Shuffle Your Sums! Growing Mathematical Mind-Sets.

Jen our subject leader for maths, sent me some pictures of her latest growth mind set ideas that she has been trialling with 3 of her classes. I was intrigued to find out more not just because  I’m keen to see how far GM is being embedded in our classrooms [and staffroom] but because maths was one of my weaker subjects at school and I’m fascinated to see the strategies my colleagues use to support mathematicians like me! Our maths faculty have been changing their pedagogical approaches quite rapidly over the last year in preparation for the challenges the new G.C.S.E. will bring [if it ever actually happens] with its emphasis on confidence, fluency, problem solving and reasoning. Some of our learners however, do find some of the problem solving style of questions tough and aren’t quite as resilient in their pursuit of mathematical glory as they might be. Jen has been working on supporting a more resilient approach beginning in year 8.

I mentioned her work and initial thoughts in a previous blog

“Jen, our subject leader for maths, sees a natural relationship between the teaching of maths and GM, especially as the curriculum/G.C.S.E. requirements are changing. In between the Learning Walk interviews she asked me to drop in on 2 different maths lessons where she was introducing new GM ideas and was saying that the year 10 students found it hard to think ‘YET’-when they are finding a topic hard they shout “I can’t do it” and they know the “YET” bit is coming but getting there seems a long way off! I suggested that she needs to help them to think about getting to YET by trying to consider different possible strategies-we have to teach them, and model,  how to think strategically when they get stuck-they can’t just tough it out and come up with something. Thinking of the mantra 3BME or similar, I suggested [being in maths!] a formula for them to consider of 3BY-3 ideas to try to get to YET-see how it goes!”

She has worked hard to encourage her most recalcitrant students to try to avoid not doing anything at all other than giving up in their First Attempt At Learning by offering hints after they have tried at least something with their FAIL. The skills to ‘grow’ your maths mind set need to be taught and nurtured-the students don’t just appear ready, willing and able to accept failure or to think of different coping strategies-and nor do we. The hints given have allowed the students to see Miss model mathematical thinking and the opportunity to bridge the gap between their FAIL and Second Attempt At Learning.

You can see the problem set below for low/middle ability year 9 students.

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In their first attempts the student in the first photo worked out the number of flags but not the area of the triangle.

Hints are provided and the student moves on to their SAIL. If they get their FAIL correct, I suggested being given a NAIL-new attempt at learning so we could shout NAILed it-Jen is sleeping on selling that to her colleagues!

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The year 8 students shared their FAILS with each other as they attempted a question devised by Clair.

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Joe struggled with his FAIL, received some handy hints and got SAILing.

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Jimmy’s FAIL could read the Venn but didn’t add any details.

Hints were given and the SAIL followed.

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The hints may be in the form of reminding the students what they know already or reminding them of ‘stuck’ strategies they’ve used before. Sometimes Jen just re-emphasises the question to help the students re-read and think again-just as we encourage in their exams. Building up their confidence to cope with the ‘YET’ aspect of growth mind-set, which some of our younger students raised as a concern on our learning walk, http://blog.meolscophighschool.co.uk/?p=1712 will, I feel, be well worth the patient effort on our behalf. Jen filmed a couple of the lessons with IRIS and the faculty will be able to see the reaction of some of the students who struggled at first.

Beth has also been trialling the use of ‘hints’ and I went into her lesson to see the year 9 class working on advice a rugby coach might give based on maths to make a successful kick over the posts. You can see the FAILs, SAILs and final attempt in their books-Miss gave hints between each attempt. The use of coloured pens indicates when the students tackle their ‘challenge’ questions-these are rewarded with Growth Mind Set Star school bulletin nominations and postcards home.

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It’s too early to find concrete data evidence to make comments about the impact of the idea. Jen’s year 10 class did achieve decent grades in last week’s internal exam but this may be due to other factors, although individual student success stories are beginning to build. Zoe told me that her very low ability year 11 class had responded well and they seemed to see the hints as giving them the chance to start afresh, rather than being simply wrong. If the approach can build their confidence and make them stop and think-“where have I met this problem before” rather than giving up-brilliant for their maths exam and a good lesson for life.

Being resilient and overcoming obstacles isn’t just an aspect of Meols Cop GM for students-the maths curriculum changes expect a lot of our teachers too. As teachers we sometimes think that our students will never be able to tackle tougher questions and I’m sure that the original consensus amongst the faculty might have been “OMG some of our kids will never cope with this problem solving stuff!” Always expecting excellence of your learning or teaching can be difficult when changes may make you less certain of your ability, skills and knowledge. The faculty are working extremely hard to support and encourage each other –I thanked them this morning but as mathematicians they want to see the data that will prove their ideas are working [or not] I also know that they are on their 3rd version of our new assessment system-it would be easy to run with their first idea but they want the system to work and are prepared to trial, possibly fail, adapt and go again until they get it where they know it will work best to support learning. It would be remiss of me not to also mention that in response to the curriculum changes, Jen had asked her colleagues to change their approach to the year 9 curriculum half-way through the year-faculty growth mind-set in action-thank you!

