1. PaCT Mathematics Connections to good pedagogy

2. Developmental progression of learning less clear. Detracting from teacher broad content knowledge. Focus on incremental progress. Post national standards 0123 4 5 Early Add 6 Adv. + Early x 7 Adv. x Props. 8 After After After End End End End End 1 Y 2 Y 3 Y Y 4 Y 5 Y 6 Y 7 Y 8

4. Post national standards Reporting against a universal expectation for time at school eg. Well Below, Below, At, Above (instead of reporting level of achievement) Narrows the teacher focus around the expectation for time at school of the year level they teach.

5. High stakes Post national standards

6. High stakes + limited assessment tools Post national standards PAT Maths easTTle Maths Diagnostic Interview GloSS

7. High stakes + limited assessment tools Narrowed focus for teaching Post national standards

8. Tendency to teach to the ‘useable’ assessment measures

9. When using PaCT... Judge all aspects at a point in time. Need relatively current knowledge of where a student is at across all aspects.

10. When using PaCT... Judge all aspects at a point in time. Need relatively current knowledge of where a student is at across all aspects. Need shorter cycles of revisiting ‘strands’

11. Integrating ‘Strands’ within ‘maths time’ Making sure numeracy strategies are well integrated into other strands and vice versa. eg. teaching fractions & probability, or addition and algebra at the same time 1, 1, 2, 3, 5, 8, 13, … Next five? Rule?

12. Maths across the Curriculum Looking for teachable moments and monitoring the maths aspects as part of teaching in other learning areas. eg. building a model animal enclosure to meet its needs.

13. International rugby field: Playing field length - Min 94m, Max 100m Playing field Width - Min 68m, Max 70m In-goal length - Min 6m, Max 22m In-goal Width - Min 68m, Max 70m Biggest and smallest area? Hot Spots/enrichments that revisit prior learning

14. When using PaCT... Some important aspects in PaCT haven’t been a big focus of other assessment tools. Need to include these in teaching.

15. Symbols and Expressions Not really taught explicitly -knowing 5+6 =? but not 5+?=11 -Common errors eg. To solve 3+9 writing 3+7=10+2=12

16. So... Emphasis on recording thinking ❏ using number lines, arrays, set diagrams etc. ❏ correct use of = sign ❏ understanding number properties eg. associative, commutative etc. ❏ setting problems that involve a variety of unknowns

17. When using PaCT... The illustrations emphasise how the students demonstrate their thinking and understanding.

18. Lack of Understanding Children were taught to manipulate numbers using strategies almost as algorithms without any real depth of understanding. This was evident when students were challenged when problem solving in other contexts or when several steps were involved.

19. Performance of Understanding Using a variety of contexts within instructional groups, or rich tasks/problem solving to demonstrate understanding of concepts eg. fraction of a number - what’s 2/3 of 24? -using time, money, measurement, shape, sets of objects etc.

20. When problem solving Importance of teacher observation/questioning/monitoring - rove, rove rove! Importance of developing students skills in problem- solving and describing mathematical thinking. http://nzmaths.co.nz/mathematics-inquiry-communities http://www.nzmaths.co.nz/bracken/pd/Introduction_to_MIC/index.html set problems/investigations that involve several steps

21. 2 step problem example You heard that NZ beat England 15-12. (Yay!) The points could have been scored in a number of different ways. What is the chance that NZ scored more tries? (assuming each way is just as likely as another)

22. Still wondering... how useful information within PaCT is to inform teaching what assessment information is important to record and how to best keep track of it (and what other assessments give us important information)

23. Good pedagogy Regular practice activities that connect to prior learning - with rigour. Cross-curricula learning to keep cycling through mathematical aspects, connect to other contexts, see maths as real life Blend knowledge and strategy teaching (not assessed separately in PaCT) - flow in learning Problem-solving - observe and question students articulating, manipulating, recording show understanding through authentic application require complexity of reasoning or judgement students recording it! Teacher roving - observing, questioning, challenging, alternatives, discussing Problem solving groups, trained in expectation of contribution, allow maths discussion (set expectation), learning from each other. teach what to do if stuck. teach questions to ask. Mark your work! Reward persistent behaviour. Symbols and expressions - understanding and using (like the surface features of writing, phonics and grammar of reading) Guided maths - use problems not ‘routines’ Knowing what to look for at the developmental level- critical content knowledge of the teacher