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From maths bite to mathematical feast
Here are some maths routines that have greatly influenced my teaching, and my own personal relationship with maths. Using these routines regularly in the classroom can be transformative - for starters, they help us see that everyone has mathematical ideas worth sharing.
A few things I've learned about running maths routines:
They are short - usually 5 to 15 minutes. Keeping them short will help ensure that energy and engagement don't lag
They are regular. Running them regularly will have bigger benefits for skill-building and developing student confidence over time.
They are often run as a stand-alone item. That is, they aren't necessarily connected to the main lesson. They are a good way to:
- build up a particular maths mindset, behavior or skill
- see the connected nature of maths, to revise past concepts,
- tune into a future topic
- simply share a few minutes of mathematical joy.
Last year, I began thinking about these short, regular and often stand-alone events as mathematical bites. Later, I noticed how:
A maths bite can in fact lead to a mathematical feast.
Let me explain with an example.
From mathematical bite...
A recent Maths Teacher Circles session brought together people from a range of contexts - from primary and secondary teaching to maths consulting and university maths specialisations.
Presenter Carmen Brading kicked off her segment with the Notice & Wonder routine, using this prompt:
A variety of ideas were shared by the group. A few examples:
Noticings
The paint is blue.
It's a cube made from smaller cubes.
It's a 4 x 4 x 4 cube.
Wonderings
How much paint will it take to cover the cube?
How many litres does the tin hold?
What are cases 1, 2 and 3?
Is the cube suspended or on a surface?
In the space of about 3 minutes, over 30 observations and wonderings were shared in the chat. Through this mathematical bite, we had accessed a variety of perspectives. We had engaged in observation and asked questions. We were engaged and our curiosity was piqued.
To mathematical feast...
Carmen then posed some questions that invited us to think mathematically. They were questions that flowed naturally after the Notice & Wonder routines:
If this 4 x 4 x 4 cube was painted on all sides, how many of the small cubes would have 3 blue faces? How many would have 2? 1? 0?
It was the beginning of an invitation to dive into an exploration; a mathematical adventure involving painted cubes.
Choice and ownership
Before we set off to investigate, Carmen highlighted the sheer scope of this problem providing additional, extending questions to consider. Having a menu of entry points gave us ownership and the power to differentiate for ourselves.
Some began by building with snap cubes. Others by sketching using isometric paper. Quite a few tables were created and used to organise and track mathematical observations. While connected by the same problem, we were each able to make decisions that would shape our individual investigations.
How is this like a feast? When presented with a problem that's open like this one, we've a spread of mathematical options to choose from. Decisions need to be made about what moves will make a good start to the (mathematical) meal.
We might go straight to a dish (strategy) we are familiar with, one that feels like a good place to start. That dish (strategy) might be particularly tasty (appear to be valuable) and so we help ourselves to more (stick with it for a while). Or perhaps that one isn't quite hitting the spot, so we look for and consider other options to pursue.
Together with others
Time spent in breakout rooms allowed us to talk through ideas with others and to gain additional insights on the task. In small groups, we stepped inside the shoes of students to make sense of and tackle a problem.
How is this like a feast? Imagine being at a long table with others. It's the people closest to you that you will be interacting with, observing, having fun with. We might see someone help themselves to a lot of something that you hadn't noticed was there. It may spark your curiosity to try it too, either now or later. It might prompt you to ask a question.
Translate this to a mathematical context. We might see something new (a strategy in action) that provokes our curiosity. Perhaps we get a taste (find out more) by asking a question. We may learn something new from that encounter, whether an idea we can apply in the moment or something to try at a later time. Either way, asking the question is a step that gets us a little closer to our next mathematical milestone.
Regarding the image below: Samantha and I were at the same feast (session), at different parts of the table (breakout rooms). There was a common dish we started with (building with snap cubes, jotting down observations) there was a dish she got stuck into that I wasn't even aware of (Desmos graphing). While I didn't get a tasting this time round, it's on my list to learn more about and explore in the future.
Why is this analogy useful?
To be honest, I'm not yet entirely sure. I wonder if it could be a way of helping to communicate an idea of what mathematical experiences can look like, sound like and feel like. This is an idea I continue to explore and make sense of, including exploring these questions:
How can we build curiosity and confidence in maths for all students?
How can we do this in a way that's inclusive, rather than segregative?
If you have anything to add to this discussion, please feel free to share. I'd love to learn from your thinking!