When mathematics instruction focuses on making connections, students become aware of the relationships between mathematical topics. As students see how new ideas relate to what they have studied before, they will see these ideas as extensions of what they have previously learned. Moreover, when students see the connections between concepts and processes, they are more likely to remember "how to do the mathematics" (process) because they can draw on their understanding of "what it means" (concept). As we look at the mathematics curriculum in the middle grades and how we present it to students, we can see that if we focus on the mathematical connections, students will come to expect mathematical ideas to be related. Instruction should include the expectation for students to focus on relationships and commonalities between mathematical ideas, models, and strategies. For example, as students in the middle grades use two- and three-dimensional models to develop spatial reasoning skills, they are building on their previous experience with relationships between two-dimensional figures. These concepts will connect to other strands of mathematics as students work with scale models, minimum and maximum values, and graphic relationships in algebra and calculus.

  Applying mathematics to other subjects