Learning math should be more like learning how to drive a car

I can’t take credit for this analogy. I first heard it in a fantastic TED talk from Conrad Wolfram on Teaching Kids Real Math with Computers. Since watching that talk 8 years ago, I’ve spent a lot of time thinking about the message and analogy.

I’ve drawn a comic here to illustrate a silly scenario.

When first learning how to drive, we obviously wouldn’t focus on how internal combustion engines work. The basics of learning how to drive include getting to know what each of the controls does. What it feels like when pressure is applied to the gas and brake pedals. How much the steering wheel needs to rotate to do a right angle turn. These can only be learned and understood through the act of driving. Of course there are numerous rules of the road and signs to learn about; but those also come with a clear purpose.

Why then does it not appear silly that we approach learning mathematics by focusing on the inner workings of how the ‘engine’ works? The inner workings are important and valuable, but they do not need to be a pre-requisite to being able to think about the math concepts.

Take Calculus for example, a large part of our math education builds up the skills from K-12 to do this topic. However, students never get to actually think about Calculus or even know what it is by the time they graduate high school. They spend time building up and practicing arithmetic operations, solving equations, combining like terms, determining slopes of lines, and so on. Each of these skills on their own can certainly be valuable and can tap into rich mathematical concepts; but unfortunately, they can also be learned as requisite procedural skills that are seen as necessary before moving onto ‘harder’ concepts.

Students often see Calculus as a mysterious topic that they will never be able to reach or understand.

I tried an experiment with my 6 year old daughter. I showed her this picture and asked her what shape it was:

She didn’t know the name of it. I asked her if it was a circle and that she knew was a firm “no!”

I showed her this picture next and asked her if it was a circle:

At first she said “no”… but then she said “but it’s a better circle than the first one.” When I asked her why, she replied that “it has more sides and is more round”.

I showed her this last picture:

She exclaimed “There! That’s the best circle!”

Boom. My six year old daughter was thinking about the ideas of Calculus. Calculus is a branch of mathematics that is partly built on the idea of many, many sides that get really, really small. She was able to imagine shapes with more sides and how that would look as a shape; at the same time imagining what would need to happen to the length of those sides.

She doesn’t know what an equation is, and certainly doesn’t know how to differentiate a function. Yet, the thinking came naturally to her because she had a visual as an anchor. Even if she didn’t have the terminology to communicate mathematically, she was trying to use words that meant something to her.

This begs the question: “What really are the basics of mathematics?”

Do kids really need to learn all the way up to how to differentiate functions before we introduce them to the beautiful ideas of Calculus? Would we ask someone to learn how to build an engine before they were allowed to drive?

Being able to drive a car has become a large part of functioning in today’s society; it is a skill that the majority of adults have learned. We give the message that math is just as important since we make everyone learn it. In his TED talk, Conrad Wolfram says that there is nothing wrong with engineering and building engines, if that is your passion. It is specialized though, and you wouldn’t ask everyone to do it. Just as in math, should we make everyone learn it and then teach it in a way that is specialized?

Or can we get more students using and ‘driving’ math and seeing the relevance and beauty in it. Perhaps that would even result in getting more people passionate about diving deeper into the “inner workings”.