One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. The NCTM Connections Standard (2000) states: “Problem selection is especially important because students are unlikely to learn to make connections unless they are working on problems or situations that have the potential for suggesting such linkages” (p. 359).
To help students see and use the connections among various mathematical between this problem situation and various mathematical topics. In addition, their explorations
of multiple approaches to proofs led beyond proof as verification to more of illumination and systematization in understandable yet deep ways (de Villiers
1999); expanded their repertoire of problemsolving strategies; and developed their confidence, interest, ability, and flexibility in solving various types of new problems. These benefits, in turn, will be passed on to their own students.