When mathematics instruction focuses on developing and refining the habit of looking for connections, all students -- both those already inclined to see links and those who may view mathematics as a group of isolated subjects -- become more aware of the relationships between mathematical topics. Moreover, when students see connections between concepts and between processes, they have a valuable tool for remembering how, and deciding when, to apply a particular concept or skill. Instruction should include the expectation for students to focus on relationships and commonalities between mathematical ideas, models, and strategies.

Connections may be among mathematics topics, to other school subjects, and to situations in the world beyond school. A lesson that is rich in connections should have a central mathematical goal and should include elements that help students use their prior knowledge to access new information. Problem-solving situations often serve to offer a specific context that can draw out students' awareness of connections. Through the use of questioning and group discussions, students should be encouraged to bring up connections. At the same time, the teacher should be prepared to introduce new connections that go beyond what the students are able to think of independently.

Use the information you learned in this session to plan a lesson for one of your own classes. Of course, you will need to find a task that builds on a concept that your students have had previous experience with. The task may also have connections beyond the mathematics classroom. Students need to understand your expectation that they will focus not only on the specific problem, but also on its connections to other mathematical concepts and beyond. Think of questions you might ask to help students move their thinking forward.

After you have created your lesson plan, use the Classroom Checklist (an Adobe PDF document) to evaluate it.

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