Mathematics Is A Thinking Tool, Not Just A Subject In School

Thinking is our birthright as humans. It’s one of the things we do best, most of the time.

Kids should see mathematics as a thinking tool to use to engage with the world. I want a school mathematics that teaches kids to engage with the world around them using the tools of mathematics. I want a school mathematics wherein kids produce powerful representations of interesting mathematics, both with their spoken words, and on paper. Representations are the products of thought.

Mathematics does not belong to schools, although school is where we do the most mathematics, for most of us. We don’t just leave mathematics behind when we walk out the school doors for the last time, though.

I want kids to see numbers as something to play with, almost toy with, like a cat with a toy mouse. I want them to enjoy stripping numbers down to their prime factors. I want them to attack problems with confidence and skill.

The other day, I asked kids to consider what number occurs most often, when rolling 2 dice, and why. All day, kids came up to me with their ideas. And you try to tell me they aren’t interested in mathematics? I asked them to consider something that is probably intuitive, and to apply their powerful thought to it.

And you try to tell me “they” only care about social media and celebrities and the latest pop cultural happenings? I doubt that very much.

School mathematics around the world is a chopped salad full of little bits and pieces chopped into fine little bits. Yes, curricula could be more coherent, but the good news is all the little bits are just full of interesting things to think about.

Arithmetic is interesting to think about and do (and how on Earth did we end up killing this beautiful topic, and turning it into an endless array of worksheets? Start with the sequence 1+1… with young kids, and build the operations on top of this foundation.

My own personal pedagogical principle is this. You can adopt it or discard it as you like. It’s my hidden principle that I don’t often talk about.

Be more interesting.

7 x 8 is interesting. If you don’t think so, it’s because you’ve never played with it. Play with number facts while you learn them.

Figuring out how the multiplication algorithm works is interesting.

Fractions are interesting. How do they work? Why are operations with fractions so “weird”?

Prime numbers are one of the most interesting things there are. People spend lifetimes thinking about primes. How do they work?

The third thing you need to do is to pay attention to what kids are thinking, and what they are saying and writing. How are they using the powerful thinking tool we call mathematics?