What We Know

In mathematics, there are three kinds of connections educators should expect and help students to make:

• connections between areas of mathematics, including new topics and those that have been mastered;
• connections between mathematical situations and real-world situations;
• connections between mathematics and other academic content areas.

In fact, we can view mathematical learning as a series of connections. "The growth of mathematical knowledge can be viewed as a process of constructing internal representations of information and, in turn, connecting the representations to form organized networks" (Hiebert & Carpenter, 1992, p. 80).

Brain research tells us that learning can take place only when we can fit new ideas and information into our schema, the connections and categorical rules we have for information we have already internalized. As a result, it is imperative that teachers help students activate their schema and make connections between new topics and learned topics. This ensures that learning is not a series of unrelated facts and ideas (EDThoughts: What We Know About Mathematics Teaching and Learning, 2002). In addition, well-connected knowledge is remembered better (Bruner, 1960).