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Rich tasks, maths talk and cultural competencies 22 nd May, 2014, Christchurch Robin Averill Slide 2 Whia te iti kahurangi, ki te tuohu koe me maunga teitei. Pursue that which is precious, and do not be deterred by anything less than a lofty mountain. Mt Merapi, Indonesia Slide 3 The cultural competencies (Ttaiako) Mori learners enjoying achieving educational success as Mori Ako Whanaungatanga Manaakitanga Wnanga Tangata Whenuatanga Slide 4 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Slide 5 10 9 8 7 6 5 4 10 9 8 7 6 5 4 Slide 6 Lets investigate number traps! Lets try 1 Lets try 5 well record our working. Think of a number Divide it by 2 Multiply it by 3 and add 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 7 Lets investigate number traps! 5, 16, Think of a number Divide it by 2 Multiply it by 3 and add 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 8 Lets investigate number traps! 5, 16, 8, Think of a number Divide it by 2 Multiply it by 3 and add 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 9 Lets investigate number traps! 5, 16, 8, 4 Think of a number Divide it by 2 Multiply it by 3 and add 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 10 Lets investigate number traps! 5, 16, 8, 4, 2, Think of a number Divide it by 2 Multiply it by 3 and add 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 11 Lets investigate number traps! 5, 16, 8, 4, 2, 1 escape! Now try other numbers Think of a number Divide it by 2 Multiply it by 3 and add 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 12 Lets investigate number traps! Think of a number. Follow the instructions. Can you escape? Try other numbers. Can you always escape? Can you find any patterns? Can you design another trap by changing the rules or the condition for escaping? Think of a number Divide it by 2 Multiply it by 3 and subtract 1 This is now your number Is it 1? Is it odd? Yes No Escape!! Slide 13 Our own experience with persistence When do you persist with something? Why? When do you not persist? Why not? Slide 14 I persist when I know why Im doing it I know I can do it! Its fun! My friends are doing it Im being paid I can take a break when I need to I can get help when I need it Im encouraged to Ive got a good strategy and I know Ill get there in the end Slide 15 I give up when I cant see the point I dont enjoy it Im crap at it Others are giving up Im tired or hungry Only people not like me are persisting Ive tried hard but I just dont understand it Its dumb Ive got better things to do Slide 16 Themes Classroom environment Developing mathematical confidence Strong mathematical discourse High expectations Choice of task: Meaningful purposeful mathematics Connections between thinking, representations and mathematical ideas Slide 17 Persistence for mundane or challenging tasks? Slide 18 Sullivan et al., 2013 Slide 19 Making opportunities for strong maths discourse Probability example What is one thing that might happen to you tomorrow? How can we order our events to show how likely they are in relation to one another? I will see an unusual bird I will go shopping I will ride a motorbike I will read a history bookI will play some musicI will do gardening Slide 20 Language of direction Tokerau North Hauuru Rwhiti West East Tonga South tata near mamao far Slide 21 Talk moves (Chapin & OConner, 2007) RevoicingThe teacher tries to repeat what has been said by the student and then checks with the student that their revoiced statement is what was said So are you saying....? Is that right, Lena? Asking students to restate someone elses reasoning The teacher asks a student to repeat or rephrase what has been said by another, then follows up with the first student. Can you repeat what Ana just said in your own words? Ana, is that what you meant? Asking students to apply their reasoning to someone elses reasoning Teacher asks students to apply their own thinking to someone elses idea. Do you agree with Jons idea? Why/why not? Prompting students to add-on to someone elses idea The teacher asks students to build on someone elses idea. Tom, can you add to Jons idea? Using wait timeThe teacher waits at least 10 seconds for students to think and rehearse how they will explain their ideas. Take time to work out your answer and decide how you will explain it. Slide 22 Fermi problems How much toothpaste was used in New Zealand this morning? Slide 23 The cultural competencies (Ttaiako) Mori learners enjoying achieving educational success as Mori Ako Whanaungatanga Manaakitanga Wnanga Tangata Whenuatanga Slide 24 Durie, 1998, whare tapa wha model for health and well-being (family/social, physical, cognition, thoughts, spiritual) Slide 25 Cult rep frameworks Similarities: Participative teaching students at the centre and as connected active partners Key elements embedded in te Ao Mori (te reo me tikanga Mori) Holistic (draw on/link to more than cognitive elements) Knowledge of individuals High expectations Slide 26 What do the models offer? Teaching tools (C, c, feedforward, feedback, coconstruction...) Reflection and evaluation tools (ako, wnanga, manaakitanga...) Challenges (personal knowledge, te reo, tikanga, current contexts...) Ways to develop (relationships, coconstruction, communication...) Same or different for different sector groups (schools, departments...)? Slide 27 Culturally responsive practices Whare tapa wha Pronunciation/greetings/farewells Use of students language/s Acknowledging students culturally located knowledge Using suitable protocols Using a range of pedagogies Slide 28 Please can we have more maths? Whia te iti kahurangi, ki te tuohu koe me maunga teitei. Pursue that which is precious, and do not be deterred by anything less than a lofty mountain. Mt Merapi, Indonesia Slide 29 References Bueno, J., Weinberg, R. S., Fernandez-Castro, J., & Capdevila, L. (2008). Emotional and motivational mechanisms mediating the influence of goal setting on endurance athletes performance. Psychology of Sport and Exercise, 9, 786799. Cheeseman, J., Clarke, D., Roche, A., & Wilson, K. (2013). Teachers views of the challenging elements of a task. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics yesterday, today and tomorrow, Proceedings of the 36 th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 154-161), Melbourne, VIC: MERGA. Durie, M. (1998). Whaiora: Mori healthd. (2 nd ed.). Auckland, New Zealand: Oxford University Press. Hackenberg, A. (2010). Mathematical caring relations: A challenging case. Mathematics Education Research Journal, 22(3), 57-83. Hackenberg, A. J. (2010). Mathematical caring relations in action. Journal for Research in Mathematics Education, 41(3), 236-273. Jarvis, S., & Seifert, T. (2002). Work avoidance as a manifestation of hostility, helplessness, and boredom. Alberta Journal of Educational Research, 48, 174187. Locke, E. A., & Latham, G. P. (2002). Building a practically useful theory of goal setting and task motivation: A 35-year odyssey. American Psychologist, 57, 705717. Slide 30 References Locke, E. A., & Latham, G. P. (2006). New directions in goal-setting theory. Current Directions in Psychological Science, 15, 265268. Meyer, D. K., Turner, J. C., & Spencer, C. A. (1997). Challenge in a mathematics classroom: Students motivation and strategies in project-based learning. Elementary School Journal, 97, 501521. Middleton, J. A., & Jansen, A. (2011). Motivation matters and interest counts. Reston, VA: National Council of Teachers of Mathematics. Number trap from Holding, J. (1991). The investigations book. Cambridge: Cambridge University Press. Price, D. A., & Yates, G. C. (2010). Ego depletion effects on mathematics performance in primary school students: why take the hard road?. Educational Psychology, 30(3), 269-281. Rollard, R.G. (2012). Synthesizing the evidence on classroom goal structures in middle and secondary schools: A meta analysis and narrative review. Review of Educational Research, 82(4), 396-435. Seifert, T. L., & OKeefe, B. A. (2001). The relationship of work avoidance and learning goals to perceived competence, externality and meaning. British Journal of Educational Psychology, 71, 8192. Slide 31 References Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488. Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation: An International Journal on Theory and Practice, 2(1), 50-80. Sullivan, P., Aulert, A., Lehmann, A., Hislop, B., Shepherd, O. Stubbs, A. (2013). Classroom culture, challenging mathematical task and student persistence. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics yesterday, today and tomorrow, Proceedings of the 36 th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 618-625), Melbourne, VIC: MERGA. Tzur, R. (2008). Profound awareness of the learning paradox. In B. Jaworski & T. Wood (Eds.), The mathematics teacher educator as a developing professional (pp. 137-156). Sense: Rotterdam.