‘Weighing’ or ‘Fattening’ the Pig? or “Using NAPLAN as assessment for learning”

1. ‘Weighing’ or ‘Fattening’ the Pig?or “Using NAPLAN as assessment for learning” Dr Thelma Perso Executive Director Literacy and Numeracy Taskforce NORTHERN TERRITORY DEPARTMENT OF EDUCATION AND TRAINING January 2010

2. 3 accountability questions: • Are our students learning what they should be 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

3. What does the data say? Assessment of learning Assessment for learning At the macro level – Australia wide, state-wide At the school level – Whole-school, classroom

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: • Making sure it doesn’t keep happening • (Teacher PD and whole-school approach) • data-driven model of improvement Turbo-charged: • Reaching down and ‘pulling the kids up’

6. Will ≠ Skill

7. Who owns the problem? • We do – every department employee • Intervening NOW to ensure low achieving students meet year 5,7 expectations in two years • The role of the Year 4,6,8 teachers • The role of ALL teachers – whole school problem

8. What is numeracy?

9. 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”

10. Subject English compared with Literacy • Literacy is a capability, not a subject • 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 • Literacy is about making choices about what tool/capability to apply when (vocab, text form, grammar, punctuation, reading a narrative v’s reading a web page etc) • …You need the repertoire to make choices from….

11. maths and numeracy- what’s the difference? • Numeracy is a capability, not a subject • Knowing the tools of Mathematics compared with having the disposition and confidence to use them in a variety of contexts and for a variety of purposes and audiences • Numeracy is about making choices about what tool/capability to apply when (mental, written, calculator, level of accuracy required, measuring tool, algorithm, etc) • …You need the repertoire to make choices from…

12. Definitions: ”Numeracy is the effective use of mathematics to meet the general demands of life at school and at home, in work, and for participation in community and civic life” (MCEETYA, 1997) “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)

13. 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, and • Grounded appreciation of context (AAMT 1997)

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. 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? • Making assumptions that students can apply their mathematics learning outside the classroom… • Fear • Numeracy testing programs

16. 3 aspects to numeracy: • Mathematical numeracy • Strategic numeracy • Contextual numeracy • NB Mathematical numeracy on its own is not sufficient, despite being easiest to measure

17. 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!

18. 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”. National Numeracy Review 2008

19. ‘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.

20. 2008 Year 3 NAPLAN 43% of (one state) students got this wrong Issues: Multiplicative thinking is critical by Year 3 (from 3+3+3+3 to 4X3) Literacy issues: ‘total number of wheels’; ‘number sentence’ ‘complete’ Transfer between visual to literal to symbolic

21. 2010 Year 3 Question 24 44% 25% 14% 15%

22. Year 3 Question 25 25% 16% 10% 47%

23. Year 7 non-calculator, qu 13 • Which number is greater than 0.08? • 0.1 b. 0.009 c. 0.07 d. 0.0089 a. 78% b. 9.8% c. 2.1% d. 9.1%

24. What does this mean? • 22 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

25. Year 7 non-calculator qu. 30 % results: • 10.4% 20.1% 44.4% 23.9%

26. Yr 7 non-calculator qu. 25 • 19.1% 48.7% 13.4% 17.2%

27. Proportional reasoning: qu 15 • 52.6% 7.9% 21.1% 17.6%

28. 11% 59% 10% 19%

29. Year 9 non-calculator • What is the answer to 6.6 ÷ 0.3? 0.022 0.22 2.2 22 8% 33.5% 40% 16%

30. 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 ’Working Mathematically’ (ACARA: Proficiency strands) -which includes the meta-cognitive processes that sit around computation

31. 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!

32. What’s absolutely critical? – de-cluttering the curriculum; numeracy expectations • 3 maths content strands • Number is critical - place value, decimals, fractions - multiplicative thinking (by year 3) - proportional reasoning (by year 5) 4 rows

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

34. 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)

35. Thank you…. • Thelma.perso@nt.gov.au

37. YEAR 3 NUMERACY

38. Year 3 Question 5 5% 5% 5% 84%

39. Year 3 Question 10

45. Year 3 Question 24 44% 25% 14% 15%

46. Year 3 Question 25 25% 16% 10% 47%