Mathematically Speaking

1. Mathematically Speaking

2. APP S & L Brookfield lesson study Pedagogy of talk in maths Activities to enhance maths talk Workshop Foci

3. Speaking and listening skills inherent in Using and Applying; Problem solving, Reasoning and Communicating Using and Applying – responses from P levels onwards, EYFS; NC PoS S and L Guidelines

4. Solving Problems Representing - analyse, do, record, check, confirm Enquiring - plan, decide, organise, interpret, reason, justify Reasoning - create, deduce, apply, explore, predict, hypothesise, test Communicating - explain methods and solutions, choices, decisions, reasoning What is Using & Applying Mathematics?

5. Communicating Use the correct language, symbols and vocabulary associated with number and data Communicate in spoken, pictorial and written form, at first using informal language and recording, then mathematical language and symbols Reasoning present results in an organised way understand a general statement and investigate whether particular cases match it Explain their methods and reasoning when solving problems involving number and data KS1 PoS

6. Communicating Organise work and refine ways of recording Use notion diagrams and symbols correctly within a given problem present and interpret solutions in the context of the problem communicate mathematically, including the use of precise mathematical language Reasoning understand and investigate general statements [for example, 'there are four prime numbers less than 10', 'wrist size is half neck size'] search for pattern in their results; develop logical thinking and explain their reasoning. KS2 Pos

7. These are the skills that children need to learn to make progress: generate and explore ideas and strategies, pursue lines of mathematical enquiry and apply logic and reasoning to mathematical problems make and test generalisations, identify patterns and recognise equivalences and relationships develop, select and apply a range of mental, written and ICT based methods and models to estimate, calculate, classify, quantify, order and compare communicate ideas and justify arguments using mathematical symbols, diagrams, images and language interpret findings, evaluate methods and check outcomes NC: Skills

8. Speaking and Listening, Using and Applying, and APP

9. What we did Met as a trio to decide objectives, class, teacher and focused teaching technique Chose activities and planned lesson Taught lesson, with two observers (3 children chosen) Pupil conferencing, reflection, evaluation Lesson Study Using APP S & L

10. Based on contextualised problems Emphasis on shared ideas using a prop for turn taking Mini plenaries for discussion, reflection and progression (collating strategies) Class discussion regarding supportive sharing of strategies through turn taking The lesson

11. Less able Mathematician – felt empowered by the opportunity to be heard All children felt more like a team – “…from a liquid to a solid …now definitely a rock” Valued the supportive nature of sharing strategies The Pupil Conferencing

12. Sharing and building on others’ strategies as a skill, would need explicit teaching Using a prop for turn taking: a powerful tool Support the empowerment of LA in Maths by giving enough time for thoughts, and space to share ideas Further enhanced by having more time Reflections

13. Talk for Learning Developing Meaningful Maths Dialogue

14. Pick a domino

15. Domino Trick 1. Take a domino tile 2. Pick a side of the tile, multiply number by 2 3. Add 3 4. Multiply the result by 55. Add the other side to the result6. Ask for the result 7. Subtract (3 x 5) from the result8. You have now both numbers in the tile.

16. “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 ofmathematical ideas and applications.” Williams Report 2008

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

18. Select one of the statements The statement you have chosen may be either correct or incorrect. Discuss it between you: you have to decide whether it is right or wrong. If you think it is correct then you should explain how you know. If you think it is incorrect then you should explain what is wrong with it and give an example to show it is wrong. More likely than probable

19. Take a number Square it Subtract the original number What do you find out about the answer? Why? Refine your explanation until it is as clear and concise as you can make it. Odd or even?

20. How will you develop the characteristics of effective dialogue in your school? Discussion

21. 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