Five, Basic, Creative, Problem-Extension Methods for a Fixed Syllabus

Abstract

We provide five basic methods for creatively extending a given base problem. For a given base problem, each of the five methods provides a distinct technique for extending the base problem to a more challenging level. The five methods may roughly be called plug-in, reversal, multi-step, comparison and iteration. We illustrate application of these five methods in a variety of levels of course difficulty: elementary arithmetic, high school algebra, geometry, college English, and actuarial-financial courses. These five methods can also be used as a basis for differentiated instruction. These five basic methods naturally arise from certain common features of all computer languages and provide a uniform model of cybernetic flow between syllabus topics and problems.