Maths is Colourful – Not Black & White

When I was 9, I suddenly discovered that scientists (those people I pictured as always wearing white lab coats) hadn’t worked out everything there is to know about our world.

Not only did it blow my mind, but what's more – later on, I realised that maths was the same.

Our understanding of maths is constantly evolving.

I’m a child of the 90s, growing up right when Andrew Wiles was proving Fermat’s Last Theorem in 1993 – and opening up wondrous new mathematical possibilities for the world.

Andrew Wiles, standing in front of a blackboard which reads: Fermat's equation: x^n + y^n = z^n.
This equation has no solutions in integers for n>= 3.
Andrew Wiles. SOURCE: AP Photo/Charles Rex Arbogast

So often though, we present maths as:

  • a fixed and finalised body of knowledge,
  • a ladder of skills to be dutifully attained,
  • information that's there to be doled out and unquestionably consumed.

Yet, maths is full of ongoing discovery. 

Remember, in early 2023, that thing called the Einstein tile?

It's a shape that:

  • can be copied & fitted together over & over (& over),
  • but without a repeating pattern, and
  • is a revolutionary finding your students will actually understand.
The aperiodic "hat" monotile is a simple construction generated from the symmetry and edge lines of a hexagon (faintly outlined below the tiling). According to the paper, the tile admits uncountably many tilings which do not repeat. One of the infinite family of Smith–Myers–Kaplan–Goodman-Strauss tiles.
The aperiodic “hat” monotile

Maths is also full of both historical controversies (think: when irrational numbers, 0 & complex numbers were first identified) & contemporary controversy (think: every bit of COVID-19 or political data you've ever looked at).

Maths is a tool for making sense of our world. It's used for purposes that are mundane, good & bad. So, when we only look at it in black & white terms, we seriously limit the possibilities it can offer.

But, what can we do to bring out the colour in maths & see it differently? Here are 3 strategies you can use with your students-

(They're designed to complement what you're already doing – NOT add more to your plate)

Strategy 1: Meaning

Help students to search for meaning in the maths they're doing by inviting reflection, discussion & asking question like:

  • What does this actually mean?
  • How does this work?
  • Why doesn't this work?

Strategy 2: Purpose

Help students to understand the purpose of the maths they're learning by going beyond each skill & concept, and asking questions like:

  • Why does this matter?
  • What does it help us to do?
  • What does it not help us to do?

Strategy 3: Connections

The above two strategies only make sense when we start to look for connections between mathematical ideas.


  • How does this compare to what we already know?
  • What's similar? Different?
  • What's familiar? New?


Maths is full of ongoing discovery & controversy. It's colourful – not black & white.

We can help students to see this by focusing on:

1. Meaning,
2. Purpose, and
3. Connections.

Join the Conversation


  1. This is a super important topic to me.

    I want all kids and teachers to be aware that new ideas are happening in math all the time, and that everyone can participate in creating new mathematical questions and ideas.

    But even more, I want all kids and teachers to experience being mathematically creative themselves. How? As a puzzle designer, someone who loves creating puzzles, I think creating a puzzle is the math equivalent of writing a one-stanza poem. It’s a creative act that everyone can do. So I give workshops to kids and adults giving them a chance to invent their own puzzles.

    I have a lot to say on this, so I’m going to write about it in my math blog. Consider this a teaser.

    1. When we’re passive recipients of maths, it’s easy to forget that someone (i.e. anyone) can create new mathematical ideas and questions, as you say.

      My current favourite example of this is the spirolaterals problem. It’s accessible to really young kids, has had academic papers written up on it – and was first conceived of by a teenager.

      Look forward to seeing your blog, Scott!

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