Buying In

​I have just finished my 4th year of teaching at Tarleton Academy, where I started as an NQT. Throughout that time the school has taught mixed attainment in all subjects – apart from Maths. This is largely because as a faculty we have contested for years that ‘maths is different to other subjects’ and ‘you can’t teach mixed attainment classes in maths.’ So when I was asked to go to the first #mixedattainmentmaths conference in January 2017 on a Saturday afternoon in Birmingham I was against the idea. In addition, at this point I had a rule – no working on a Saturday. However I reluctantly decided to go along (partially because I didn’t have an excuse not to go!) with an open mind and at the very least get some ideas to develop my teaching.

I went to the conference with my school’s Director of Standards Jo Bacon (@miss_jobacon) and we were ready to sink our teeth in – starting with a team selfie.

The fact that so many people had given up their time – including those running workshop sessions who did it for free – and travelled from all over the country is a testament to the hard work Helen Hindle had put in to organising the event. The opening presentation began and went through the purpose of the conference, including what the sessions were about and why we were all here. Being someone who had been sceptical of teaching mixed attainment maths I was ignorant of one of the underlying fundamental reasons behind it – no child has a fixed ‘ability’. This struck home with me straight away. Why do we tell students at an early age that they are of certain ability? And what impact does this have on students? But then how do we cater for students at different stages in their learning? I needed to know more and I was keen to find out.
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​​My first session was with Mike Ollerton on using geoboards and that’s all it took for me to see what teaching mixed attainment classes was all about. I am sure anyone who has had the pleasure of learning from Mike will appreciate how amazed I was, having gained so many ideas in such a short space of time. I have since used ideas from his session on several occasions with fantastic results, but that is for another blog!

​My next session also had a massive impact, thanks to Zeb Friedman who shared her experiences of teaching mixed attainment classes in Key Stage 4. There were many things that I took from her session, and the resource I liked the most was learning journeys. I love how she uses GCSE questions along with a learning journey at the very start of a unit so that students can see the types of question they might expect to be asked. A mini write-up of my experiences of using Zebedee’s ideas can be found at http://www.mixedattainmentmaths.com/blog
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By the end of the day I was fully on board. Having the opportunity to learn from such experienced, knowledgeable people with a passion for teaching mixed attainment maths made a massive impact on my development as a relatively inexperienced teacher, and I can’t thank each of them enough. Since the first #mixedattainmentmaths conference I have tried a number of the ideas that were shared and I am looking forward to sharing my experiences, but for now I am happy to say that it has changed my perspective on teaching, and the way that I teach. I have since changed my rule on working on Saturdays, and I have bought in to mixed attainment maths.

Helen Hindle - @helenhindle1

My rationale for choosing to work with mixed-attainment groups  
The reason I feel so strongly about the importance of teaching mathematics in mixed attainment classes is because in the schools that I have worked in which did set, Pupil Premium students were disproportionately represented in the lower sets. The Social Mobility Commission report suggests that this isn’t unique to those schools, they found that ‘children from low Socio-Economic Status backgrounds…are more likely to be placed in low ability groups.’ (Shaw, Menzies, Bernades and Baars, 2016, Page 37). They go on to describe the profound negative impact that this can have on pupils’ future social mobility.

Equality of opportunity and achievement
If schools use examination and assessment results to group pupils then it is possible to see why pupils from low Socio-Economic Status backgrounds often end up in the lower sets. One of the conclusions from the Social Mobility Commission report is that, ‘Overall, family influences such as parental engagement with education and expectations have a strong effect on the educational attainment of children.’ (Shaw, Menzies, Bernades and Baars, 2016, Page 36). Parents who place a high importance on academic achievement are more likely to check that their children are completing homework, help with homework tasks, encourage their child to attend revision lessons and may even pay for private tuition. The report found that ‘Low Socio-Economic Status White British families tend to be less engaged in their children’s education …and this may play a role in explaining attainment gaps.’ (Shaw, Menzies, Bernades and Baars, 2016, Page 36.)

