‘Weighing’ or ‘Fattening’ the Pig?

1. ‘Weighing’ or ‘Fattening’ the Pig? Dr Thelma Perso Executive Director Curriculum February 2009

2. What does the data say? At the macro level – Australia wide, state-wide At the school level – Whole-school, classroom

3. 3 accountability questions: • Are our students learning? • How do we know? • What are we doing about the ones that aren’t? These questions operate at all levels: they are the Minister’s questions, my questions and your questions

4. Your level: • School data, classroom data • Does NAPLAN data ‘gel’ with classroom data? • If it does, what are your intervention strategies? • 2 types: ‘preventative’ and ‘turbo-charged’

5. ‘preventative’ and ‘turbo-charged’ Preventative: • Teacher PD • data-driven model of improvement Turbo-charged: • Reaching down and ‘pulling the kids up’

6. Who owns the problem? • Intervening NOW to ensure low achieving students meet year 9 expectations in two years • The role of all Year 8 teachers • Intervening NOW to ensure the next lot of Year 7 students meet expectations next year • The role of ALL primary teachers – whole school problem

7. Recommendation 1National Numeracy Review 2008 • “That all systems and schools recognise that, while mathematics can be taught in the context of mathematics lessons, the development of numeracy requires experience in the use of mathematics beyond the classroom, and hence requires an across the curriculum commitment. Teacher education (pre and in) should thus recognise and prepare all teachers as teachers of numeracy, acknowledging that this may in some cases be ‘subject specific numeracy”

8. maths and numeracy- what’s the difference? Compare ‘literacy’ with ‘English language competence’: Knowing the tools of English compared with having the disposition and confidence to use them in a variety of contexts and for a variety of purposes and audiences

9. Similarly: ”Numeracy is the capacity to bridge the gap between ‘mathematics’ and ‘the real world’, to use in-school maths out of school; People are considered more or less numerate based on how well they choose and use the mathematics skills they have in the service of things other than mathematics” (Willis, 1998)

10. And from AAMT: Numeracy involves the disposition to use, in context, a combination of: • underpinning concepts and skills from the mathematics discipline • Mathematical thinking and strategies • General thinking skills (common sense), and • Grounded appreciation of context (AAMT 1997)

11. Pedagogy – the key to developing a numerate disposition • Knowing a lot of maths isn’t sufficient • How does a teacher ‘teach’ a disposition or attitude of confidence? • Assuming students can apply their mathematics learning outside the classroom… • Fear • Numeracy testing programs

12. 3 aspects to numeracy: • Mathematical numeracy • Strategic numeracy • Contextual numeracy • NB Mathematical numeracy on its own is not sufficient, despite being easiest to measure

13. Mathematical numeracy requires a deep understanding of numbers and how they work in calculation, and measurement and spatial sense E.g using common sense to know • 6.25 + 1.3 can’t possibly be 6.38 since the answer must be more than 7 • If I buy two items marked $2.50 under a sign saying “50% off” that I will pay $2.50 • If I subtract 297 from 302 then that is the same as finding the difference between them or how much more is one than the other, and is best done mentally These examples rely on deep understandingsnot an ability to calculate!

14. What is numeracy? • interpret numbers when they are used for different purposes • understand how numbers can be expressed • use estimation techniques appropriately to make and check calculations • use a variety of calculation methods • choose and use appropriate technology • use the language of measurement appropriate to the task • choose and use measuring tools and instruments appropriate to the task • use estimation techniques • use measurement techniques to solve problems • recognise that some measures are obtained by combining two or more other measures • recognise and describe common shapes • use shapes appropriate to the task • choose and use appropriate equipment for a particular purpose • recognise and interpret the conventions of visual representation • use spatial techniques to solve problems • recognise and understand the part chance plays in everyday life • recognise and interpret estimates of chance events • judge the quality and appropriateness of data collection • understand and use common methods of summarising and displaying data • make and question judgements based upon data presented • make predictions based upon data presented

15. Mathematical Literacy • Code breaker • Comprehension • Use/application • Critical literacy

16. Recommendation 8: • That the language of mathematics be explicitly taught by all teachers of mathematics in recognition that language can provide a formidable barrier to both the understanding of mathematics concepts and to providing student access to assessment items aimed at eliciting mathematics understandings”.

