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There are many recommendations on how to teach mathematics but fewer about the teaching of mathematics’ classes with Indigenous students. This webinar will examine how six principles for effective mathematics teaching were adapted to advice for teachers of schools with high numbers of Indigenous students.

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- 1. Finding a focus for ongoing teacher learning in mathematics: Six key principles Peter Sullivan 6 principles
- 2. Overview • Some stories • Six principles 6 principles
- 3. A story from a Grade 3 lesson I taught at Bathurst Island 6 principles
- 4. Football scores Saints 105 Bombers 98 6 principles How much are the Saints winning by? (Work out the answer in two different ways)
- 5. Football scores Saints 25 Bombers 18 6 principles How much are the Saints winning by? (Work out the answer in two different ways)
- 6. From a grade 3 lesson in the Kimberleys 6 principles
- 7. How many ways to make $10 6 principles
- 8. 6 principles
- 9. A suggestion as part of a geometry unit written for MiTK 6 principles
- 10. • Have pile of cubes. Ask the students to: – Build something using 15 cubes. Describe what you have built. – Build something which is 3 cubes high and 3 cubes wide made with 15 cubes. Describe what you have built. – Something like “make a tower of 3 cubes, put a yellow cube to the left, and blue cube to the north, …” • Repeat, adapting to the level of success of the students. 6 principles
- 11. A lesson I plan to teach to a year 8 class next Tuesday at CMS (Alice Springs) 6 principles
- 12. ONE HECTARE PARK • A conservation park is to be enclosed by a fence that has exactly 6 internal right angles. What might the park look like? • The total area of the park is 1 hectare. What might be the perimeter of the park? (give two different answers) 6 principles
- 13. What are the common characteristics of those tasks? 6 principles
- 14. Six principles as the basis of sustainable improvement 6 principles
- 15. What is the point of these six key principles ? • We can all do these things better (although you will find many of them affirming of your current practice) • Much advice is complex and hard to prioritise • The principles can provide a focus to collaborative discussions on improving teaching • The principles can be the focus of observations if you have the opportunity to be observed teaching 6 principles
- 16. Improving teaching by thinking about pedagogy • The following principles are a synthesis of: – Good, Grouws, and Ebmeier – Productive pedagogies – Principles of learning and teaching – Hattie – Clarke and Clarke – Anthony and Walshaw 6 principles
- 17. Key principle 1: • Identify important ideas that underpin the concepts you are seeking to teach, and communicate to students that these are the goals of your teaching, including explaining how you hope they will learn 6 principles
- 18. Feedback - better when they know … • Where am I going? –“Your task is to …, in this way” • How am I going? –“the first part is what I was hoping to see, but the second is not” • Where to next? –“knowing this will help you with …” 6 principles
- 19. In terms of learning intentions, we know • It is much more difficult to describe the purpose of lessons than we think • The learning intention should – not restrict – nor lower the ceiling – but provide focus to the students – and the teacher 6 principles
- 20. In terms of the subtraction lesson • There are many ways to find the difference between two numbers 6 principles
- 21. In this lesson, I need you to • show how you get your answers • keep trying even if it is difficult (it is meant to be) • explain your thinking • listen to other students 6 principles
- 22. 6 principles goals
- 23. Key principle 2: • Build on what the students know, both mathematically and experientially, including creating and connecting students with stories that both contextualise and establish a rationale for the learning 6 principles
- 24. Part 1: Using data 6 principles
- 25. • It is more important to know what the students know than what they do not • Learning mathematics is not a hierarchy of sequential steps on a ladder, but a network of interconnected ideas • Students can work on tasks that are beyond what they know – Students at GP 2 can work on GP 4 tasks 6 principles
- 26. Part 2: Connecting with “story” 6 principles
- 27. • A chameleon has a tongue that is half as long as its body ... • … how long would your tongue be if you were a chameleon? 6 principles
- 28. Part 3: Creating experience 6 principles
- 29. 6 principles
- 30. 6 principles goals readiness
- 31. Key Principle 3 • Engage students by utilising a variety of rich and challenging tasks, that allow students opportunities to make decisions, and which use a variety of forms of representation 6 principles
- 32. 6 principles For students to learn, two sets of factors must align • The first set of factors include that the: –students have the requisite prior knowledge; –curriculum is relevant to them; –classroom tasks match their expectations; –classroom tasks help them make connections –pedagogies use their knowledge and experience; –assessment regimes measure their learning.