The dangers of limiting pupils’ achievements
Once pupils have been placed in a ‘set’ this sends messages to both pupils and teachers about what these pupils are capable of achieving. Pupils too often develop a fixed mindset about their mathematical ability, assuming that they are “rubbish” at maths and that there is no point in trying as they are only going to fail anyway. Hattie describes how students assessed as lower-attainment often ‘underestimate their achievement and, over time, they come to believe their lower estimates and lose the confidence to take on more challenging tasks.’ (Hattie, 2012, page 79). While research carried out by the Education Endowment Foundation states that ‘It appears likely that routine setting or streaming arrangements undermine low attainers’ confidence and discourage the belief that attainment can be improved through effort.’ (Education Endowment Foundation, 2017, Page 2).
Teachers often follow different schemes of work for lower attainment groups, thereby limiting the learning opportunities for these pupils. Research carried out by Wiliam, and Bartholomew revealed that ‘..teachers teaching bottom sets…had lower expectations of their students, frequently set work that was undemanding…used a narrower range of teaching approaches and hardly ever responded to students’ frequent requests for more demanding work…’ (Wiliam and Bartholomew, 2001, Page 7). It is therefore not surprising that once placed in a lower ability group pupils continue to fall further and further behind. Research conducted by Francis and Wong revealed that pupils placed in lower ability sets rapidly ‘begin to construct themselves as ‘not much good’ and ‘not academic’, with implications for their future learning, aspirations, and classroom behaviours.’ (Francis and Wong, 2013, Page 5.) These implications mean that once a pupil is allocated to a lower attainment group they are unlikely to move out of it.

Problems of disaffection and self-confidence
The issues with setting are not restricted to pupils in lower attainment groups. Nardi and Steward argued that there exists ‘a large group of learners who are ‘quietly disaffected’ and whose mathematical potential has yet to be fulfilled.’ (Nardi and Steward, 2005, Page 1). They conducted research into the attitudes of year 9 pupils in ‘middle sets’ and concluded that these ‘quietly disaffected’ pupils, ‘seemed to perceive mathematics as a demanding subject, in which only exceptionally intelligent people can actually succeed.  Lack of success in mathematics tended to be interpreted by the students as being due to lack of intelligence on their part, which led to overwhelmingly negative feelings about their own mathematical ability.’ (Nardi and Steward, 2005, Page 4). Research carried out by Boaler, Wiliam and Brown revealed that setting can also have a negative effective on the way that pupils in higher attainment classes perceive maths and their experiences of learning mathematics. ‘Approximately one-third of the students taught in the highest ability groups were disadvantaged by their placement in these groups because of high expectations, fast-paced lessons and pressure to succeed. This particularly affected the most able girls.’ (Boaler, Wiliam and Brown, Page 6, 2000).

​Problems of labelling and associated language
When working in schools that set I was dismayed to hear the language associated with setting from both teachers and pupils. Higher attainment classes were frequently described as ‘top sets’ while lower attaining classes were described as ‘bottom sets.’ The language of ‘top’ and ‘bottom’ sends messages about the desirability or undesirability of sets. I’ve heard teachers telling poorly behaved students that they ‘don’t deserve to be in the top set’ and unless their behaviour improves they will be ‘moved down’ a set. Poorly behaved students often do underachieve in terms of attainment because their behaviour had prevented them from learning successfully in their lessons. Too often these pupils do move down the sets once their attainment results show that they aren’t ‘top set’ material. I have also heard teachers deciding what certain sets are going to be capable of achieving before having even met the students in those classes. For example, I remember one teacher coming to me with his new timetable after seeing that he had a year 11 class, set 4 of 5, to tell me that he couldn’t be expected to get any C grades out of that class. At the time, he hadn’t even seen his class list, all he knew about the class was the set number.

Impacts of teaching mixed-attainment groups
When I have led departments in which practice has moved from setting to mixed attainment it has had the following impact:-

• Pupils and teachers developed growth mindsets
• Pupil collaboration became embedded
• Pupils were more active in their learning
• Student voice revealed that pupils' attitudes towards mathematics were much more positive
• There was far greater collaborative planning and sharing of pedagogy across the department, which lead to greater cohesion across the department
• There was a clear vision and ethos in Maths which both pupils and teachers could articulate
• Teachers' expectations of behaviour and attainment were raised
• There was far greater differentiation evident in the planning and delivery of lessons
• There was a wider range of types of activities evident in the planning and delivery of lessons
• There was a significant improvement in the % of pupils achieving or exceeding their monitoring grades in all classes and year groups
• Behaviour across the department dramatically improved, with a greatly reduced number of incidences of pupils being removed from the classroom and 'Attitude to Learning' scores improved across all classes and year groups
• Pupils' own expectations of behaviour and attainment were raised.

