Developing Mathematical Resilience Workshop

1. Friendly & Unfriendly numbers • You have a pile of numbers on each table. • Work with someone else to decide if you think each number is ‘friendly’, ‘unfriendly’ or ‘neutral’ • Place each number under the appropriate heading

2. Developing mathematical resilience & improving progression Day 1: Introduction to the growth zone model, mathematical resilience & coaching approaches <LOCATION> <DATE> <TRAINERS>

3. Introductions • Spend a few minutes introducing yourself to others on the same table • Find out what other people do & where they work • Discuss why you have enrolled on this course

4. Hopes & fears • Everybody take two sticky notes • On one, write your best hopes about the course • On the other, write your worst fears about the course (NB These will be kept anonymous, & will be referred to again later in the morning)

5. Course aims • To introduce teachers to the ideas of mathematical resilience and the growth zone model • To support teachers to develop mathematical resilience as they enhance their own maths skills • To equip teachers with strategies and resources to develop mathematical resilience in their learners

6. Course content

7. Maths accreditation • GCSE mathematics • Level 3 Award in Mathematics for Numeracy Teaching • ASDAN Mathematics Award • Other qualifications?

8. Coaching accreditation • Certificate in Coaching for Mathematical Resilience (CfMR): • Level 1 • Level 2 • Level 3 • Postgraduate Certificate in Developing Mathematical Resilience (Level 7)

9. Learning outcomes for Day 1 By the end of this session participants will have: • Considered the aims & content of the course • Explored affective barriers to maths learning • An understanding of mathematical resilience & the growth zone model • Developed their understanding of active listening skills • Experienced & analysed ALIVE maths activities • Begun the processes of reflection & target setting

10. Sharing insights • Work in pairs & share your personal experiences of maths learning • Write these on sticky notes • Stick your notes on the board under the two columns

11. Maths Teaching A.L.I.V.E. maths Accessible Linked Inclusive Values-based Engaging (Johnston-Wilder et al, 2015) T.R.I.E.D. maths Tedious Rote Isolated Elitist De-personalised (adapted from Nardi & Steward, 2003)

12. Heads & Tails A.L.I.V.E. maths Accessible Linked Inclusive Values-based Engaging

13. ‘It is not just behaviour it is managing fear, it is managing a very deep sense of failure, being rubbish’. ‘In the early stages [of teaching] it’s 90% psychology and only 10% maths’ (Quotations from maths teachers: ETF (2014) ‘Effective Practices in Post-16 Vocational Maths’)

14. Maths Anxiety “A feeling of tension, apprehension, or fear that interferes with maths performance” (Ashcraft, 2002) Results in: • Negative attitudes & motivation towards maths • Avoidance • Lower grades • Negative self-perceptions • Impact on working memory http://www.mccc.edu/~jenningh/Courses/documents/math_anxiety.pdf

15. Heads & feet On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

16. Heads & feet Solve this pair of simultaneous equations: x + y = 8 2x+ 4y = 22

17. What works for you? • What strategies have you found useful to overcome learners’ affective barriers & engage them in maths learning? • Discuss briefly with the person next to you. • Feedback key ideas.

18. Carol Dweck:Growth mindsets https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve

19. Positive norms (Jo Boaler) Key messages: • Everyone can learn maths to high levels • Mistakes are valuable • Questions are really important • Maths is about creativity & making Sense • Maths is about connections & communicating • Depth is much more important than speed • Maths is about learning not performing

20. Mathematical Mindsets For more information about Boaler’s ideas & approaches: www.youcubed.org • Detailed handout on positive norms: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/Positive-Norms-UK-Version1.pdf • Video for students ‘How to learn Maths’ https://www.youcubed.org/students/

21. Growth zone diagram

22. Key points • Cruising in the comfort zone can build self-confidence & provide opportunities for practice & automaticity. • New learning happens in the growth zone – it should be safe to make mistakes, get stuck, require support & find activity challenging & tiring. • The danger zone is where what is being asked is not within the learner’s reach at the moment, even with support. Stress increases and little or no useful learning takes place.

23. Zin Obelisk In the ancient city of Atlantis a monument called a Zin Obelisk was built in honour of the goddess Tina. The structure (a cuboid) took less than two weeks to complete. Your task is to determine on which day of the week the monument was completed.

24. Which zone are you in? • Having seen the task, which zone are you in – green, amber or red? • Use your RAG cards to show this • If you’re in the red, what might help you get back into the growth zone?

