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From Brussels Sprouts …

From Brussels Sprouts …. … to Summer Strawberries. Engagement. mathematical?. …involvement in the activity of the classroom. Relationship with mathematics Views of maths Feelings about maths Perception of ability Mathematical knowledge Habits of engagement.

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From Brussels Sprouts …

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  1. From Brussels Sprouts …

  2. … to Summer Strawberries

  3. Engagement mathematical? …involvement in the activity of the classroom.

  4. Relationship with mathematics • Views of maths • Feelings about maths • Perception of ability • Mathematical knowledge • Habits of engagement

  5. Engagement in mathematics is important because of the nature of the subject. There’s so much in maths. If I get behind in maths, it would probably be the worst subject to try and catch up on (Debbie). I am aware that I need to try my hardest. I am more attentive than in other classes. I know we need to know this (Sean).

  6. Tensions … I didn’t work to the depth required because I was bored with it (Jason). I work hard in other subjects. I talk the most in maths. In other subjects I’m quiet the whole time because I’m doing it (Tracey) It’s easier to talk than making my brain hurt (Bridget).

  7. Students develop habits of engagement. Homework Getting ready to learn How they ask questions How much they socialise How much they get involved in class discussions How they listen How they engage in each mathematical task

  8. A mathematics problem: g 48 16 and ¼ hours .. or is it? A machine prints four books in 10 minutes. How many will it print in two hours? How many hours would it take to print 390 books?

  9. Reflect on your feelings and engagement How did you feel before you saw the problem? How did you feel after you saw the problem? How aware were you of others doing the problem? Did these feelings affecting your doing of the problem?

  10. Reflect on your feelings and engagement Imagine the problem was given to a class of mixed-achievement Year 10 students as a starter. What range of behaviours would you observe?

  11. Relationship with mathematics 5. Habits of engagement Context of the moment Engagement in a mathematical task Unique learning experience and outcomes

  12. Context of the moment When students engage in a mathematical task, they are each situated in a unique context of the moment.

  13. Relationship with maths All Blacks romantic relationships issues with friends after-school jobs parents’ divorcing other subjects lack of vegetables family illness Teacher classroom hot classroom cold too bright social awareness seating arrangements Who I sit next to totally affects me (Moira) Engagement in a mathematical task

  14. Students have habitual pathways of engagement when doing a mathematics task Avoidance Superficial engagement Full engagement

  15. Pathway of Engagement - Avoidance Some things I just don’t attempt (Debbie). Look at what I did today. No maths (Mark). Going to the toilet, ruling up pages in their exercise book, organising their equipment, programming their calculator, eating, daydreaming, writing notes to each other, writing poetry, doodling, talking socially, writing out the problem as neatly as possible …

  16. Pathway of Engagement - Superficial I try and figure the problem out. After a wee while if I really can’t do it at all, I just give up (Bridget). I kind of get frustrated when I can’t do something. I just give up (Paul) Unprepared to think deeply about a problem.

  17. Pathway of Engagement – Full engagement I’ll read it a couple of times and think about it logically and sort of see what it actually means. I talk to some other people about it … see what their methods are (Katrina). When fully engaged, students think about the processes of solving problems, they persevere, use a variety of strategies and discuss mathematics with others.

  18. Asking for help I get frustrated. Can’t you just tell me what it is? Maths is like a silent movie because you either understand the storyline by following the action and another person explaining it, or you sit back, bewildered. Is this an indication that a student is engaged? I need the teacher to go over answers I get wrong. The way I learn is by the teacher explaining it to me and helping me understand on my level.

  19. Students have a set of engagement skills that operate at different levels of effectiveness.

  20. Perseverance Integrity Intimacy Independence Concentration Utilisation of feelings Cooperation Reflection

  21. The skill of continuing to do a mathematical task, despite experiencing difficulty. Perseverance

  22. Perseverance Commitment to searching for mathematical truth and understanding Integrity

  23. Perseverance Integrity Emotional engagement with mathematics Intimacy

  24. Perseverance Integrity Intimacy The skill of solving problems autonomously. Independence

  25. Perseverance Integrity Intimacy Independence The skill of remaining focussed, despite disruption. Concentration

  26. Perseverance Integrity Intimacy Independence The skill of being resilient to negative feelings felt during a task, and instead using them as a signal to persevere or change strategy. Concentration Utilisation of feelings

  27. Perseverance Integrity Intimacy Independence Concentration Utilisation of feelings The skill of discussing mathematics, solving the tasks cooperatively, and to ask for help as a strategy, rather than as a form of disengagement or dependence. Cooperation

  28. Keep going Integrity Intimacy Independence Concentration Utilisation of feelings Cooperation Being self-aware. Reflecting on own and others’ engagement. Reflection

  29. What can we doto enhance engagement? • Help students to recognise and act on feelings of confusion and worry when working on mathematical tasks. • Encourage students to develop effective engagement skills. Hmmmmmmm …….

  30. Some ideas … Be explicit about the importance of doing mathematics to learn. Get to know students’ engagement. Wait until everyone is ready to learn before revealing the problem. Give students a variety of problems of different contexts, difficulty, depth, and length. Make sure ALL students have the opportunity to experience confusion. Talk about your own engagement and/or the engagement of a tame mathematician. Normalise and EMBRACE confusion. Ask students to try a problem by themselves for a time before talking to a friend or asking for help. Ask students to reflect on how they solve problems. Report formally on engagement skills to school and parents.

  31. When doing maths … • Try the problem yourself before asking for help. • Don’t give up when you are stuck. • Seek understanding as well as an answer. • Expect confusion • Concentrate. Maths is thinky. • Remember that mistakes are windows into your thinking. • Cooperate with others. • Be proud of your progress. • Reflect on your doing.

  32. Naomi Ingram University of Otago, College of Education naomi.ingram@otago.ac.nz

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