- 33. 6 principles The second set of factors relates to • whether the students –are motivated to learn –see participation in schooling as creating opportunities –are willing to persist –connect effort and success
- 34. Why challenge? • Learning will be more robust if students connect ideas together for themselves, and determine their own strategies for solving problems, rather than following instructions they have been given. • Both connecting ideas together and formulating their own strategies is more complex than other approaches and is therefore more challenging. • It is potentially productive if students are willing to take up such challenges. 6 principles
- 35. 6 principles This connects to “mindsets” • Dweck (2000) categorized students’ approaches in terms of whether they hold either growth mindset or fixed mindset
- 36. 6 principles Students with growth mindset: • Believe they can get smarter by trying hard • Such students – tend to have a resilient response to failure; – remain focused on mastering skills and knowledge even when challenged; – do not see failure as an indictment on themselves; and – believe that effort leads to success.
- 37. 6 principles Students with fixed mindset: • Believe they are as smart as they will even get • Such students – seek success but mainly on tasks with which they are familiar; – avoid or give up quickly on challenging tasks; – derive their perception of ability from their capacity to attract recognition.
- 38. Teachers can change mindsets • This connects to – the things we affirm (effort, persistence, co- operation, learning from others, flexible thinking) – the way we affirm • You did not give up even though you were stuck • You tried something different • You tried to find more than one answer – the types of tasks we pose 6 principles
- 39. Getting started “zone of confusion” “four before me” •representing what the task is asking in a different way such as drawing a cartoon or a diagram, rewriting the question … •choosing a different approach to the task, which includes rereading the question, making a guess at the answer, working backwards … •asking a peer for a hint on how to get started •looking at the recent pages in the workbook or textbook for examples. 6 principles
- 40. Key Principle 3 • Engage students by utilising a variety of rich and challenging tasks, that allow students opportunities to make decisions, and which use a variety of forms of representation 6 principles
- 41. Related to those 4 tasks above .. • To what extent – Are they challenging? – Are they engaging? – Do they allow student decision making – Do they encourage different representations? 6 principles
- 42. 6 principles goals readiness engage
- 43. Key Principle 4: • Interact with students while they engage in the experiences, and specifically planning to support students who need it, and challenge those who are ready 6 principles
- 44. Enabling prompt 6 principles
- 45. Basketball scores Eels 18 Carp 13 6 principles How much did the Eels win by? (Work out the answer in two different ways)
- 46. Basketball scores Cats 8 Dogs 3 6 principles How much did the Cats win by? (Work out the answer in two different ways)
- 47. Extending prompt 6 principles
- 48. Darts scores Parrots 1005 Galahs 988 6 principles How much did the Parrots win by? (Work out the answer in two different ways)
- 49. 6 principles goals readiness engagedifference
- 50. Key Principle 5: • Adopt pedagogies that foster communication, mutual responsibilities, and encourage students to work in small groups, and using reporting to the class by students as a learning opportunity 6 principles
- 51. A revised lesson structure • In this view, the sequence – Launch (without telling) – Explore (for themselves) – Summarise (drawing on the learning of the students) • … is cyclical and might happen more than once in a lesson (or learning sequence) shepp secondary Launch ExploreSummarise
- 52. Football scores Saints 18 Bombers 13 6 principles How much are the Saints winning by? (Work out the answer in two different ways)
- 53. 6 principles goals lesson structure readiness engagedifference
- 54. Key teaching idea 6 • Fluency is important, and it can be developed in two ways – by short everyday practice of mental calculation or number manipulation – by practice, reinforcement and prompting transfer of learnt skills 6 principles
- 55. One aspect is transfer 6 principles
- 56. Another aspect is fluency 6 principles

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