 
Developing my practice
Teaching is complex whichever way pupils are grouped. However, I firmly believe that working with mixed attainment classes made me change my practice. There is a myth that teaching mixed attainment classes is harder, a myth which I believed in until attending Jeremy Hodgen’s workshop at the first Mixed Attainment Maths conference. Jeremy pointed out that there are lots of countries in which setting in mathematics is not typical and that when these teachers move to England and are asked to teach sets they find this difficult because it is different to what they are used to. Teaching mixed attainment classes is for many teachers in England, different to what they are used to and therefore seems difficult. This is why I believe it is so important to build a community of mixed attainment maths teachers who are happy to share their experiences and ideas and to support one another to develop their practice of teaching mixed attainment classes.

​References
Ethnicity, Gender and Social Mobility
28th December 2016
Social Mobility Commission - Shaw, Menzies, Bernades and Baars,
 
It’s not which school but which set you’re in that matters: the influence of ability-grouping practices on student progress in mathematics.
2001
Dylan Wiliam & Hannah Bartholomew
 
Teaching and Learning Toolkit - Setting or Streaming
2017
Education Endowment Foundation
 
Visible Learning for Teachers - Maximizing impact on learning
2012
John Hattie
 
What is preventing social mobility?
A review of the evidence
March 2013
Professor Becky Francis and Dr Billy Wong
 
Attitude and Achievement of the Disengaged Pupil in the mathematics Classroom (Updated)
March 2005
Nardi, E. and Steward, S.
Students’ experiences of ability grouping— disaffection, polarisation and the construction of failure
2000
Jo Boaler, Dylan Wiliam and Margaret Brown

For most teachers being observed or having a learning walk can be a most stressful event however this can be magnificently compounded if the observer has no specialist knowledge of mathematics whilst evaluating a mathematics lesson. Consequently this can mean a teacher can unjustly be put on a performance contract and their career potentially ruined, when in fact they might be exactly what mathematics education requires.

A possible solution to this particular area of concern may be found in a report mentioned by Mike Ollerton at the mixed attainment conference June 2017, 'Made to Measure', May 2012 by Ofsted, in particular paragraphs 127 and 128. The evidence of the study of the report supports the fact that for senior leaders whose specialism is not mathematics, gaining an understanding of what the best mathematics education
involves presents a significant challenge. For mixed attainment classes to be successful and for teachers to feel confident to deliver such classes then we need to have on board the Senior Leadership Team. They need to have the right training or indeed be chosen appropriately for their mathematics speciality, if there is no budget for professional development.

​How does the observer measure progress in a mixed attainment mathematics class when as John Mason once said, “teaching takes place in time, but learning takes place over time” (Griffin, 1989)? Can the observer see that they may need to follow up with further sequential observations or learning walks? How can learner performance be effectively reported to management in a mixed attainment class?
___________________________________________________________________
Mathematics: made to measure, Messages from inspection evidence,
Published: May 2012, Reference no: 110159
''127 - Increasingly, subject leaders and senior staff also monitored provision through ‘learning walks’ (where several classes were each visited for a short time). These have the potential to provide leaders with a quick overview of teaching and learning and can be used for specific checks such as: adaptation of work to different sets/groups of pupils; consistency of approach among teachers; use of talk; and compliance with school and departmental policies, for instance on methods of calculation. However, schools’ records showed that learning walks were frequently concerned with checking generic features or policy requirements such as displaying lesson objectives, having seating plans, and making ‘next step’ comments in marking. They rarely focused clearly on the quality and mathematical detail of learning and progress over time; for instance, how well the activities were leading to the intended learning for all pupils, and whether the approach/resources promoted understanding and made links with prior learning”.

“128. A further positive development has been a broadening of leaders’ monitoring activities to include features such as scrutiny of pupils’ work; questionnaires or interviews with staff and pupils; and checks on planning, use of homework, assessment records and the quality of marking. These activities were sometimes distributed through the school year or they were concentrated in an intensive period of review of the subject. While in most of the schools the systems and structures were suitable, the lack of attention to mathematical detail impeded faster improvement. Sometimes a weakness was identified but then not followed up in the areas for development or linked to professional development. For senior leaders
whose specialism is not mathematics, gaining an understanding of what the best mathematics education involves presents a significant challenge''.
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Griffin, P. (1989). Teaching takes place in time, learning takes place over time.
Mathematics Teaching, 12–13.

