Part ? Content

1. Part ? Content • Revisit SOLO • Activity 1: 2.6 Linking SOLO, vocabulary and the standard • Activity 2: 2.7 Putting what we know into practice. • Activity 3: Developing parallel tasks by students • Activity 4: Developing an exam question – generalising patterns • Activity 5: Literacy strategies • Activity 6: Correcting a paper to provide excellence opportunities.

2. Understanding Levels of Thinking using: SOLO TAXONOMY (after Biggs and Collis 1982)

3. Evaluate Explain Generalise Predict Fully justify Model Compare Form an equation Analyse Relate Apply And hence solve…. Solve (in context). Simplify+. SOLO TAXONOMY (after Biggs and Collis 1982) Describe Solve Calculate Simplify Factorise Define Identify Do simple procedure Unistructural Multistructural Relational Extended abstract Prestructural

4. Describing words for each type of Thinking Visual image of the type of Thinking Type of Thinking Compare Form an equation Analyse Relate Apply And hence solve…. Solve (in context). Simplify+. Evaluate Explain Generalise Predict Fully justify Model SOLO TAXONOMY (after Biggs and Collis 1982) Define Describe Solve Calculate Simplify Factorise Define Identify Do simple procedure Extendedabstract Unistructural Multistructural Relational Prestructural

5. What does it mean? Really there’s not much there. For example: What does clockwise mean? Err….. What?? Prestructural

6. What does it mean? There’s one idea there. For example: What does clockwise mean? Err….. You turn this way Unistructural

7. What does it mean? Angle LMN = 600 There are a number of ideas. For example: Find the size of angle LMN Multistructural

8. What does it mean? Classify There are a number of ideas and links are be made between these ideas For example: Angle LMN = 450 Angles on a line Base angles isos. triangle Find the size of angle LMN with reasons Relational

9. Extended abstract What does it mean? There is a range of ideas which are linked together plus some knew or extended thinking is added. For example: We know: KJL = LMN (alt angles) JKL = LNM (alt angles) This does not mean that KJL = JKL, so there is no reason why triangle KLJ must be isosceles just because the lines are parallel. If JK is parallel to NM must triangle JKL always be isosceles?

10. Why is Teacher telling me this?(Two Reasons) • It’s incredibly interesting • It parallels NCEA marking perfectly and thus, thinking about levels of thinking (metacognition) puts us in a more likely position to achieve at higher levels

11. Compare Form an equation Analyse Relate Apply And hence solve…. Solve (in context). Simplify+. Evaluate Explain Generalise Predict Fully justify Model SOLO TAXONOMY (after Biggs and Collis 1982) Describe Solve Calculate Simplify Factorise Define Identify Do simple procedure Multistructural Unistructural Relational Extended abstract Prestructural So How do they match up? Achieved with Merit Achieved with Excellence Not Achieved Achieved

12. What can I do? • Read each question and look for the instructional word which suggests which level of thinking is being asked for • Read through your own answers and assess what level of thinking you have applied

14. Activity : 2.6 2.7 2.11

15. Task : TES E8

16. Task: parallel task developing

17. Task: Rewriting a poor task.

19. Literacy strategies

20. Why focus on literacy in Mathematics? “Since any teaching strategy works differently in different contexts for different students, effective pedagogy requires that teachers inquire into the impact of their teaching on their students.” (NZC, p.35) Assessments written in English will always be, to some extent, assessments of English (Abedi, 2004; Martiniello, 2007 Lower language proficiency tends to be associated with poorer mathematics performance (Cocking & Mestre, 1988; Wiest, 2003).

21. Why focus on literacy in Mathematics? Research indicates that students peform 10% to 30% worse on arithmetic word problems than on comparable problems presented in a numeric format (Abedi & Lord, 2001; Carpenter, Corbitt, Kepner Jr, Lindquist, & Reys, 1980,Neville-Barton & Barton, 2005).

22. Literacy skills need to be taught systematically and consistently. • Learners should be given regular opportunities to consolidate their literacy skills by using them purposefully in order to learn. Key literacy skills that can be developed in Maths include: • Using talk to explain and present ideas • Active listening to understand • Reading for information • Writing short and extended responses

23. Listening and Talking Listening and talking can enhance the learning of mathematics when: • learners have regular opportunities to explain and justify their understanding of mathematical concepts • learners are given opportunities to discuss and explore ideas with each other, and share their mathematical reasoning and understanding • learners work collaboratively • learners use correct mathematical vocabulary

25. Active ways to engage with the text • highlighting e.g. highlight or underline specific information such as key words or phrases • supplying missing words or phrases e.g. in text, expressions, tables, diagrams, charts, labels, etc • sequencing e.g. getting learners to correctly sequence the steps in a solution • matching e.g. matching cards showing multiple representations of the same mathematical concept • classifying – Carroll diag. e.g. odd-one-out • evaluating mathematical statements e.g. true/false, always/sometimes/never • summarising e.g. condense facts/processes into key points • produce synopsis from researched information

27. Connectives • For adding information – and, also, too, as well as • For sequencing ideas or events – then, next, afterwards, since, firstly, secondly, finally, eventually • To compare – like, equally, similarly • To contrast – but, instead of, alternatively, otherwise, unlike • To show cause and effect – because, so, therefore, thus, consequently • To further explain an idea – although, however, unless, except, apart from, yet, if, as long as • To emphasise – in particular, especially, significantly • To give examples – for example, such as

28. Prepositions Prepositions locate nouns, noun groups, and phrases in time, space or circumstance e.g. at, on, onto, before, from, to, in, off, above, below • The temperature fell to 10 degrees • The temperature fell by 10 degrees • The temperature fell from 10 degrees

29. Activity • Matching words /equations