Linda Shardlow Head of Mathematics

1. Meddling in the Middle – Who are my students becoming by spending time with me and who am I becoming as a teacher? Linda Shardlow Head of Mathematics

2. Meddling in the Middle • “Sage on the Stage: The teacher’s job was to instruct, inspire, scold, cajole. A ‘pupil’s’ job was to listen, attend, absorb, regurgitate.... • Guide on the Side: Child-centred education ,‘the child-as-learner’ and teachers as ‘facilitators of learning’. • Meddlers in the Middle: co-learning with kids, modelling how to take risks, do experiments, and how to be resilient when those experiments don’t come off” Professor Erica McWilliam and Peter Taylor, 2012

3. Jay McTighe Carol Ann Tomlinson Acknowledgements Judy Willis John Hattie Dr Timothy Sharp Carol Dweck Dylan Wiliam Will Richardson Julie Landvogt AtulGawande Ron Ritchhart

4. So…to begin What is teaching? “Teachers are responsible for bringing students into contact with ideas, ways of thinking, perceiving etc. that they might not encounter if left to their own devices” John Mason Blog Post April 7 2016

5. George Polya’s Ten Commandments Be interested in your subject. Know your subject. Know about the ways of learning: the best way to learn anything is to discover it by yourself.Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place. Give them not only information, but "know-how", attitudes of mind, the habit of methodical work.Let them learn guessing. Let them learn proving.Look out for such features of the problem at hand as may be useful in solving the problems to come - try to disclose the general pattern that lies behind the present concrete situation.Do not give away your whole secret at once-let the students guess before you tell it-let them find out by themselves as much as feasible. Suggest it, do not force it down their throats.

6. KnowThy Impact(Visible Learning for Teachers – Maximising Impact on Learning by John Hattie)

7. Percentage of Achievement Variance Teachers Students Home Peers Schools alPrincipal Potentials for Learning

8. Teaching Mathematics Six Key Principles* Provide students with high challenge, low threat experiences • Articulating Goals (Learning Intentions) • Making Connections • Fostering Engagement • Differentiating Challenges • Structuring Lessons Purposefully • Promoting Fluency and Transfer Formative assessment – formative feedback -assessment for learning. Meddling in the middle. *Teaching Mathematics Using Research-Informed Strategies, a 2011 ACER research paper by Peter Sullivan

9. Hattie’s Effect Sizes 0.4 is the average effect size

10. Sustainable Learning Building Skills for Independent Learning Jennifer S. Pease and Jeffrey P. Carpenter ASCD Express 28/2/13 From the US Office of Educational Technology website on the draft report titled Promoting Grit, Tenacity and Perseverance http://www.ed.gov/edblogs/technology/research/ “We suggest three strengths teachers should seek to develop in their students so that they can assume more responsibility as learners: self-regulation, persistence, and collaboration.” “This report takes a close look at a core set of non-cognitive factors—grit, tenacity, and perseverance—that are essential to an individual’s capacity to strive for and succeed at important goals, and to persist in the face of an array of challenges encountered throughout schooling and life”

11. IQ does not predict any growth in maths achievement “It’s not how smart we are; it’s how motivated we are and how effectively we study that determines growth in math(s) achievement over time”* The children who improved in math(s) over the years were disproportionately those who said they “agreed” or “strongly agreed” with statements such as, “When doing maths, the harder I try, the better I perform,” or “I invest a lot of effort in maths, because I am interested in the subject”– even if they had not started out as high-achieving students. In contrast, kids who said they were motivated purely by the desire to get good grades saw no greater improvement over the average. As for study strategies, those who said they tried to forge connections between mathematical ideas typically improved faster than kids who employed more cursory rote-learning techniques. *Kou Murayama in Child Development journal, Dec 2012

12. The Road Map Resilience in the face of challenge, persistence, positive mindset. • Strategic, frequent and analytical feedback helps students reflect on their learning in effective ways and understand the mathematics better, learning to think mathematically AND use skills. • We want students to become more self-managing learners and plan their own learning pathways, both individually and collaboratively. • And have a mindset that believes appropriate effort equals improvement. • And that mistakes are necessary, won’t destroy their world and can be used instructively.

