is central to our teaching of math, and we value children’s thinking as a basis for our decision-making about the curriculum.
Using CGI, teachers start with what children already know about math and build on it to move them toward deeper levels of understanding. Children solve problems in ways that make sense to them using real-world contexts. During problem solving, multiple strategies are shared, honored and highlighted. Children are expected to articulate their thinking and collaborate with others. Students are encouraged and supported to persevere through challenging problems, and mistakes are viewed as opportunities for learning. We focus on conceptual understanding as a foundation, and gradually progress to more abstract representations of math concepts.
This approach is different from the traditional method of teaching the symbolic computation first, and then expecting students to apply the concepts to problem solving situations. CGI research consistently demonstrates that teachers who know the details of their students’ mathematical thinking have higher achieving students.
In 2016 we completed a three-year professional development with educators from the El Segundo Unified School District. We asked them to comment on how the experience affected teaching and learning in their classrooms. Here is what they said:
Three years ago I wanted to teach every student exactly how to solve a problem
Now I enjoy watching the students take ownership and solve it their own way and teach each other.
Three years ago I used a lot more math worksheets and did more teacher directed lessons.
Now I use more math journals where students can show their work through drawings, numbers, words, etc. & I take more of a coaching role, while lessons are student centered.
Three years ago I showed students how to attack a math problem.
Now I listen to how students produced their own game plan.
Three years ago students were very used to the routine of direct modeling/lesson, worksheet(s), activity. Students had very few problem solving strategies and frustration was high if they didn’t understand or get it correct right away.
Now they persevere when faced with a challenging problem and are proud when they work through it. They see math in a new light as they understand multiple perspectives/strategies of their peers. Great teamwork!
Three years ago students either got it or didn’t, and I struggled to help the “low” students understand what I was teaching.
Now all feel successful and that they can access and achieve any and all math that is presented to them. There is a much deeper and richer understanding of what they are doing.
Three years ago students were looking only to me for the answer.
Now they seem excited about problem-solving, sharing strategies, and using different ways to solve problems. They love hearing their ideas validated by other students.