We talked about how arithmetic problems can be thought of spatially, as geometry. Addition and subtraction are just steps forward and backward from a starting point. Multiplication can be thought of the same way. For example, if you want to multiply 2 times 4, it’s like you’re taking a segment 2 units long, “multiplying” it, and then assembling the pieces.
The Clear Science staff finds it easiest to think of addition and subtraction as the same thing. Subtraction is just addition of a negative number. (“Addition” means move on the line, “negative” just means go backwards instead of forwards.) Similarly, multiplication and division are the same thing. The difference is that in multiplication, you start with the pieces and make an assemblage. In division, you begin with the assemblage and then chop it into pieces.
These are simple concepts, but easy to overlook: there is more than one way to think of numbers. The purpose of primary education is to figure out how you do it. But when the Clear Science staff offer tutoring, we often find that people don’t realize you can puzzle through problems in ways such as these. Math is not a list of rules to memorize—rather it is a way of thinking clearly.
