We felt that discrete mathematics would be an excellent course for these diverse students because with two years of mathematics as a prerequisite, all of them could begin on an equal footing. The topics for term one included graph theory and coloring, apportionment and voting theory, fair division, tessellations and combinatorics, with algorithms as a theme through the year. In the second term, students study coding theory, matrices, fractals and chaos, and sequences and recursion. The teacher has the option to add topics of particular interest to them, such as knot theory, bin-packing, or game theory, and they are given the freedom to decide how long they wish to spend on a topic. As yet there is no textbook for this course which further keeps it from becoming lock-step and codified.
Teachers rely instead on modules from a number of sources and create some materials themselves.
Initially, when we brought up the idea of a discrete mathematics curriculum at a meeting of Manhattan's mathematics supervisors, we were unnerved when it was met with dead silence. Since it is new, few mathematics teachers and supervisors had studied discrete mathematics, and it was difficult for many of those people who saw themselves as the subject experts to admit that they had no idea what discrete mathematics was. So we began little by little to change the minds of many of them. It helped a great deal that the NCTM's conferences and their Mathematics Teacher began to have an increasing number of workshops and articles about discrete mathematics. We began piloting the course in 1994 with teachers who had studied discrete mathematics and were committed to its implementation.