Talk in Mathematics The role of dialogue in the learning and teaching of mathematics

Code Breaker! B x D = CDB x EE = BB B x F = DAB x H = ED B x A = EAB x E = B B x EI = BIB x EA = FA B x C = ACB x J = HI B x B = HBB x G = JC

Are we, the teachers, ‘good listeners’?

Do we praise all contributions to discussion?

Where do we pitch the tasks around which pupils will talk?

We can generally recall; 10% of what we read 20% of what we hear 30% of what we see 50% of what we both hear and see 70% of what we say 90% of what we say and do simultaneously Ekwall and Shanker

Williams Report 2008 “Talking mathematics should not be seen simply as a rehearsal in class of the vocabulary of mathematics, novel and important though that may be for the young learner. It should extend to high-quality discussion that develops children’s logic, reasoning and deduction skills, and underpins all mathematical learning activity. The ultimate goal is to develop mathematical understanding – comprehension of mathematical ideas and applications.”

Define Me! RectangleSequence Partitioning Place value SymmetryEdge

Taboo!

Williams Report 2008 It should extend to high-quality discussion that develops children’s logic, reasoning and deduction skills, and underpins all mathematical learning activity.

The Ancient Art of Mathematical Paper Folding

Talk Prompts What can you work out? If you know that, what else do you know? Can you tell me what your thinking is? Shall we test that? Does it work? Do you still think that is …..? Do you agree that ………….? Why is that bit important? So, what must it be? Is this always true?

Prove whether… An odd number added to an even number will always give you an odd number All quadrilaterals will tesselate

I know…so I also know… I found the pattern… I know… so I also know… It follows that… I found the pattern… so… I think… because… I thought… but now… I agree with… because… I… therefore… This is similar to… so… I considered… because… so now I will… I disagree with… because… I found… I chose… because… Perhaps… I could try… …is important because… When… it reminded me of… We could test that by… So… It can’t be… because… I thought… but now I think… because… It could be… because… First I did… then I tried… I agree with…I disagree with…I decided… I knew I needed to… and this helped me… I think that…and… I think that… but… I noticed… I decided to change…because …

Williams Report 2008 The ultimate goal is to develop mathematical understanding – comprehension of mathematical ideas and applications.”

Pyramid property statements It has an even number of edges Each face has at least one line of symmetry It has an even number of vertices No face is a quadrilateral All faces are the same shape

Pyramids – common misconceptions A pyramid always has a square base The base is always a regular polygon The base is always horizontal The triangular faces cannot be vertical The apex is always above the centre of the base A pyramid always has an apex

Is a cone a pyramid?

Effective Features of Talk (EPPI) Going beyond ‘Initiate, Response, Feedback’ Focusing attention on mathematics rather than ‘getting the answer right’ Encouraging high quality dialogue Working collaboratively with pupils Transformative listening Scaffolding Enhancing pupils’ self-knowledge about using dialogue as a learning experience

Key Messages Effective dialogue: Provides regular opportunities for all children and adults to talk about mathematics in order –to challenge mathematical ideas –to refine thinking –to confirm understanding Involves listening and responding to one another’s ideas to build on and secure learning Develops and shares models of how mathematical language can be used accurately Links to and between practical, written and all other forms of mathematical communication Is an integral part of effective mathematics learning

Key Messages Talk is crucial to developing reasoning skills Children need scaffolds to support their explanations Adults need to model effective talk and reasoning The atmosphere needs to be supporting of questioning and there needs to be the expectation that talk will occur

What can you tell me about this rectangle?