Beyond the Math Box: There Are No Dragons!

My mother was a child psychologist and she always used to say that if a child is old enough to ask a question they are old enough to get a straight answer, and that the answer should go into all the depth that the child is interested in. That approach hasn't always been easy with Adam, but it's paid big dividends.

Sometimes, when talking about math, questions come up that go beyond the topic at hand. It's pretty common to set aside those questions, saying that you will focus on the subject that the answer involves later. I call this the "here be dragons" approach, because you set a boundary that you're not willing to cross.

I think that not being willing to answer a question is a good curiosity-killer, and that the "here be dragons" approach is counterproductive because when you do get around to the subject you were avoiding before, the connection to the original topic has weakened and the motivation to learn the new topic has diminished. It might even lead the child to think of the new topic as too hard if you can't answer the original question right away.

As an extreme example, once a child learns subtraction, the topic of negative numbers naturally comes up as soon as she tries to subtract a larger number from a smaller number. Yet, it's traditional when that happens to brush off the question and not answer it for years, because negative numbers are a more advanced topic.

I understand why people do that. Negative numbers are definitely more abstract than positive ones. But they are not that more abstract than zero, and they teach that concept on Sesame Street.

I taught Adam about negative numbers the first time he asked about subtracting a bigger number from a smaller.  The way I approached it was to count down to find the answer with him, and then when we got to zero before running out, I explained that the answer couldn't be a regular number because we didn't have anything left to take away, but there was something called negative numbers that we could use, and showed him how to continue the count down past zero.

There was no need for a "here be dragons" approach. He was quite satisfied with the answer. After he asked a few more questions with answers that involved negative numbers, he became more comfortable with the idea and started to think of them as legitimate numbers. I could tell he did because he started wanting to know what happens when you added, subtracted, and multiplied them.

I didn't have to go into great detail about negative numbers when he asked that first question. He didn't learn about absolute value until much later. But my answer had enough detail for him to understand the answer to his question and that's all that was needed.