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Research into practice: What we can learn from research into good tasks

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  1. Research into practice: What we can learn from research into good tasks Peter Sullivan AISNSW 2010

  2. What are the challenges you are experiencing in teaching mathematics your school? AISNSW 2010

  3. Timeframe (too much curriculum) • Kids did not problem based teaching • Making it relevant, especially for low achievers • Buildinhg confidence • Diverse ability range • Retention • Busy lives of kids • Extension • External influences incluidngnaplan, parent expectations n… • Levels of concentration • Gaps in prior knowledge • Disruptions to school routine AISNSW 2010

  4. Overview • Findings from research • The Australian mathematics curriculum • 5 principles for improving teaching AISNSW 2010

  5. tasks and Teacher actions • We investigated ways that particular types of mathematics classroom tasks create different opportunities for students and different challenges for teachers. • the type of task influences the nature of the learning (e.g., Christiansen & Walther, 1986; Hiebert & Wearne, 1997) AISNSW 2010

  6. Task processing model from task to lesson (Stein, 1996) Mathematical task as presented in instructional materials which, influenced by the teacher goals, their subject matter knowledge, and their knowledge of students, informs … … mathematical task as set up by the teacher in the classroom which, influenced by classroom norms, task conditions, teacher instructional habits and dispositions, and students learning habits and dispositions, influences … … mathematical task as implemented by students which creates the potential for … … students learning. AISNSW 2010

  7. Teachers transform tasks • Stein et al. (1996) noted the tendency of teachers to reduce the level of demand of tasks. • Doyle (1986) and Desforges and Cockburn (1988) attribute this to complicity between teacher and students to reduce risk • Tzur (2008) … two key ways that teachers modify tasks: • at the planning stage; • if responses are not as intended. AISNSW 2010

  8. Our goals were to describe • how the tasks respectively contribute to mathematics learning • the features of successful exemplars of each type • constraints which might be experienced by teachers • teacher actions which can best support students’ learning

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  10. Self ratings of perception of mathematics in % (n = 930) AISNSW 2010

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  13. While there was not much difference overall between levels, there was a big difference (mean 3.5 to 5.5) between classes AISNSW 2010

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  15. In summary • At each of these middle years levels there is a range of satisfaction and confidence, and teachers should be aware of this • Teachers make a difference and they need support to both find out the students levels of satisfaction and confidence, and to do something about it if they are low

  16. Qu 9 • In this table there are three maths questions that are pretty much the same type of mathematics content asked in different ways. • Put a 1 next to the type of question you like to do (learn) most, 2 next to the one you like (learn) next best and 3 next to the type of question you like (learn) least. • We don’t want you to work out the answers. AISNSW 2010

  17. Preferences for liking, and learning from, the task types as a % (Q9) AISNSW 2010

  18. 11. ... Put a 1 next to the type of question you like to do (learn from) most, 2 next to the one you like (learn from) next best, and 3 for the type of question you like (learn from) the least: AISNSW 2010

  19. Preferences for the Task Types as a percentage AISNSW 2010

  20. From a different survey after a unit of work AISNSW 2010

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  22. Student opinions about their mathematics classes: Some free format responses AISNSW 2010

  23. In summary, it seems that the students were extraordinarily articulate about what they wanted in their maths lessons • In synthesising the responses, students like lessons that • used materials (although these were not structured materials), • were connected to their lives, • involved games, • were practical with some emphasis on measurement, • in which they worked outside, • The see “like” and “learn” as different • with the method of grouping being important, and • over half of the students claim to like to be challenged. AISNSW 2010

  24. What does this mean? AISNSW 2010

  25. In summary • The students were extraordinarily articulate about what they wanted in their maths lessons • The first characteristic of the responses is the diversity of aspects on which the individual students commented, suggesting that there is no commonly agreed ideal lesson, and there are many ways to teach well. AISNSW 2010

