Students Collaborating

Student collaboration supports the Standards for Mathematical Practice as students should be able to "understand the approaches of others to solving complex problems and identify correspondences between different approaches" (MP 1) and "justify their conclusions, communicate them to others, and respond to the arguments of others" (MP 3).

Teacher Facilitation

Teachers facilitate student learning by asking questions and selecting particular students to present their mathematical responses to help the class make new connections.

Teachers as Learners

Teachers in Downey are continuously striving to learn more about students' thinking and the research behind it. Over 80 teachers and administrators attended the 2015 CGI National Conference in Los Angeles.

What characterizes a CGI classroom?

Teachers pose a variety of problems; problem solving is the focus of instruction.

1CGI does not involve a particular class configuration, does not use a pre-specified set of problems in a given sequence to teach the curriculum; and teachers who use CGI are not limited to specific resources. One teacher might read a children’s book to provide context for the story problems. Another could refer to a recent field trip to a city park. A third might use a textbook as a teaching resource.

Many problem-solving strategies are used to solve problems.

2Children are provided with multiple opportunities to decide how to solve problems. Teachers who use CGI usually tell the children to solve the problems any way they can. They also encourage students to use any tools they want, in a way that makes sense to them and that they can explain or show.

Children communicate with their teachers and peers how they solved the problems.

3Perhaps the most striking feature of CGI is that these teachers have a sense of ownership of this knowledge of children’s thinking. It empowers them to make decisions, often on the spot. They know when to push, when to hold back, and how to make a problem easier or harder. They know how to support children to make sense of problems in their own ways. They know when to use a story problem and when not to. They know what problems to give next to support children’s learning. They know how to listen.

Teachers understand children’s problem-solving strategies and use that knowledge to plan instruction.

4CGI teachers use their knowledge of problem types and solution strategies to make decisions about their curriculum. This knowledge helps them determine what each child understands and then decide how to help the child extend their understanding.