The question that I receive the most often from parents and teachers is, “What is wrong with the ‘normal’ way that we were taught math?”
This is usually followed up by complaints about the “new” math. I respond with one answer, “The math that we are teaching children today is not the new math, it is the old math. If you learned math from about 1960 onwards, you were taught the new math!” This is perplexing for many to understand, yet my father signed up for a math course in the 1960’s that was indeed called, The New Math; this course taught the standard algorithms of North America that many of us know today, in addition to a few others that are pretty neat. All of these algorithms have one thing in common: they focus on digit thinking and they are all short-cuts that reduce the amount of math we actually have to think about; furthermore, they take away one of the most essential skills that we need: estimation. This means that the most thinking that you will do while adding or subtracting is thinking about math facts up to 9 + 9 and 10-9; the most thinking that you will do while multiplying or dividing is thinking about math facts up to 9 x 9 and 89/9. All ‘orders of magnitude’ become lost. Let me explain.
Lets take addition to start. We are taught to start by going right to left (even though all reading up to this point goes left to right). You add up the ones digits and then if they have a sum greater than 10, you ‘carry the 1’ – and right there is the problem! You are not carrying a ‘one’, you are carrying a ten! We do the same thing with subtraction….”cross out the 4 and make it a 3 and borrow 1″ – and there is the problem again because you are borrowing 10 and not borrowing 1.
To be continued….
Seeing Math is Believing Math 