  26. The ways of working in class are clearly important for students, and however the teacher intends that the student work, the reason for this needs to be clarified for the students.. AISNSW 2010

  27. A preliminary task • In 5 words or less, write down an aspect of teaching mathematics that you would advise beginning teachers to ensure they think about in all of their lessons AISNSW 2010

  28. But first ... • An underlying assumption is that at least some learning should come • from engagement of individuals • with • tasks • each other AISNSW 2010

  29. Some of the key decisions • Mathematics success creates opportunities and all should have access to those opportunities • The curriculum should prioritise teacher decision making • The curriculum should foster depth and important ideas rather than breadth • Students can be challenged within basic topics, including the advanced students AISNSW 2010

  30. There are 3 content strands • Number and algebra • Measurement and geometry • Statistics and probability AISNSW 2010

  31. … and 4 proficiency strands • Understanding • Fluency • Problem solving • Reasoning AISNSW 2010

  32. Key teaching idea 1: • Identify big 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 AISNSW 2010

  33. An example for us to discuss • Write a sentence that has5 words, with an average of four letters per word (no 4 letter words) AISNSW 2010

  34. Some questions • What is the mathematical point of that task? • What is the pedagogical point of that task? • How do you make these points explicit to students? AISNSW 2010

  35. AISNSW 2010

  36. Some questions • What mathematical actions can be addressed by working on that task? AISNSW 2010

  37. Which card is better value? Please explain your thinking. AISNSW 2010

  38. Some questions • What is the mathematical point of that task? • What is the pedagogical point of that task? • How do you make these points explicit to students? AISNSW 2010

  39. year 7 • Determine mean, median, and range and use these measures to compare data sets explaining reasoning including use of ICT AIZ Zone 2 & 3 Day 1

  40. year 7 • to understand and become fluent with written, mental and calculator strategies for all four operations with fractions, decimals and percentages AIZ Zone 2 & 3 Day 1

  41. year 8 • Generalise from the formulas for perimeter and area of triangles and rectangles to investigate relationships between the perimeter and area of special quadrilaterals and volumes of triangular prisms and use these to solve problems AIZ Zone 2 & 3 Day 1

  42. year 9 • Work fluently with index laws in both numeric and algebraic expressions and use scientific notation, significant figures and approximations in practical situations AIZ Zone 2 & 3 Day 1

  43. year 9 • Solve problems involving linear simultaneous equations, using algebraic and graphical techniques including using ICT AIZ Zone 2 & 3 Day 1

  44. year 10 • Understand and use graphical and analytical methods of finding distance, midpoint and gradient of an interval on a number plane AIZ Zone 2 & 3 Day 1

  45. Key teaching idea 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 AISNSW 2010

  46. Establish classroom ways of working • Examples of “norms” • errors are part of learning • all students must persist • all students must be willing to justify their thinking • working as a community of learners benefits everyone AISNSW 2010

  47. An idea we can discuss • 5 people went fishing. The mean number of fish caught was 4, and the median was 3. How many fish might each person have caught? AISNSW 2010

  48. Some questions • What mathematical actions can be addressed by working on that task? • What might be the challenges in turning this into a lesson? AISNSW 2010

  49. What are enabling prompts? • Enabling prompts can involve slightly varying an aspect of the task demand, such as • the form of representation, • the size of the numbers, or • the number of steps, so that a student experiencing difficulty, if successful, can proceed with the original task. • This approach can be contrasted with the more common requirement that such students • listen to additional explanations; or • pursue goals substantially different from the rest of the class. AISNSW 2010

  50. Factors contributing to difficulty • It may not be clear which aspects may be contributing to a particular student’s difficulty, but by anticipating some of the factors, and preparing prompts that, for example, • reduce the required number of steps, • simplify the modes of representing results, • make the task more concrete, or • reduce the size of the numbers involved, • the teacher can explore ways to give the student access to the task without the students being directed towards a particular solution strategy for the original task. AISNSW 2010