Going from the person standing up in a meeting when mixed ability was mentioned and being the one to say I don't think this is for maths, to being a total convert and implementing this in all of key stage 3 from September. 

I had attended the conference having trialled mixed attainment in year 9 and having had successes and learning curves. My biggest learning gain of the conference was getting past the in built I must stand at the front and do an example of a new topic because all learners don't know it. Helen Hindle's workshop showed how all learners can be stretched and there was no lid on learning through the key learning aids being on the table and structured tasks where learners pick their individual starting point. Pupils help each other whilst the teacher works the classroom with teacher questioning to get pupils to their goal. The learning journeys made this very clear to the pupils who were visually able to see their own journey.

The second highlight of the day were the Cre8ate maths resources with applications to real life. Ready made resources that were engaging for all types of learners and encouraged growth and progress, again without being teacher led pupils could achieve their goal. These resources perfectly complemented mixed ability teaching.

The key I learned from all the workshops is how to question for all pupils to achieve! 

Thanks you so much ! I now feel fully prepared and I am already using the ideas in lessons.

​I attended the first Mixed Attainment Maths conference in January and really liked what I saw.  In the past I have researched self-efficacy/setting and peer relationships and the effects on outcomes for lower attaining students so I am particularly interested in this area. The research that I read centres on the damage that setting does to students; but in my school we continue to set for ability.

This year is the second with a new Head of Maths who has a fresh take on setting. We have a new approach to banding and this has opened up the classes somewhat and the spread of prior knowledge is now greater and therefore a field in which these new ideas can be practised. As a result we are designing a new SoW for year 7 with facets of Mixed Attainment Maths ideas added in!

In my classes I now make a big effort to use mindfulness and the power of 'Yet', and my younger students are at pains to ensure they remember to tell me that they don't quite understand yet.  We use learning journeys so that they may map their progress and they get quite excited when they can measure their progress for themselves.  This worked very nicely with Year 7 when working on probability, and really boosted their confidence!

From the conference, I have also used an idea from Inquiry Maths which my (streamed top set) year 8 loved, as did my bottom set year 9.  I feel that a mixed ability class would really flourish with this sort of activity.  I have noted on many occasions that those streamed lower down in the sets tend to have better reasoning skills for shape but lack the language to approach questions on higher papers.  Time to reintroduce my WordWall!  I felt with these separate classes that a meeting of minds could work out really well, but cannot arrange such a meeting due to timetabling.

For most of my teaching career I have been assigned the bottom sets as this is an area of interest for me. I have had a few year 9 classes which have been fairly spread in ability and had a quotient of about 15-20 students.  In year 10, these classes have shrunk, in one notable year to 6 students, and these students are then in no doubt that they have been scrapped by the school and probably therefore by society.  It was a heart-breaking start to the new year.  I am interested in mixed attainment classes particularly for this class and going forwards, the challenges would inspire me to be a better teacher.
I was very disappointed when due to a disaster with the home plumbing, I was unable to attend the Sheffield conference.  I feel that this whole movement is one with which I would like to work collaboratively and to share ideas.  I would like more info, and more ideas!
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(As a result of Mike’s session the woodwork teacher is currently making me a set of geoboards and I can't wait to use them!!!!  Thank you.)

On a Saturday in the middle of June, I found myself at the Sheffield Hallam University ‘Mixed Attainment Maths’ conference.
The reason for my attendance was that I had begun to notice a visibly growing interest in the maths community, (particularly on Maths social media sites), about teaching maths in mixed attainment groups. I saw the conference as an opportunity to gain some deeper insight and understanding of the pedagogy associated with it.

I have always been interested in understanding different teaching and learning styles, and as teaching mixed attainment groups is an area I have had little experience of, I wondered whether it would be something that could work at my current school. I teach in a comprehensive school where classes are setted by ability group, however, as so often is the case, even in a setted environment there is a wide range of abilities. So, my hope was that whatever I would observe and learn at conference, I might be able to apply the principle of in my setted but widely varied ability group – fortunately my hopes were answered and that is exactly what I was able to take away.

