Where are we? Today's students live in a computational world. Machines do the calculation on problems they will formulate, but they are not learning formulation. Problem solving is modeled for them as recognition of something they have seen before. They do not build a foundation of conceptual understanding to support reasoning out their own formulation. They are taught in a linear curriculum with one formula following another. The world they will encounter can't wait for problems to appear as formulas in school. The problem is not the recognition of its existence, it is figuring out what to do about it, to bring the issue down to earth where it can be grappled with. Arithmetic is a good place to start. For problem formulation it is necessary to see what it can do. I say "see" because we need to comprehend it "all at once in one piece". It needs to be in a form that can be thought about. We need to reason out its role in a problem. It is a ques
Arithmetic - for the TwentyFirst Century Understand the Concepts