1. Informing our teaching and learning: SHIFT 2015 Can pedagogical approaches developed in Shanghai and Singapore inform our own teaching and learning in primary mathematics and beyond? Jenny Field Principal Lecturer in Primary Education j.field@gre.ac.ukj.field@gre.ac.uk 1

2. What does the data say? TIMSS (Trends in International Mathematics and Science Study) 63 Countries: Children aged 10-14 ‘East Asian countries continue to lead the world in mathematics achievement TIMSS 2011’ p7 Singapore average percentage 73% England 48% (content and cognition) Pisa (Programme for International Student Assessment) 65 Countries: Children aged 14 2012 mean score: Shanghai 1 st England 26 th 2

3. Lessons from Shanghai 3 2014 15 Government Focus: Large Exchange Programme involving 60 teachers from Shanghai

4. Mathematics Curriculum Framework (CPDD, 2013) Singapore

5. Attitudes to mathematics Discuss in groups: What is the stereotypical attitude towards this subject? Why do you think this has come about? Research indicates 3 key factors School Experiences Parents Media ‘Knowing how many of the teachers in my school feel about maths, training up specialists is definitely the way forward.’ Local MaST Teacher 2013

6. A British Problem? Mathematical skills are not in decline worldwide. Attitudes towards mathematics differ hugely between countries A British Culture Issue?

7. Royal Society report (Primary Science and Mathematics: Getting the Basics Right) 2010 “Recent evidence has highlighted how children’s initial experiences of education can have profound implications for their future success and well-being. Children are innately curious about the natural world. But, year after year, large proportions are ‘turned off’ science and mathematics by the time they reach secondary school.”

8. ‘our children are not stupid; our children are not inherently inadequate; our children are not born hating maths, we just manage to convince them that they should!’ Carol Vorderman Guardian 17 th June 2008

9. ‘Cockburn (1999) identifies that teachers who dislike maths will find it difficult to be enthusiastic about teaching it. Fox and Surtees (2010) recognise that such enthusiasm is essential and infectious and a key way in which we can really improve attitudes. Whereas ‘teacher anxiety’ has a counter effect, as these anxieties ‘can often be passed on to the children they teach’, thus perpetuating the cycle of negativity, Haylock (2010:5). Research by Askew et al (1997) agrees that ‘teachers’ own negative attitudes to mathematics’ can have a significant influence upon children’ Donaldson, G. Field, J. Harris, D. Taylor, H. and Tope, C. (2012) Becoming a Primary Mathematics Specialist Teacher. London: Routledge

10. 10 Cultural Variation

11. Their Curriculum 11 Representation and Modelling – focus on conceptual understanding Does that surprise you?

12. Focus on Variation and Reasoning What happens if we add 6 to: 15, 25, 35, 45 Which of these 2 answers is correct and why? Which is the odd one out and why? 12

13. 13 Consistency and Progression in approach to solving problems

14. 14 Singapore Approach

15. Lining up objects in a row 15 Children start by counting familiar things, then using cut-out pictures they can physically line up in a row. With one block representing one item (1 to 1 correspondence)

16. 16 Drawing boxes around pictures Then children start to draw pictures of the things they are counting, with a box around each picture. So there's one box for each thing they are counting.

17. 17 3. Labelling boxes. Once they are confident with drawing boxes to count objects, children start to write the number of boxes as a figure above the drawing 1 2 3 Over time they drop the pictures and just draw the boxes 1 1 1 2 3

18. 18 Eventually they no longer need to draw all the boxes. They just draw one long box or bar and label it with the number. This step away from one-to-one representations to symbols is crucial but can take time.

19. 19 Do we have a common progression?

20. Addition - Aggregation There are 3 footballs in the red basket 2 footballs in the blue basket. How many footballs are there altogether?

21. Addition - Augmentation Peter has 3 marbles. Harry gives Peter 1 more marble. How many marbles does Peter have now? Concrete Abstract

22. Subtraction - Comparison Model Peter has 5 pencils and 3 erasers. How many more pencils than erasers does he have?

23. Moving to the abstract Peter has 5 pencils and 3 erasers. How many more pencils than erasers does he have?

24. Generalisation

25. Part-Whole Model: Example 1 There are 120 boys and 80 girls in a school hall, how many students are there altogether ? There are 200 boys and girls in the school hall. If there are 120 boys, how many girls are there? Boys Girls 120 Boys Girls 120 200 80

26. Multiplication Peter has 4 books Harry has five times as many books as Peter. How many books has Harry? 26 4 44444 One to many correspondence (scaling)

27. Multiplication – have a go Helen has 9 times as many football cards as Sam. Together they have 150 cards. How many more cards does Helen have than Sam?

28. Ratio 28 Tim and Sally share marbles in the ratio of 2:3 If Sally has 36 marbles, how many are there altogether?

29. Have a go A herbal skin remedy uses honey and yoghurt in the ratio 3 : 4. How much honey is needed to mix with 120 g of yoghurt? 29

30. 30 Sam Tom 12 48

31. Fractions in year 3 in new NC ‘Add and subtract fractions with the same denominator with one whole’ Using the bar Video clip – then have a go Reasoning about fractions (KS1) https://www.ncetm.org.uk/resources/43609 31

32. Exam results Laura had $240. She spent 5/8 of it. How much money did she have left? Overall percent correct, Singapore: 78%, United States: 25%. 30 $240

33. Proportion Take a Strip and a paperclip

34. Your Strip Represents 10p Show me 5p Show me 2p Your Strip Represents £1 Show me 50p Show me 20p Your Strip Represents 1 metre Show me 50cm Show me 20cm Your Strip Represents £5 Show me £3 Show me £3.50

35. What do our students struggle with? 10% 35 0 100% 1 50% 0.5 ½ 0.1 1/10

36. Algebra k, m and n each stand for a number. They add together to make 1500 k + m + n = 1500 + + = 1500 m is three times as big as n k is twice as big as n Calculate k, m and n

37. 37 In many ways it is this consistency and progression in modelling that appears to makes the difference

38. Some examples 38

39. As we established earlier … These countries were not doing well in 1965 They took time to research and make changes. What research did the draw upon? The 5 Wisemen: Piajet Viagoski Diennes Skemp Bruner Ideas established in the WEST Have they had the same impact here? Why? 39