In my Maths Specialist class today my students were looking at circle theorems. Here’s some fun ones.

Often in maths classes, these theorems are presented as facts to be learnt. You then use those facts to solve a question like this.

BORING! The real excitement isn’t to be had in applying a rule, the real fun is in PROVING the rule. But, as is often the case, the more fun thing is also the more challenging thing. We were having a little bit of trouble.

It was then that we had to go right back to basics. These are 15 year olds, they’ve already learned a lot and forgotten quite a bit too. But the lovely thing about Maths is it’s all connected. We just had to go back and join the dots.

You might not want to watch the video above, it’s over ten minutes long. But in it, I attempted to “PROVE” and “CONNECT” most of the geometry they learned in grade 1 through to grade 10. The video is essentially “proofs (in a loose sense) of the geometric properties below.

The rules above are interesting, but unless students CONNECT all these rules together, there’s no way to understand what’s going on, and there’s no way to retain all that information.

#### Math is an UNBROKEN line.

This is an important and often overlooked part of mathematics by teachers and students alike. The way a true Maths education should happen goes something like this…

Step 1. Students learn how to count.

Step 2. Students learn to add (fast counting).

Step 3. Students learn to multiply (repeated adding)

…

From Step 1 to Step 157, there is no leap. While the maths may get challenging, it never appears as if by magic. Each step builds upon the previous (or several of the previous) and no student ever needs to make a mathematical leap of faith.

#### Drawing the Connections.

Here’s a graphical organiser I made a couple of weeks ago for my year 11 Maths Methods class about completing the square (a topic that some teachers would be happy to say “just trust me on this”)

Maybe maths isn’t an unbroken line… Maybe

#### Maths is a WEB

And it’s our job, as maths teachers, to make sure that as much red string as possible is put on that wall, connecting everything to every other thing where ever possible.

#### Be Explicit About It

If you’re a maths teacher all that red string is laid out in your brain, connecting all that maths to all that other maths, with no piece of information existing as an island.

But this isn’t the case for students. They are still in the process of laying down string. If they are struggling with an idea, there’s a very real chance it’s because they don’t know where the string goes.

Maths is all, like, connected, dude.

How can help your students lay down their web of red string?