My good friend Steve recently expressed his irritation with helping his son with math homework. Steve was noticing that the new ways of teaching kids how to do pretty basic things (such as adding) are actually more difficult than the old fashioned way we learned to do things.
This is not the first time I’ve noticed this irritation. My wife expresses it frequently. The truth is that I can sympathize with where these people are coming from, but I don’t have a problem with these new methods. In some cases, it’s accurate to notice that the new ways actually do make things more difficult.
In other cases, I’d like to suggest that this only appears to be the problem, that these things are more difficult. There’s actually a different problem, lurking underneath.
The thing that is interesting to me is that it’s not just irritation I’ve noticed from some people. There’s also this sense of indignation. (Just for the record, I don’t get that sense from the aforementioned Steve.) Irritation we ought to expect. Indigination, though? I think that requires a little pondering.
I’d like to suggest that some of this indignation is borne out of this idea that you’re not supposed to do things the new way. The “real” way to do things is the way we were taught.
Feeling this way about math is almost to be expected. On the surface, math doesn’t appear to be a very subjective thing. It’s not a place where it appears we need to make much room for a diversity of opinions.
The thing that we forget, when we get indignant about new and different ways to do math is that the objective part is in the solution to math problems. The objective part is that 2 + 2 = 4. It would be pretty silly to debate the truth of this fact.
But this does not mean the method that a particular person uses to determine this answer is any more sacrred than any other way. It does not mean that the symbols that we all agree to use have any inherent use.
For example, somebody at some point decided that the little half-rectangle house thing was a good way to calculate division. This person decided that one number could go inside the house. The other other number goes to the left of the house. They divised this whole ritual that ends up with the answer on top, and the remainder (or decimal) to the right of the answer.
Somebody decided that we ought to use a line to mean subtraction. They decided that we would start with the ones. They thought it made sense to go top to bottom and left to right.
There are many ways to calculate correct answers. There are countless symbols we can use. These methods and symbols aren’t bad. They are necessary. But they aren’t true in the same sense that the answers are true.
Math homework is not important in the cosmic scheme of things. But I think the lesson is critically important, here.
We human beings have this tendency to mistake the process for the end product. When we have found a method that consistently gets us true answers we have this tendency to make an idol out of the path. We want to assume that our method is the only way to consistently find truth.
(A caveat: I’m not saying that all paths are equally good. I’m saying that all paths that consistently lead to the truth are eqaully good.)