Developing pattern awareness in the early years

1. Developing pattern awareness in the early years Sue Gifford

2. From last time:Develop a story to promote problem solving The doorbell rang Pat Hutchins The great pet sale Mike Inkpen Pirates’ gold NRICH Mouse Counts Ellen Stoll Walsh 9 ducks nine Sarah Hayes 5 friends counting OxfordOwl web animation Caterpillar sandwiches, foxes and chicks.. Make up your own? How did you get on?

3. Shape space and measures: ELG Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.

4. National curriculum Y1 Number & place value: Guidance They recognise and create repeating patterns with objects and with shapes. .. counting in twos, fives and tens from different multiples to develop their recognition of patterns in the number system (for example, odd and even numbers) Y2 Number & place value: Guidance As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations. Geometry: Statutory ..order and arrange combinations of mathematical objects in patterns and sequences Guidance..work with patterns of shapes, including those in different orientations.

9. Recognising patterns

10. Growing patterns

13. Patterns in time…

14. What is pattern? Any predictable regularity, usually involving numerical, spatial or logical relationships.. In early childhood ..Repeating patterns, spatial patterns, and growing patterns The way the pattern is organised is its structure Mulligan & Mitchelmore (2009: 34) The power of mathematics lies in relations and transformations which give rise to patterns and generalisations. Abstracting patterns is the basis of structural knowledge, the goal of mathematics learning (Warren 2005 cited by M&M)

15. Why is pattern important? • Pattern awareness predicts later mathematics achievement Rittle-Johnson et al (2016) • Students who recognise the structure of mathematical processes and representations acquire deep conceptual understanding. • High achievers are good at visualising, involving recognition of pattern and structure. • Low achievers produce poorly organised pictorial and iconic representations.High achievers use abstract notations with well–developed structures Mulligan & Mitchelmore (2009: 33)

16. Awareness of Mathematical Pattern and Structure Mulligan et al

17. PASA Pattern and Structure AssessmentMulligan, J., Mitchelmore, M., Stephanou, A. (2015)

18. 5 Mathematical structuresMulligan et al • Sequences: repeating and growing patterns • Shape and alignment • Equal spacing • Structured counting: unitising • Partitioning: fractions

19. Developing pattern awareness

20. Dotty Triangle Levels

24. Focused on one element of the pattern Dots Number Shape

25. Focused on two elements of the pattern dots and the number dots and the shape

26. Focused on three elements of the pattern but the rule is not quite right Three dots on each side of the triangle

28. Extending the pattern: What do you think comes next?

29. Extending the pattern

30. 10 Dotty triangle

31. Different kinds of patterns • Repeating patterns: ABC, ABC,.. • Regular arrangements eg dot patterns • Growing patterns: staircases; 2,4,6,8 • Reflecting patterns: ABB C BBA

32. Regular arrangements: Subitising number talks

33. Repeating patterns Contexts: • trains, towers • stickers, stamps • found objects • action patterns • others?

34. Forest school patterns

35. Fruit kebabs

36. Teaching pattern awareness:repeating patterns Pattern structures: AB, and beyond: ABC, ABCD, ABB, ABBC etc Linear patterns, circular patterns Do children identify the unit of repeat? What is your pattern? What is your rule? What kind of pattern is it? What is the unit of repeat?

37. Teaching pattern awareness:repeating patterns Activities • continue: practically, verbally, in units • copy: one at a time, in units • create: same / different colours • repair: extra ones, reversals, missing • explain: whole string, unit, ABB • draw from memory? • identify screened part ?

38. Pattern novices copying & continuing

39. Patterns Erikson early mathematics website http://earlymath.erikson.edu/big-ideas/patterns-are-sequences-repeating-or-growing-governed-by-a-rule-they-exist-both-in-the-world-and-in-mathematics-pre-elementary-1st-grade-math-activities/ Child31

40. Pattern novices and errors:- identifying?- ‘local’ repair?

41. Pattern experts and errors:structural repair

42. Pattern expert: generalizing Sean made an ABBC pattern with bears. The teacher introduced the terminology of ‘ABBC pattern’. Sean: So it could be dog, cat, cat, sheep?

43. Using letter codes? Simon Lewis’ reception class

44. Pattern expert: generalizing

45. Mary Baratta-Lorton: Maths Their Way(1976) London: Addison-Wesley

46. Mary Baratta-Lorton: Maths Their Way(1976) London: Addison-Wesley

47. Pattern Expert: Recording repeating action patterns What is the action pattern?

48. Activity: follow these!Make up your own and record

49. Musical instrument pattern

50. Activity • Using the materials at your table make a circular repeating pattern around a plate • What might a child learn? • What questions might you ask?