1. Lead Teacher Meetings Whangarei Term Two 2011 2 & 3 June Dianne Ogle

2. Overview of Day Feedback from Meeting One – what have you tried Effective Pedagogies in Mathematics Moderation – National Standards examples, features of moderation process. Key Ideas – continued Update on What’s happening – ALiM, SMT Where to next.

3. Effective Pedagogies in Mathematics – Anthony & Walshaw BES findings have been summarised in a booklet published by International Academy of Education. Will be sent to schools. It is intended to be a catalyst for systemic improvement and sustainable development in education. 10 principles – that are not stand-alone indicators – of best practise.

4. Beliefs that inform the principles Look at page 6 of Effective Pedagogy in Mathematics Think about each of the beliefs mentioned and what are the implications of each one. Work collaboratively to unpack what each belief implies.

5. Effective Pedagogy in Mathematics What does it look like, sound like, feel like?

6. Effective Pedagogy in Mathematics In groups of three, become familiar 3 of the principles. What does each principle look like, sound like and feel like in action? What are the common threads - next steps: –As a teacher –As a Lead Teacher of Mathematics

7. Effective Pedagogy in Mathematics – Challenges Alton-Lee has identified key challenges that exist for each of the Principles. What are they – summarise the ones you worked on before What are the common threads - next steps: –As a teacher –As a Lead Teacher of Mathematics

8. Where to from here? What do you feel are the key challenges facing your school with regard to effective pedagogies? Where might you start? Identify one action you will take.

9. Clear the Decks You need a pack of cards, picture cards removed. Decide on the target and discard any cards that are equal to or greater than the target number. Layout an array of cards face up so that the number of cards on show is one less than the target number. Play by clearing away any two cards that add to the target number. Replace the cards as soon as they are chosen. Aim is to clear the whole pack of cards. Read the number sentence as the cards are cleared away. An array if the target number is 6

10. Moderation/Teacher Judgment Three Elements: –Teachers attending to the learning students produce –Appraising this work against a reference framework –Making an explicit response such as feedback or judgment on the learner’s work Overall teacher judgment has an added complexity in that the judgment process is applied to a range of data.

11. Overall Teacher Judgment According to the Ministry of Education fact sheet (MOE, 2010) on overall teacher judgment, “An OTJ draws on and applies the evidence gathered up to a particular point in time in order to make a judgment about a student’s progress and achievement. Using a range of approaches allows the student to participate throughout the assessment process, building their assessment capability.... No single source of information can accurately summarise a student’s achievement or progress. A range of approaches is necessary in order to compile a comprehensive picture of the areas of progress, areas requiring attention, and what a student’s progress looks like.”

13. What is moderation? The process where teachers compare judgments to either confirm or adjust them

14. The Process Involves close collaboration to establish a shared understanding of what achievement of an outcome looks like and whether or not a student has demonstrated achievement of the outcome.

15. Underlying assumptions Reflective, secure professionals; open minded Well developed interpersonal skills Deep content knowledge Strong pedagogical and assessment knowledge/skills Understandings of curriculum; progressions Provision of exemplars Understanding of standards School culture of ongoing professional learning

16. A framework for moderation Confirm or adjust quality judgments Ultimate purpose of moderation Interpersonal skills Theoretical / content knowledge Frame of reference Culture of professional learning Clear about OTJs Common understandings Clear criteria and exemplars Use of moderation process Making effective OTJs Attending to the components of moderation Understanding and using moderation High quality teaching and learning

17. What makes moderation easier? Planning (the process and content) Teachers familiar with curriculum/standards Agreed criteria Start with the same tasks, aims and criteria Explicit easy criteria to judge Sufficient samples of student work Open-ended tasks Providing context of tasks Time and trust to fully discuss student samples

18. What makes moderation more difficult Teachers having different interpretations of curriculum, standards, underlying concepts Culture of blame, mistrust, resistance to change or ongoing learning Insufficient evidence of achievement Setting a range of different tasks, aims, criteria Poorly set tasks Limited time

19. Engaging with the Standards through a rich task Figure It Out Geometry Level Three Pages 14 & 15 ‘Fun Run ’ Using your NZC, and the mathematics standards what type of responses would you expect to hear from students who meet the standard at year 5, 6, 7 or 8?