13. How can we help students? Deliberately and purposefully attending to: • Analytical Scaffolding – noticing what students are doing in their mathematics and giving feedback • Social Scaffolding – allowing students to have a voice, opportunities for discussion and articulating their thinking, working together • Scaffolding that increases students’ capacity to self monitorand drive their own learning See Engagement in mathematics: defining the challenge and promoting good practices by Max Stephens, University of Melbourne, 2011

14. Don’t let any student “opt out” of learning Engagement in Mathematics Creating a culture of thinking mathematically What is mathematical thinking? Making thinking visible • Looking for, and noticing, patterns. • Noticing similarities/differences. • Formulating generalisations. • Testing these. Finding the limits. Justifying/Proving. • Reformulating. • Predicting. John Mason, Open University, UK, refers to the following mathematical ‘powers’: • imagining & expressing what is imagined; • particularising, specialising, & generalising conjecturing & convincing yourself and others; • organising & characterising; • focusing and de-focusing. • Opportunities for students to ‘play’ and discover for themselves. • Opportunities for students to articulate what it is they have discovered. • Use of discussion – “think, pair, share”, microlab & group work. • Use of mini whiteboards. • Use of wait time • Use of Pose, Pause, Pounce, Bounce • Use of exit cards, traffic lights etc. • Use of peer and self assessments. • Types of questions asked and who responds + “Why do you say that?”

15. David Perkins “Education should provide opportunities to provoke, surprise and upset and if it’s not doing that, it’s not doing its job” Getting “wild” is about shaking students out of surface understanding…elements of surprise…multiple connections help students get around shallow understanding.

16. Curiosity + Prediction = Sustained Attention • Judy Willis advises using curiosity as a routine in learning. Not only does this improve focus but resilience also improves as students become used to dealing with new and different situations.

17. Example of wildness in mathematics • Surd Arithmetic

18. Using web resources Parabolas and Angry Birds – TES resources http://www.teachmaths-inthinking.co.uk/activities/angry-birds.htm

19. The power of flipping http://ed.ted.com/on/FptWR31B

20. “People have this naive notion that teaching is really just explaining. And that the way to be a better teacher is to improve your explanations. Not so! Teaching is really about creating experiences that allow students to construct meaning”* Frank Noschese, Award-winning maths/sci teacher in the US, writing on his blog

21. Analytical scaffolding

23. Idea from Thinkers, a book of activities to provoke mathematical thinking.

24. Used with Y11 Mathematical Methods: Give an example of an equation of a power function that has a graph with an asymptote at x = 3(Think: what is it about your equation that makes the asymptote?)What if it also must have an asymptote at y = -2?What is your equation now?What if it has to have these qualities but also have two x-intercepts?What if it must also go through the origin in addition to all of the above?

25. Stop and Think Think about a class you taught todayHow did you give opportunities to students to think and then make this thinking visible?How do you know what to do next with these students?

26. See assessment as feedback on teaching John Hattie says “Of course..assessment is about the student, but the power of interpretation and the consequences of assessment are more in the hands of the teachers.” (Visible Learning for Teachers p 163) He proposes that all assessment is seen as feedback FOR TEACHERS on the extent to which learning has taken place and WHAT TO DO NEXT.

27. Feedback • Focusedteacher feedback that is both frequent and diagnostic is a key factor in increasing student self-efficacy and their ability to control their own learning • It needs to focus on how to progress from prior to desired outcomes. • Hattie recommends rapid, frequent feedback to assist with meeting achievable challenges and Judy Willis advocates this so that incorrect knowledge doesn’t get laid down in the brain’s neural framework.

28. By using continuous formative assessment practices coupled with specific feedback mechanisms, teachers can help students pursue the path of persistence. Thoughtful formative assessments provide opportunities for students to attempt challenging tasks before performing on a summative or final assessment. Acknowledging the reasons behind their accomplishments will help foster students' self-efficacy and responsibility for their own learning and ultimately encourage future persistence (Peterson, C., & Seligman, M. E. P. (2004). Persistence [Perseverance, industriousness]. In C. Peterson & M. E. P. Seligman, Character strengths and virtues: A handbook and classification (229–248). Oxford: Oxford University Press.)

