Maths is so typically learned in isolation- written work done alone, answers checked individually by students, feedback given in private.
What if you could change that?
What if meaningful conversation became central to maths class? Conversation that's centred on explaining ideas, listening and learning from peers, and thinking carefully about strategies.
Enter Maths Talks.
Maths Talks are a way to bring conversation to the centre and support students to build understanding, reasoning skills and confidence.
Here are three of my favourite Maths Talks that can be used across the curriculum and with all ages. I've included links to resources so you can easily get started.
1. What's the Split?
Look at this image. How might you split the items into two groups? Are there any other ways you could split them?
Here are some different ways that other people have split these items. Is yours on the list? If not, share yours in the comments so we can learn from you.
all sides are the same length vs sides have different lengths
quadrilaterals vs other shapes
90o angles vs angles of other sizes
has obtuse angles vs doesn't have obtuse angles
two-dimensional vs three-dimensional
parallel sides vs no parallel sides.
What's the Split encourages students to think critically about examples and how they do and don't fit into categories. Importantly, it helps students to consider the grey areas of maths and not just accept what they're given.
In this article, I share more information and examples of What's the Split.
2. Number Search
Take a look at this shape. The green triangle is worth 1. What are the other shapes worth? How do you know?
Whenever I run this Maths Talk with primary or secondary teachers, what surprises me are the different interpretations that come through.
In the above prompt, what does "worth 1" mean to you? Here are ideas that people have shared:
area
perimeter
number of corners
interior angles
based on an algebraic rule for the number of sides
based on an algebraic rule for the total shapes shown.
Is your interpretation on the list? If not, please share it in the comments!
Number Searches encourage students to verbalise and make sense of their ideas. When you run it, you'll notice a range of strategies and vocabulary being shared. Listening to, building on and articulating their own ideas paves the way for students to develop mathematical confidence.
In this Twitter thread, I share more information and examples of where you can go with Number Searches.
3. Number Talks
Take a look at this multiplication problem. How would you solve 35x8?
It never ceases to amaze me, just how many ways there are of approaching the exact same problem.
This problem was posed by Maths Teacher Circles on Twitter and Facebook. Here are just some of the strategies that were shared (notice the different and legitimate ways of describing operations as well):
35 x 10 - (2 x 35)
30 x 8 + 5 x 8
double 35 and then quadruple the result
35 x 10 - 70
Double 35. Double that. And Double again!
(70 × 2) + (70 × 2)
7 x 5 x 8 = 7 x 40
Halve one side, double the other
70 x 8 then divide by 2.
Is your strategy on the list? If not, add it in the comments so we can learn from you.
Number Talks give students space to think freely about arithmetic. Without pen and paper, students can make sense of numbers in a way that formal procedures sometimes do not allow.
Using a Number Talk, you can highlight number concepts and properties, such as place value and the distributive law. These are ideas that often are made explicit in the senior years of school but are just as relevant earlier on.
In this article, maths educator Alex Box shares more information on this type of Maths Talk.
What is a Maths Talk?
Each of the above routines - What's the Split, Number Search and Number Talks - are examples of Maths Talks. After much back and forth on twitter with helpful insights from teachers and academics, I arrived at this definition.
A Maths Talk is:
5-15 minutes: A short, stand-alone problem that can lead to further investigation.
A ‘strategising’ problem: It allows multiple strategies to be highlighted and can build capacity across the proficiencies.
Purposefully crafted: A carefully chosen problem. The teacher seeks to learn about and/or to lead their students.
Solved slowly: Students take their time, make sense of and take ownership of the processes they are using.
Conversational: Students verbalise and listen to ideas. The teacher records each student’s thinking for all to see.
In short: A Maths Talk is a bite that can lead to a feast.
Why?
It opens up unexpected delights: students will learn new ideas from their peers, and the problem itself can lead to a much richer investigation.
There is also a wealth of insights that you will learn about what your students know and can do.
Maths Talks can be used with any year level and across a vast range of curriculum topics. Not only that, but when repeated regularly they help to embed skills and to build habits, confidence and a strong classroom culture.
Maths Talks are a powerful addition to any maths classroom.