25. Working on the ZinObelisk • Ensure everyone is included & is able to contribute • If you get stuck, access help (but not the answer!) • Observe your own beliefs & attitudes in action & strategies you use to manage your emotions • Use your coloured RAG cards to reflect which zone you are in • Keep an eye on which RAG card others in your group are displaying – be responsive & supportive

26. Reflections on the ZinObelisk (1) • What were your reactions to the task? • What feelings did you experience while working on it? • What did you learn about yourself?

27. Reflections on the ZinObelisk (2) • Were you aware of being in the green, amberor red zones during the session? • What helped you stay in the growth zone? • How did you avoid or get out of the red zone? • What did your peers do to support you?

28. Reflections on the Zin Obelisk (3) • What behaviours did you expect to see while working on the task? • Did you observe them? • What do you do (or could you do) to help learners to work in a supportive & collaborative way?

29. Reflective Practice [Rolfe et al, 2001/Driscoll, 1994]

30. Four fours • Work in pairs with someone you don’t know • Use exactly four 4’s to form as many numbers as you can between 0 to 20, • You can use any combination of mathematical operators e.g. 0 = 44 – 44

31. Resilience • What does it mean to be ‘resilient’? • What do resilient learners look like? • Discuss in table groups

32. Mathematical resilience

33. A positive stance towards maths … Learners who have mathematical resilience will: • Persevere,seeking help & appropriate support when faced with difficulties • Work collaboratively with their peers • Have the language needed to express their understandings, misunderstandings & questions • Have a growth theory of learning – know that the more they work at maths the more successful they will be But for this to happen, teachers need to: • Start from where learners are at • Ensure support is available to avoid pressure on those who ‘can’t yet’

34. How much do you …? • Listen to learners • Stress high expectations & ability to succeed: • Believe in learners’ innate capacities • Provide challenge with support • Structure learning for growth & risk • Use learner-centred teaching strategies • Give learners real power & responsibility by providing opportunities to: • Express opinions • Make choices • Solve problems • Provide frequent opportunities for dialogue & 2-way feedback

35. Further reading • For further reading & research about mathematical resilience, see that course website: http://www2.warwick.ac.uk/study/cll/courses/professionaldevelopment/wmcett/maths_resilience_page

36. Active listening

37. Reflections on activities • How accessible & inclusive were these activities? • What made them so?

38. Accessible activities • Low floor/high ceiling: open problems that allow a variety of approaches at different levels • Visual representations: used to develop conceptual understanding, before moving to abstract symbols • Making sense: use contexts that are meaningful & encourage learners to develop intuitive methods, before introducing standard methods

39. Working in an MR way! • Work in groups in such a way as to include everyone – and enable everyone to feel safe • Ensure everyone has something to contribute • If you get stuck, access help (but not the answer!) • As you carry out the activity, try to observe your own beliefs and attitudes in action, and strategies you use for managing your emotions. • Use your coloured cards to reflect which zone you are in – red,amber,green

40. Security camera A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling of his shop. He places the camera in the corner of the shop (at point P) The camera can turn through 360° The diagram shows a plan view of the shop with ten people standing in it (From Bowland Maths: http://www.bowlandmaths.org.uk)

41. Security camera • Which people can the camera NOT see? • The shopkeeper thinks that 15% of the shop is hidden from the camera. Is he right or not? Explain.  • (a) What do you think is the best place for the camera, so that it can see as much of the shop as possible. • (b) How you know that this is the best place for the camera?

42. Heathrow Airport How many items of luggage pass through Heathrow airport each day?

43. Accessible activities • How ‘ALIVE’ was each activity? • In what way was each activity ‘accessible’? • How could you use or adapt these activities for your learners? • Do you know of any other accessible activities? In what way are they accessible?

44. Reflecting on activities • Were you aware of being in the green,amber or red zones during the session? • What helped you stay in the growth zone? • How did you avoid or get out of the red zone? • What active listening & other skills did you use to support your peers? • What active listening & other skills did your peers use to support you?

45. Solution focused review Reflect on how things have gone today in relation to mathematical resilience • How are we feeling? • What did we do that was helpful? • What else might we have done? • What else might others have done? On a scale of 1-10, what would 10 look like in terms of facing the challenge together?

46. Goal setting • Each day of the course you will be asked to set yourself a goal • In pairs, discuss what you would like to set yourself to commit to before day 2 • Support each other to map out your goals on the Goal Mapping template