Defining Connections
 Introduction | Varieties of Connections | Other Contexts | The Teacher's Role | Your Journal
"When students can connect mathematical ideas, their understanding is deeper and more lasting. They can see mathematical connections in the rich interplay among mathematical topics, in contexts that relate mathematics to other subjects, and in their own interests and experience. Through instruction that emphasizes the interrelatedness of mathematical ideas, students not only learn mathematics, they also learn about the utility of mathematics."

## (NCTM, 2000, p. 64)

Connections in mathematics are of importance because they can help students succeed with new concepts and see that mathematics makes sense. Students should be guided and encouraged in mathematics class to develop the habits of mind of looking for and wondering about connections. Within a topic, for instance, links from basic definitions and situations to complex applications lead to logical development and deeper understanding, while connections among mathematical topics and processes show that mathematics is not a collection of isolated ideas. Connections also help students recall skills and concepts and use them appropriately in problem-solving situations.

It is very important that today's students examine and discuss mathematical connections as a regular part of their classroom experience. In the past, textbook explanations and examples may have been deemed sufficient for helping students see relationships that might be obvious to mathematicians and mathematics educators. But as we have seen in this course, carefully constructed lessons can help students see connections among content areas, among mathematical processes -- like the ones outlined in this course -- and within their own thinking. Ultimately, students should be able to identify and use connections as part of their everyday mathematical learning. It is up to the teacher to guide students toward such proficiency and to continually be on the lookout for additional connections to draw out as part of instruction.

Connections also make it possible for students to apply their knowledge to subjects other than mathematics, including real-world situations. For this reason, opportunities to work with real-world data and the "messy" mathematics such data often entail is appropriate in the high school classroom. For instance, when students see the power of connections in working on a chemistry problem or evaluating poll data as a classroom exercise, they may establish a habit of looking for connections that will carry forth in their future academic work.

In this section, we build a working definition of some aspects of connections that we can use to help high school students gain a better understanding of mathematics.

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