29. What does formative assessment allow us to see and take notice of? • We can make learning visible: • what do students already know (or believe they know) • what new learning has been achieved and • what have students understood? • We can poke and push thinking, ask questions that deepen, broaden and extend their knowledge (ie we can “meddle”) • We can help students become better self-managers of their learning through a process of identifying where they are at and how to move forward

31. NOT just for Years 7 to 10

32. Social scaffolding

34. My version of the Microlab Protocol – Groups of 3 • Given an activity with three sets of mathematics problems. Students given around 5-10 mins to work on their problems individually • Sharing - student who did Problem 1 then has 1 minute to tell the others (with no interruptions or questions) what they did on their problem. Others do the same. • More Sharing – All students who attempted problem 1 come together and come up with the best possible response. • Back to original groups and students work on the other two problems they did not do first, with an ‘expert’ on each problem now in each group to assist.

35. Scaffolding to promote autonomy and self-regulation

36. Challenge students’ beliefs about themselves as learners Ask them • What do you believe • About Yourself? • About yourself in maths? We all make judgements about others and ourselves that aren’t necessarily true. Stop and re-think.

37. Talk to students about being mindfully proactive Many students fail to understand their role in controlling their own learning Nothing gets in unless you shine your ‘attention spotlight’ on it It’s not just about waiting for something to happen and reacting to it

38. Promoting Risk Taking and Academic Resilience through the use of mini whiteboards Mini whiteboards can assist with this as their “erasability” means students can try something, get instant feedback and try again. Mistakes are seen as a natural, and hopefully, essential, part of learning. The quick feedback also means incorrect strategies/concepts are not left too long in students’ brains to create difficult-to-move thinking links

39. My thinking is to emphasise to students the ongoing journey of learning and how it doesn't stop at the test. Mistakes are used to focus their future learning. I have 'ditched' the revision class before the test in favour of a follow up after the test class where students work in groups to assess the learning shown on the test. I have increased the frequency of written quizzes (which I call Check for Understanding quizzes) which students complete at the start of a topic (to act like a pre-test) and during the topic so that, hopefully, students don’t get ‘lost’ so often and I am given more authentic opportunities to intervene and re-direct.

41. I have actively tried to take a more ‘interventionist’ approach in the last couple of years and purposefully used formative assessment more often, engaged students in more peer-peer teaching, openly discussed approaches to learning such as mindset, garnered feedback through Google Docs survey tool and used focus-intense resources (even using mime to illustrate what a radian is with Beethoven’s 5th as background) to ‘hook’ students in and reinforce the idea that knowledge had to be made by them and guided by me, amongst others…Throughout, I talked about the importance of risk-taking, ofaccepting the difficulty and the promise of challenge, ofcontinually reflecting on errors in order to use them to support further learning and the importance of extending one’s reach.

42. From Hattie’s research

43. What I’ve noticed • Students expect to both know and give a 'why‘ • Students expect to see criteria in assessment • Students are happier to ask each other, not always me • Number of procedural questions has reduced • Students are using 'thinking language' in their reflections and acknowledging that their teacher makes them think • Students are more comfortable taking risks as they realise mistakes are a necessary part of learning • Students are more interested in knowing how to learn better, not just how to get a better mark

44. And this was drawn for me by my Year 9s at the end of last year OUR CLASS

45. Think about a class you have tomorrow. How WILL you give opportunities to students to think and then make this thinking visible?How will you know what to do next with these students? So:What are yougoing to STOPdoing?What are yougoing to KEEPdoing?What are yougoing to STARTdoing?

46. It isn’t over yet. It will never be over. The journey that is my learning, about my teaching and my students’ learning, ‘works in me like madness’“And there’s no end of voyaging when once the voice is heard”**From Gerald Gould’s poem, Wander-thirst