17. ‘Cracking the codes’ as the first step • It is the codes that give children access to the mathematics Newman (1977) examined the errors made by students as they solved worded mathematics problems and found that at least 35% of the errors made occurred before students were even able to attempt to apply mathematics skills and knowledge. The language-based errors occurred during the reading, comprehension, and transformation stages.

18. Year 3 Naplan 200843% of QLD students got this wrongIssues: Multiplicative thinking is critical by Year 3 (from 3+3+3+3 to 4X3)Literacy issues: ‘total number of wheels’Transfer between visual to literal to symbolic

19. Year 7 non-calculator, qu 13 • Which number is greater than 0.08?

20. What does this mean for QLD? • out of every hundred studentsin year 7 do not understand place value • These students will not be numerate • These students will likely not get jobs • These students will consistently fall behind…. • Unless they get intervention NOW

21. Year 7 non-calculator qu. 30 QLD % results:

22. Yr 7 non-calculator qu. 25

23. Here’s one for you: qu 15 • QLD:

24. QLD:

25. Year 9 non-calculator • What is the answer to 6.6 ÷ 0.3? 0.022 0.22 2.2 22 QLD:

26. What does this data tell me? • Huge proportions of Year 7 students do not understand fractions or place value • Teachers are focussing on methods and algorithms instead of concepts and deep understandings • Teachers are focussing on digits, numbers and symbolic representations and not seeing ‘the words’ as part of mathematics (mathematical literacy not being explicitly taught) • Teachers not teaching ‘Ways of working’/’Working Mathematically’

27. How can we intervene?1. Huge proportions of Year 7 students do not understand fractions or place value • Place value and fractions are the building blocks – these understandings are critical • This is a major risk for all future mathematics learning for these students • Let’s get focussed!

28. What’s absolutely critical? – de-cluttering the curriculum • 5 maths content strands • Number is critical - place value, decimals, fractions - multiplicative thinking - proportional reasoning 4 rows

29. How can we intervene?2. Teachers focussing on methods and algorithms instead of concepts and deep understandings QCAR Standards: Bloom’s taxonomy Heirarchy: E: Lower orderrecall (memory) translation interpretation toapplication analysis synthesis A: Higher orderevaluation

30. Teaching maths for numeracy 1. Clarify(comprehension) 2. Choose (maths, strategies) 3. Use (do the maths) 4. Interpret(common sense) 5. Communicate (explain, justify, reflect)

31. Implications: • We MUST give all students access to the full range of standards, A-E in order to report their achievement and learning honestly to parents • This means explicitly teaching higher order skills like evaluation, synthesis, reflection to all students • We must not ‘dumb down’ the curriculum by only teaching what we think they are capable of

32. How can we intervene?3.Teachers focussing on digits,numbers and symbolic representations and not seeing ‘the words’ as part of mathematics (mathematical literacy not being explicitly taught) • “The words ARE the maths” • Ensuring that every maths lesson includes transfer between the pictures to the words to the symbolic representations

33. Eg. when teaching the concept of division: • ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ ☺ • Share these smiley faces among 3 children by circling how many each will get • Write what your sharing looks like using symbols (12 ÷ 3) • Write how you would read/say this? (“twelve divided by three”)

34. ‘Numeracy is everybody’s business’ • More than rhetoric • Deep understanding of numbers and how they work occurs across the curriculum (in maths lessons it’s just contrived) • All KLAs must play their part (providing the contexts to make the maths real)

35. What are the opportunities in each/your KLA to attend to this?

36. About % of Year 7 students coming into Year 8 in 2009 do not have deep fractional understandings…. • This is a major risk for numeracy acquisition for these students and for future employment • What can you do in your learning area to address this? • (Your area can provide the context) • NB leaving it up to the maths teachers in the school is not an option!

37. KLA Opportunities: ‘seizing the numeracy moment’ • SOSE: “1/5 of Australian sheep are kept for their meat” • Technology: “how can we enlarge this photo so that it is 2/3 larger?” • Science: “3/5 of this solution is water” • English: “One quarter of the family were under the age of 15” • HPE:”0.25g of this food is trans-fat” “How many minutes in each quarter of the game?” • The Arts: time-signatures, rhythms, dance • LOTE:everything!

38. Weighing or fattening the pig? • Are our students learning? • How do we know? • What are we doing about it if they’re not? • With a sense of urgency!!!