When schools, faculties or individual teachers have to take on change and introduce new ideas the levels of stress can have a negative effect on performance. All of our teachers work hard, but being asked to work or consider working in different ways can initially increase work load and anxiety and needs the support and encouragement of others from our middle and senior leaders. Jen is a young leader who began with us as an NQT and took on the role of subject leader in her 4th year of teaching. She probably didn’t expect that to happen so quickly, although as senior leaders we should always be looking for, and developing potential leaders, sometimes situations arise and unexpected leadership is thrust upon people! Jen was telling me that she wants to survey her faculty with a NPQML style 360 degrees questionnaire to get honest answers re her leadership and the path the faculty are moving along. Thriving on feedback is a brave move but ultimately we must ask our students, parents and colleagues their opinions and encourage honest FISH feedback across Meols Cop.

The role of middle leadership is absolutely crucial in defining and shaping the current and future success of our school and we have to get it right. I can remember when I first took on leadership roles and struggling to deal with the usual issues of awkward people often older and more experienced than me, trying to introduce much needed change, trying to monitor, sorting out behaviour for other classes whilst teaching a full timetable myself and being accountable for my own results and the humanities faculty. The professional expectations required of a middle leader are much greater now and the addition of seconds in faculty are a great help. Clair and Jen work well as a duo, each with different strengths and interests and the mixture of experience and youth in the faculty supports and excites the two leaders.

We tell the students to work hard and practice hard to develop their mind set and become better learners and during my conversation with Jen it became apparent that she too was purposefully practising her own teaching skills to try to deal with an issue that we have been discussing across the school-how do we get the students to learn effectively/make their learning stick?

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https://pragmaticreform.wordpress.com/2014/04/05/cogsci/

The crucial cognitive structures of the mind are working memory, a bottleneck that is fixed, limited and easily overloaded, and long-term memory, a storehouse that is almost unlimited. If nothing has changed in long-term memory, nothing has been learned. Our teaching should minimise the overload of students’ working memories and maximise the retention in their long-term memories

@joe_kirby’s use of Willingham’s question should be posed in all of our classrooms and Jen wanted to find out more about how she could maximise retention in her math’s student’s long term memories.

Leon, our AHT, had sat down with Jen to discuss potential new approaches needed in the teaching of maths and sent her an American piece of research.

Shuffling Maths Problems

I know she has read it because I saw her notes! Along the same lines he shared this with Carmel [science subject leader]

Improving Students Learning

I had already shared an example of revision ideas building on quizzing and returning to older topics from an English school https://classteaching.wordpress.com/2015/01/29/supporting-learning-through-effective-revision-techniques/ by @shaun_allison with our staff and prepared a year 11 assembly to push the interleaving theme with the students and staff.

Asking our staff to engage with research to inform and improve their practice is relatively easy and pain free when it is very practical in nature [lesson study] and they can see immediate impact. Engaging with deeper research produced by non-teacher university colleagues can honestly be a tad hit and miss! Much as I try to provide CPD time, to really engage with some of the more detailed research does impinge on own time but the ideas gleaned and potential classroom impact can make it so worthwhile. You have to be quite resilient to cut through the language researchers use to seek the appropriate ideas that we could possibly use to help us get round learning barriers effecting our student’s learning. Jen has already borrowed ideas and began to formulate an approach of spacing out student learning by revisiting older topics to reinforce ‘stickablity’ of learning. 5 a day is a simple version already in use and proven to work-this new scheme that Jen is proposing trialling with control groups involved in year 9 and using lesson study to plan collaboratively, would see ‘quizzes’ on old topics included at the end of every modular test-not necessarily re teaching-just re-quizzing. If I have got it right it may work like this;

Topic 1 Topic 2 Topic 3 Topic 4 Topic 5
Assessmenttest on content Assessmenttest on T2 content

Quiz on T1

Assessment teston T3 content

Quiz on T1/2

Assessment test on content of T4Quiz on T1/2/3/ Assessment test on content of T5Quiz on T1/2/3/4

The 5 a day approach would continue each lesson to revisit both old and new learning. Our student voice tells us that they like this approach and that it helps them memorise their learning. By ‘shuffling’ the topics Jen hopes to see further improvements in the final G.C.S.E. grades and together with the faculty approach to growth mind-set, the students who have struggled should begin to feel far more confident in approaching the harder questions they face [previously perhaps for the first time in a school year] and have a change of learning attitude. I’ll feedback on the impact of the initiative on all students and different cohorts when it has had plenty of time to embed.

