Beyond the Math Box: How a Dad Guides His Boy Through the Amazing World of Math

In school when they tell you you have to learn your multiplication table and graph a parabola before you can learn to do real mathematics they are lying to you! - Vi Hart, What was up with Pythagoras?

Well, "lying" is a bit harsh. "Misinformed" is a better choice. But first, a little background.

I'd like to explain how it is that I've been able to teach my son Adam some math concepts that generally only math and physics majors in college learn.

I should warn you that one advantage I have with Adam is that he learns so easily and so well that I don't actually have to be a good teacher, so there is a chance this technique won't work for everyone. But I think it's worth trying.

I don't push Adam when I'm teaching him.  I'm more of a guide helping him to explore his world. I help him to discover things faster, and I lead him to things I think he's likely to be interested in. Sometimes what interests him and what doesn't surprises me. I'll give him a couple of tries and if he's not interested move on to something else.

We'll study each topic to the depth he wants and then move on to something else that interests and challenges him. It's a lot of fun to see how excited he gets sometimes when he learns about a new concept and sees how it interrelates with everything he already knows.

Sometimes he gets "stuck" on something. I don't mean that he doesn't understand, I mean that he'll just be so interested in something that he'll get fixated on it and  want to do it over and over. Sometimes I have to work a bit to get him to try something else.

Learning about other subjects can naturally lead into talking about math (and vice versa). We watched a video on a large telescope and how it has computers that adjust the shape of its parabolic mirror in order to focus it. That naturally led to a discussion about how a parabola is a shape and the properties parabolas have that are useful for a telescope, and that actually led into the topic of the other conic sections.

A lot of people believe that math builds upon itself in a linear tower, and that you have to master each topic before you can start to begin study of the topic after it, but this isn't true. There are actually a lot of different things that don't build on each other nearly that strongly. That means that you don't have to worry about teaching things exactly in the traditional order.

You don't always have to master one topic to understand the things that are based on it, either. Most people couldn't tell you anything about the Peano axioms (arithmetic is based on them), but they are still quite capable of adding two numbers together.

Even when some level of understanding of a dependency is required, it's often not at full depth.

If Adam gets interested in something that requires him to strengthen his abilities or understanding in some prerequisite, it gives him the motivation to do so. For example, Numberphile got Adam very interested in the Fibonacci numbers, and his proficiency in adding multidigit numbers soared because he wanted to be able to compute the sequence on his own.

So he may not have long division mastered yet, but that's ok -- he's six, after all, and he can divide well enough to do modulo arithmetic and convert numbers to base 12, so he's satisfied. He hasn't really needed long division for much other than that. I'm not worried -- he'll pick it up when he needs it.

Obviously, this technique can't work as well in a large group, but I think it's a great way to do individual tutoring for students of any ability level, especially those that have some level of interest in math.