When I was 9, I suddenly realised that scientists (those people I always pictured in 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. The decade when Andrew Wiles proved Fermat’s Last Theorem – and opened up wondrous new mathematical possibilities for the world.
So often though, we present maths as:
- a fixed and finalised body of knowledge,
- a ladder of skills to be dutifully attained,
- information to be handed 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.
Maths is also full of historical controversies. Think: when irrational numbers, zero & complex numbers were first identified.
And contemporary controversies. 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 & help students to see it differently?
Here are 3 strategies that you can use-
(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 maths. Invite reflection and discussion. Ask questions. For example:
- 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. Go beyond each skill and concept, and ask 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 first two strategies only make sense when we start to look for connections between ideas.
Ask students:
- How does this compare to what we already know?
- What's similar? Different?
- What's familiar? New?
Summary
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.
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.
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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