Some examples of the shapes drawn are shown in figure 2. The idea of recursion can be used in many other areas. Also, problems concerning compound interest can allow students to find patterns and write formulas that involve recursion. Another discrete-mathematics topic that is appropriate for grades 7 and 8 is networks or graphs. Students can get a feel for the vitality of mathematics when the teacher tells them that the traveling salesman problem is an important unsolved problem in mathematics.
Graph theory is full of such interesting and accessible problems.
In fact, many of the graph-theory topics covered in the high school course discussed earlier can be taught in the middle grades, using an appropriate level of depth and formality. Graphs, recursion, and finite differences are just three examples of discrete-mathematics topics that are appropriate and desirable to teach in grades 7 and 8. Conclusion Discrete mathematics is vital, exciting, and useful mathematics that should be taught in grades 7-12. Many topics can be taught, and they can be fit into the curriculum in a variety of ways. Some teacher retraining is necessary, but the small investment of time and effort needed to begin teaching discrete mathematics has substantial payoffs in terms of a richer curriculum and better-prepared students.