20. Geometry – Position and Orientation End of Year 5: describe locations and give directions, using grid references and points of the compass. End of Year 6: describe locations and give directions, using grid references, turns, and points of the compass. End of Year 7: describe locations and give directions, using grid references, simple scales, turns, and points of the compass. End of Year 8: describe locations and give directions, using scales, bearings, and co- ordinates.

21. Engaging with the Standards through a rich task Building Borders – Figure It Out pages 12 & 13 Work through the activities in ‘Building Borders’ Using your NZC, the mathematics standards and Book one, what type of responses would you expect to hear from students who meet the standard at year 5, 6, 7 or 8?

22. New Standards Illustrations New illustrations available on NZMaths. How do they add to the Standards document? How could you use them in your school?

23. Moderation Issues Dependability of evidence and that the assessment is consistent with teacher experience Moderation within and between schools Student Participation Reporting to parents, families and whanau

24. Where to next? What resources do you have available in school to support moderation, making judgments National standards examples FIO/ARB tasks – deciding how to gather evidence Capacity building in/with schools Brainstorm possibilities within your school

25. True or False Are the following statements true or false? Decide on your answer – discuss with a partner and see if you agree. 93 - 38 = 91 – 40 Cain and Ryan went shopping at the $2 shop. Cain spent half of his pocket money, Ryan spent one quarter of his pocket money. Cain spent the most. True, False or Maybe

26. Key Mathematical Ideas Key strategies from last time Equations and Expressions – what are big ideas and implications Patterns and Relationships

27. Number Sense Having a good intuition about numbers and their relationships. Develops gradually as a result of exploring numbers, visualising numbers in a range of contexts, and relating them in ways that are not limited by traditional algorithms. Grows more complex as children learn more, eventually being able to think flexibly about fractions, decimals, percent and integers.

28. Big ideas Numbers are related to each other through a variety of number relationships - more than, less than, composed of “Really big” numbers possess the same place- value structure as smaller numbers. Best understood in terms of real- world contexts Whole numbers can be described by different characteristics, even and odd, prime and composite, square, understanding characteristics increases flexibility when working with numbers

29. Key Mathematical Ideas Developing Meanings for the operations Addition and subtraction are related. Addition names the whole in terms of the parts, subtraction names a missing part Multiplication is related to addition Multiplication involves counting groups of like size and determining how many there are in all. Multiplicative thinking Multiplication and Division are related. Division names a missing factor in terms of the known factor and the product. Models can be used to solve contextual problems for all operations, regardless of the size of the numbers. They can be used to give meaning to number sentences. Van de Walle & Louvin Teaching Student Centred Mathematics,

30. Counting Principles Gelman and Gallistel (1978) argue there are five basic counting principles: One-to-one correspondence – each item is labeled with one number name Stable order – ordinality – objects to be counted are ordered in the same sequence Cardinality – the last number name tells you how many Abstraction – objects of any kind can be counted Order irrelevance – objects can be counted in any order provided that ordinality and one-to-one adhered to Counting is a multifaceted skill – needs to be given time and attention!

31. Early Number relationships Spatial relationships: children can learn to recognise sets of objects in patterned arrangements and tell how many without counting.

32. One and two more, one and two less The two more than and two less than relationships involve more than just the ability to count on two or count back two. Children should know that 7, for example is 1 more than 6 and also 2 less than 9.

33. Anchors or “benchmarks” of 5 and 10 An understanding of ten is vital in our numeration system and because two fives make up 10, it is very useful to develop relationships for the numbers 1 to 10 to the important anchors of 5 and 10

34. Part – Part – Whole Relationships To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.

35. Key Ideas – Equations and Expressions Patterns and Relationships What important big ideas can you identify? What links can you make to Effective Pedagogies and the Standards? How could you help teachers to make connections – links to True/False activity?

36. Updates GLoSS sample – being moderated by NZCER – schools testing GLoSS in June – we are close to it being available JAM – going to Learning Media ALiM projects Leadership Consultation ILC in PLD

37. References Anthony, G., & Walshaw, M. (2007). Effective pedagogy in Mathematics/Pangarau: best evidence synthesis. Wellington: Ministry of Education. Kerry Mitchell, The Education Group & Dr Jenny Poskitt, Massey University New Zealand teachers’ overall teacher judgments (OTJs): equivocal or unequivocal? (Presentation) Van de Walle, J. A., & Lovin, LouAnn. H. (2006). Teaching Student- Centred Mathematics Grades K-3 (Vol. One). Boston: Allyn and Bacon.