The speakers at conference were a varied mix of people, from those who had tutored me during my PGCE years and people that I follow on twitter. Their views had a huge impact on my way of thinking in regards to educational pedagogy and had greatly influenced my approach to teaching and my interactions with students on day-to-day basis.
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The day kicked off with an introduction from a Prof Hillary Povey who had some fantastic ideas. One which sticks in my mind was the power of ‘YET’ (the idea that something is not clear YET but will become clearer later). I managed to have a catch up with Prof Hillary during registration. She is currently working part time and is involved in educational research. She spoke with great enthusiasm about the current era in education, in particular about ‘Learning without limits ‘ .She is hopeful that the new curriculum changes in Maths will bring profound changes into the educational system. Creating a system where we as educationalists have high expectations for all students and provision of equal learning opportunities to all universally rather than based on ability level. The previous era of such hope was in the 1970’s where some excellent resources for mixed ability teaching were developed, e.g Smile activities (a resource that I often use and found to be fantastic in meeting its aims) more resources can be found on the stem website here
https://www.stem.org.uk/elibrary/resource/25755

First workshop I attended was run by Tom Francome and was about Grid algebra by ATM. GRID Algebra is a visual and kinaesthetic way to learn number and algebra and pre-algebra.  Learners build links between numeric and algebraic expressions and numbers and physical movements around a grid. It was interesting to see how a simple multiplication grid can be used to improve students understanding of fundamental principles of algebra. I found it an excellent tool not only to tackle common misconceptions in algebra but also make students get hooked into the learning. Students can begin to solve quite complex algebraic equations without realising it. It of course lends itself very well to mixed attainment groups where students can move according to their own pace.

Second workshop was my highlight of the day. It was run by Andrew Blair, the creator of the inquiry maths website. He spoke passionately about teaching mixed attainment groups and his website is full of excellent prompts that can be used in any maths lessons.
He ran an activity with us to give us a flavour of how it would work in a class with students. It was an eye opener to see how a prompt in the middle of the page led us into quite a very high level of maths discussion involving the use of DESMOS to graph our findings.
It was very obvious that in his class, students would work in collaboration, building on prior knowledge and constructing their own path in learning mathematics with teacher playing the role of facilitator to help navigate this journey of learning.  Although Andrew intended to run his prompts in mixed attainment classes, I think they would be equally useful in a setted group situation. I envisage myself using these ideas in near future.

Third workshop was run by Colin Jackson and was an introduction to resources freely available on ‘cre8ate maths.’  Again, the way the tasks were set, they were extremely applicable to mixed attainment groups. The particular task that we worked on during the session was called ‘Building shapes’, again another fantastic low floor high ceiling resource.

Fourth workshop was run by Leann de Belder and was on problem solving in a mixed- attainment class. In this session we discussed different views on fluency problem solving and reasoning. The highlight of the session for me was the notion that students brought their own prior knowledge to the lesson, and attempted carefully set problems to help them explore their own mathematics, with teacher facilitating their learning through modelling and questioning.
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On reflection, of course developing lessons that are suitable for mixed attainment is time consuming but with collaboration from colleagues, we as teachers genuinely do have a mechanism in mixed attainment teaching to open up whole new segments of engaging maths to a wider student audience than we currently do in our current system of setting pupils.

​Teaching children mathematics in mixed-attainment groups is fundamental to providing all children with their access and entitlement to a common, statutory mathematics curriculum, as defined by HMG. However, teaching is complex and how anyone learns to teach is dependent upon many factors including the beliefs and values they hold and the ethos within the schools in which they practice. However, when we place our focus on learning then according to Gattegno [1971: ii] A radical transformation occurs in the classroom when one knows how to subordinate teaching to learning. It enables us to expect very unusual results from the students - for example that all students will perform very well, very early and on…

​My experiences, initially as a young teacher and later as a HoD in a school, led me to believe in the value of teaching mathematics in mixed-attainment groups. These values were based upon:

• inclusivity;
• equality of opportunity;
• access and entitlement to mathematics;
• not labelling children on some kind of ‘ability’ scale;
• not accepting that any student’s ‘ability’ was fixed;
• being aware of and open to students surprising me.

​How anyone might create the conditions for teaching mixed-attainment groups depends upon the range of strategies we use, the questions we ask and the types of resources we have access to and how we utilise these strategies and resources when planning lessons and designing tasks for use with our students. An earlier quotation from Gattegno (1963, 63) offers some insight into task design: All I must do is to present them with a situation so elementary that they all master it from the outset, and so fertile that they will all find a great deal to get out of it. Given the increasingly strong element of problem solving and reasoning emerging, from the 2014 National Curriculum and the subsequent impact of this upon assessment at GCSE and A-level, such strategies and resources need careful consideration with regard to subordinating our teaching to learning.

