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Talk in Maths

Talk in Maths. LJMU 25 th January 2010 Sue Killen. Williams Report.

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Talk in Maths

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  1. Talk in Maths LJMU 25th January 2010 Sue Killen

  2. Williams Report “Talk in mathematics should not be seen simply as a rehearsal in class of the vocabulary of mathematics, ... 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

  3. Opportunities • Child to child • Child to teacher • Teacher to child

  4. A Climate for Learning • Safety – ethos that encourages ‘having a go’ and mistakes are ok • Relationships – meet and greet • Learning - pair/share, VAKE • Time - wait time, down time

  5. Puppets&Props

  6. Barrier games & Clue cards

  7. Child to child Working collaboratively to solve problems

  8. Data Handling

  9. Kennel Club Four dozen dogs live in 6 different coloured kennels. The smallest kennel has 6 dogs and the orange kennel is the largest with 10. The yellow kennel and the green kennel are the only ones with the same number of dogs. The 13 youngest pups are in the red and blue kennels housing the least number of dogs. The purple kennel has 2 more dogs than the blue kennel. How many dogs are in each kennel?

  10. I know that there are 48 dogs altogether and the orange kennel is the largest with 10 dogs 10 8 8 6 7 9 13 pups live between red and blue, so one of these must have 6 and the other 7 If blue has 6, that means purple would have 8 10 + 8 + 7 + 6 = 31 48 – 31 = 17 You can’t divide 17 by 2 to get an equal number for green and yellow So blue must have 7 and red must have 6 This means purple has 9 (48 – 32 = 16 and 16 can be divided by 2 to give 8 in yellow and green

  11. Block A Counting, partitioning and calculating Using and applying mathematics Counting and understanding number Calculating Block B Securing number Facts, understanding shape Using and applying mathematics Knowing and using number facts Understanding shape Block C Handling data and measures Using and applying mathematics Measuring Handling data Using and applying mathematics Block D Calculating, measuring and understanding shape Calculating Measuring Understanding shape Block E Securing number facts, calculation and relationships Using and applying mathematics Counting and understanding number Knowing and using number facts Calculating

  12. Links with APP

  13. Using and Applying Problem Solving Communicating Reasoning

  14. Child to teacher Show what you know

  15. Key Stage 117 + 8Key Stage 264 - 37

  16. Teacher to child Explaining and Questioning

  17. ExplainingModels and Images

  18. Mathematical Vocabulary • Mathematical vocabulary versus everyday language odd, difference, face, table, mean, operation • Encourage children to explore the meanings for themselves • Incorporate mathematical vocabulary into your displays http://www.teachers.ash.org.au/jeather/maths/dictionary.html

  19. Effective Questioningin Mathematics

  20. Traditional teacher questioning • Teacher asks a question • Children put their hands up • Teacher takes an answer • Teacher accepts, rejects or develops the answer • Teacher asks a further question

  21. Learning is enhanced when … • We ask fewer but better questions • Seek better answers, giving children sufficient ‘wait time’ to think and respond • Sustain thinking during dialogue by using alternatives or extensions to questions that challenge children’s thinking

  22. Strategies for encouraging extended dialogue • Allow thinking time before taking responses • Use ‘think, pair, share’ • Do not respond immediately after a child has replied – often they have more to say • Challenge the response – ‘Tell me why…’, ‘But what about…?’ • Ask the child to elaborate – ‘Can you say more’

  23. Types of Questions • Recalling facts • Applying facts • Hypothesising or predicting • Designing and comparing procedures • Interpreting results • Applying reasoning

  24. Types of questioning Recalling facts: • What is 13 add 7? • What is double 30? • How many sides does a pentagon have?

  25. Applying facts: • Tell me two numbers which have a difference of 12 • Tell me any multiple of 2 • Give me two numbers which total 20 • What are the factors of 42?

  26. Hypothesising or predicting: • Estimate the number of marbles in this jar • What is the next number in this sequence: 17, 15, 13, ?

  27. Designing and comparing procedures: • How might we count this pile of straws? • How could you solve 46 + 43?

  28. Interpreting results: • What can we say about even numbers? • What can we say about multiples of 5?

  29. Applying reasoning: • The seven coins in my purse total 23p. What could they be? • Complete this pattern to make it symmetrical

  30. Count these cubes A chew costs 3p, a lolly costs 7p. What do they cost altogether? What are four threes? How many centimetres are there in a metre? How could we count these cubes? A chew and a lolly cost 10p altogether. What could each sweet cost? Tell me two numbers with a product of 12 Tell me three lengths that together make 1 metre Closed and open questions

  31. Problem Solving How do we give children regular access to problems that will develop their ability to use and apply their skills and knowledge in the SATs tests, without it becoming dull and arduous?

  32. A shop sells batteries in packs of four and packs of two. Task: Discuss…. What could the question be asking? Consider how to extend your Y6 children into level 4/5 problem solving.

  33. A shop sells batteries in packs of four and packs of two. Simon and Nick want two batteries each. They buy a pack of four and share the cost equally. How much does each pay? Mary buys 2 packs of two batteries. Hamid buys 1 pack of four. How much more does Mary pay than Hamid?

  34. Discuss: What could the graph be about?

  35. Abbie takes the temperature outside at midday on the first day of each month. The graph shows her results from January to December. How many months on the graph show a temperature between 10°C and 20°C? Find the difference in temperature shown on the graph between July and August.

  36. Calculations Effective: • How many number sentences can you give me using these numbers 7, 3 and 10? Less effective: • 3 + 7 = ? • 7 – 3 = ?

  37. Calculations Effective: • Why do 17 + 9, 18 + 8 and 19 + 7 all give the same answer? Less effective: • What is 17 + 9, 18 + 8 and 19 + 7?

  38. Classifying questions Prompting questions Probing questions Promoting questions

  39. Prompting questions: • direct children to the knowledge and skills they have already learned • help children to use knowledge to derive new facts and skills • help children to understand the problem and decide how they will begin to tackle it • draw children’s attention to alternative approaches, methods or ideas they have used previously • offer children simpler starting points and illustrations of how they might tackle a problem

  40. Promoting questions: • set children challenges so they can apply their ideas and reasoning skills and deepen their understanding • encourage children to enquire by setting up and testing hypotheses of their own • stimulate discussion about efficiency and the merits of alternative strategies • foster children’s ability to think, to review their approaches and solutions, and identify other, more efficient, strategies they might use

  41. Probing questions: • establish the extent to which children’s understanding is secure • help children to identify and correct any errors they have made and why they might have made them • encourage children to review their ideas and methods and seek ways of improving their work • support children in articulating their strategies and choices, and use correct mathematical vocabulary and notation • sharpen children’s thinking skills and ability to hypothesise, test and justify

  42. For children who are starting a piece of work: • How are you going to do this? • What do you already know? • What do you need to find out or do? • Do you need to add or subtract? • Can you do it in your head or do you need to use pencil and paper? • Do you need any equipment? • What do you think the answer will be? Can you estimate?

  43. For children who are stuck: • Can you tell me what you have done so far? • Is there something you already know that might help? • Would a number line/cubes/counters help? • Could you draw a picture?

  44. While children are working: • Can you tell me what you have done so far? • Why did you decide to add/subtract? • Could there be a quicker way of doing this? • What did you notice when…?

  45. Using ICT Which Number Where? Sum, Product, Difference

  46. Maths Magic!

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