How do you teach arithmetic? One approach is through the rote memorization of algorithms. For adults, that may be the obvious solution since that is how we solve simple addition and subtraction problems. But why do we carry-over in addition or borrow from in subtraction?
To illustrate this concept, I turn to base ten blocks. I had purchased a set of base ten blocks last year for supplemental Singapore Math instruction at home. We’ve used it on-and-off to illustrate math concepts. Lately, when my child has difficulty with a math question, I bring out the box of base ten blocks. With little assistance, my child is able to calculate three digit subtraction using the base ten blocks. And, after she has tackled a few questions, I return to the questions and explain the algorithm for notating the exchange of 1-ten for 10-ones.
I had also purchased mathlink cubes and ten frame boards. The base ten blocks are the most useful by far. Instead of memorizing algorithms, the base ten blocks let children figure the calculation themselves. Then, the algorithm becomes a short-cut of what they already stand.