As you can see in the additional section below, it’s a piece of in-house and external research we need to follow carefully. A nice post I read last night shared the possibilities of spaced learning-from @Eddie Kayshun http://t.co/bwbkGxCgwo explains his approach to spacing learning in lessons and has other links to research information. Mike Bell’s Evidence Based Teaching Network yesterday put forward spaced learning in their ‘worth trying’ section. I’m not an expert on neuroscience but experience and gut feeling tells me there may be something in it!

There is a lot of evidence that practice is absolutely necessary to form long-term memories.  It’s entirely possible for a student to appear to have learned in the lesson – but to know nothing about it next week.  This is because the brain-cells have reset to zero because the pathway has not been exercised in time.

In the research there is a distinction between ‘massed-practice’ which happens at the end of the topic (after several lessons) and ‘spaced practice’ which happens at regular intervals after the first learning.  The classroom evidence is backed-up by the neuroscience – spaced practice is much more effective (ES 0.7 – high)

BEYOND MATHS-spreading news of the same issue

We have discussed current ideas that I had gathered at our subject leaders meeting and via our regular emailing of great ideas shared by other schools and educationalists on twitter. This opens up another potential blog of how social media can support CPD-if we are to be the best teachers/school that we can be-we need to bring the best possible practice and research into our school so we can take what is appropriate for our learners and teachers and adapt it for our use. Busy teachers and middle leaders don’t always have the time for this-it should be someone’s role-it isn’t acceptable for us to wait until we go on a course or a local pow-wow to bring the best local, national and international ideas into MCHS. Nor is it acceptable to ever be complacent and rest on our progress measures/Ofsted laurels-as a school we should have the mind-set of being inspired by the success of others. There are lots of like-minded people who will help and openly share their ideas with other schools. Before our meeting I read a super blog by Rachael Edgar @Dubai_Teachmeet in which she had collated her own work and other schools ideas on assessment and making learning stick

http://dubai-teachmeet.com/2015/02/22/assessment-after-levels-dont-reinvent-the-wheel-just-steal-the-hubcaps/

I shared some of her summaries of ‘making it stick’ and discussed Belmont Community School’s English scheme of learning which modelled interleaving and Swindon Academies assessment and teaching ideas to encourage the retention of learning. Our scientists immediately asked me if I knew of a similar approach in science and so I tweeted Dan Brinton @dan_brinton and David Didau @learningspy who had worked on Belmont’s example and Dan put me in touch with their science leader @Julie Ryder2. Julie kindly agreed to send us her scheme of learning which includes interleaving ideas. No questions asked, just generosity of spirit. @davidfawcett27 , having seen my tweet request then sent us his PE scheme of learning so one quick message resulted in quality school to school support. For wonderful collations of thoughts, research and practical school responses to GM and making learning stick, Ruth Powley-@powley_R, is the lady I turn to and borrow from.

http://www.lovelearningideas.com/blog-archive/2015/1/24/growing-gritty-learners

https://ruth-powley.squarespace.com/blog-archive/2015/2/27/velcro-learners

Face to face visits are equally thought provoking and fruitful ones provide the very best professional development. Eyes can be well and truly opened at what is happening elsewhere and needs to be happening here! Recent visitors have included South Wirral, Range, Holy Family, St Peters and St Pauls, St Augustines and KGV and we are really grateful to Wakefield City Academy for allowing in Hannah and Jen and for South Wirral [Tim, Sophie, Allan] on the 27th, Leon to Whalley Range on the same day, Wellington School for Carmel/Hannah, Flixton GS [Sam] and other arrangement talks have been opened with Lytham, Holmfirth, Crossley Heath and Poynton.

Despite the gloom that surrounds much of education, many teachers are trying to re-claim their profession and their CPD and as a consequence, shifting their own practice based on research and evidence, in a way I haven’t experienced before in my many years of teaching and leading. These are exciting times for those willing to develop their own mind set and engage. As leaders we have to set the right example by being prepared to model the traits of GM openly and explicitly-if we don’t, why should others follow?

5 thoughts on “Shuffle Your Sums! Growing Mathematical Mind-Sets.

  1. Cynthia Day

    This is extensively documents and thoughtful. Especially appreciate how you unpacked the somewhat dry content of set theory (etc) out onto post it notes and notebooks to EXPAND it and make it accessible and relevant. That the students are interacting around the topic is clear, as is your formative feedback. Thank you for all the links as well. Yay!

    Reply
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