Talk for Maths – an introduction Lucy Sayce-Browne lucy.sayce-browne@reading.gov.uk

Aims To do some maths To consider Talk for Writing strategies as a model for teaching problem solving in maths

Some maths How much does Greece actually owe? $271 billion. How much does the UK owe? £1.5 trillion How big is a million? Will I live for a million seconds? A billion? How else could I represent a million? Stan’s Café: https://www.ncetm.org.uk/resources/17551 Questions worth answering. Greece: $271 billion for 11 million people = £24636 each. What degree of accuracy is appropriate? UK: £1.5 trillion for 64 million people = £23622 each. But this is pounds! In dollars: $36850. Other representations of big numbers.

Talk for Writing “Children can’t write stories if they don’t have any stories in their heads.” “The richness of reading shapes the writer we become” (Pie Corbett) Why Talk for maths. Inability of pupils to transfer their knowledge into an unfamiliar context.

Talk for Maths “Children can’t solve problems if they don’t have any experience of solving real problems.” “The richness of maths shapes the mathematician we become” (Magpied from Pie Corbett) Why Talk for maths. Inability of pupils to transfer their knowledge into an unfamiliar context.

Mathematicians not calculators National Curriculum focus on depth and mastery: Write like a journalist Think (reason) like a mathematician Beware ‘surface learning’.

Talk for Writing Imitate Innovate Invent Demonstrate this in the context of maths.

Talk for Maths Immersion Imitate Innovate Invent 14 Demonstrate this in the context of maths. 14

Talk for Maths Immersion: The context of the problem is set The class discuss the problem: What do we already know? What do we need to find out? What maths will we use? What would help? Have we made any assumptions?

Talk for Maths Imitate: Pupils follow the teacher modelling a co-constructed method The pupils copy the method and practise its use Pupils are working within their comfort zone

Talk for Maths Innovate: What if……. A parameter is changed Pupils may experience cognitive conflict at this point Learning happens

Talk for Maths Invent: Pupils explore the realms of possibility Pupils create their own maths Understanding is deepened Link to Blooms Making links – SOLO.

Learning Tree Independent Guided group? Scaffolded Invent: going off in lots of directions.; making connections; crossing over…. Independent Innovate: some variation; a variable is changed…. Guided group? Imitate: one way of working, modeled by the teacher Roots = prior knowledge. Learning is built on firm foundations; drawing lots of ideas and skills together; Scaffolded

Maths stories

What has happened?

Your turn Key stage 1 I know 1 bought 6 eggs yesterday, but now I only have 2 left. What has happened? Key stage 2 Yesterday I had a £20 note in my purse but now I only have £5.50. What has happened?

More T4M teaching strategies Boxing up Maths Moves Games Magpieing Maths Sacks Using stimuli Real life contexts Photocopy of boxing up template Jump Start Literacy book – show possible other games. 27

Talk for Maths classroom Washing lines Magpie books/board Juicy mistakes Save it boxes Resources Work in progress (working walls) Maths story maps 28

Assessment Assess the mathematician not the maths Hot and cold tasks Depth and mastery Hot and cold tasks 30

Cold task Hot task

Key elements Problems are drawn from real life wherever possible: A problem is something we don’t know the answer to. Emphasis on discussion of the problem before anything is written down. Comprehension follows talk. Time for pattern spotting and generalising. ‘Inventing’ places mathematics in the learners hands – ownership. Many right answers. Ownership – self esteem building – many ways of being successful in maths. Promoting mastery goals over performance goals.

Teaching strategies Scaffold access to the task; model methods; allow pupils to imitate and work in their comfort zone Provide time to explore the situation and play with the maths Help pupils to spot patterns by encouraging systematic working and tabulation Prompt innovation and provoke cognitive conflict by asking “What if…” Provide opportunities for pupils to share what they have discovered with their peers and talk about the maths Encourage pupils to look for reasons why and justify their thinking Pose questions that encourage personal exploration and creativity: “What else can you find out that is interesting?” Link to developing perseverance; risk taking – the need for opportunities to struggle and be successful= raised self esteem. Emphasise time to play. Importance of practical resources. 33

Questions worth answering How long would it take to walk a marathon? What should I have in my sandwiches? I want to make bunting for the summer fair.... Which is the best shaped box for my fudge? Which is the best route for the postman to take? How many games will there be in our netball tournament? Will I live for a billion seconds? I want to sit in a bath of baked beans for Comic Relief. How many tins will I need to buy? If I make a model of the Great Wall of China in the school hall, how big should the bricks be? nrich ideas e.g. Handshakes; Half-time scores. Photocopy of examples.

Final reflections? For more information contact: Lucy Sayce-Browne lucy.sayce-browne@reading.gov.uk 07793 369473