​With regard to asking questions two seminal publication by the Association of Teachers of Mathematics (ATM) http://atm.org.uk) are: Questions and prompts for mathematical thinking andThinkers.
 
In terms of resources and task design http://www.inquirymaths.co.uk has the potential to make profound additions to supporting learning and teaching in mixed-attainment classrooms.
 
There are also a vast range of other resources published by the ATM and some are:

• Big Ideas
• Bigger Ideas
• Rich Task Maths 1
• Rich Task Maths 2
• Variety in mathematics lessons
• Eight days a week
• Everyone is special
• Forty problems for the classroom
• Forty harder problems for the classroom
• Learning and teaching mathematics without a textbook
• 30 years on
• More people more maths (this is an active ‘People Maths’ set of ideas)
• Functioning mathematically
• Points of Departure 1, 2, 3 and 4
• Linking cubes and the learning of mathematics

 
Gattegno, C. (1963) For the Teaching of Mathematics (Volume One), Great Britain, Lamport, Gilbert.
Gattegno, C. (1971) What We Owe Children: The Subordination of Teaching to Learning, London: Routledge & Kegan Paul.

Thoughts on the Conference - by Steve Mault
@stevemault

'I went to the Mixed Attainment Conference in Sheffield because something was missing.  Approaching the end of my eighth year of teaching and in my fourth school, I know I love teaching Mathematics but my teaching jigsaw felt incomplete.  I have always taught pupils in sets but have grown increasingly concerned with the lengthening tail of disaffection and underachievement.  Is this due to societal problems or is something wrong with our practice?  When I discovered that my children’s prospective Primary School set pupils in Mathematics from the age of seven, I thought I might have discovered an answer.  At the same time, an old friend, Zebedee Friedman, posted an advert for the Mixed Attainment Conference in Sheffield.  I knew that, if it was something that Zeb was involved with, it was bound to be good.  As I read more about Mixed Attainment, I started to question my practice.  How can it be right to deny groups of students access to parts of the Mathematics curriculum, particularly when those parts are often the richer, less procedurally focussed elements that actually give a much better representation of the maths I enjoy so much?

​The conference was exactly what I had hoped for. Helen Hindle of mixedattainmentmaths.com had brought together a range of inspirational teachers and educators, each with fascinating insights into the Mixed Attainment approach.  Mixed Attainment seems scary to someone who has only ever taught in sets.  How will the top end students be stretched?  What about those with specific learning difficulties?  What happens when students reach KS4?  How can I persuade my department that Mixed Attainment is right for us?  Workshops that introduced Learning Journeys, Low Floor High Ceiling tasks, Inquiry maths and much more, provided tools and suggestions to help answer these questions.  Refreshingly, these were current and former teachers offering guidance and support and not pretending to have a definitive one-size fits all method.  The overriding message I took from each of the four workshops I attended, was the importance of collaboration.  Creating properly differentiated, engaging tasks takes time, but by working together, it is possible to create resources that ensure that all students are both challenged and supported.  Spending time with like-minded colleagues, who shared a belief that something in the system is wrong when we are prepared to prejudge the potential of children as young as 7, was incredibly refreshing.  I would say it felt like I had completed the puzzle.'

Thoughts on the conference by @rhib83

This conference has completely opened my eyes to what proper mixed attainment teaching looks like and the endless opportunities it provides for students. In an uneasy position of changing over to mixed attainment classes from September, I found the sessions to be both inspirational and exciting and it was delivered in a very supportive environment. I'm excited and raring to go for September, full of ideas thanks to Helen and her team. See you all at the next one!

Thoughts on the conference - by Martin Jones
​@martin56jones

I knew it would happen – turn up without a pen, just like my students. In the first workshop a kind colleague lends me a spare pen for the day. We get stuck into Mike Ollerton’s activity on using a rotating arm to plot the coordinates of its endpoint for angles between 10 and 90 degrees. What do we notice, what patterns are emerging, what questions occur? Now I recall what it is like being part of a group, trying to keep up. I’m relying on my new found colleague to help me recognise where I’ve put the decimal point in the wrong place and to reassure me I’m on the right track.
Surprising us – and himself – with a blank power-point slide, Mike mentions Postman and Weingartner’s book “Teaching as a Subversive Activity”. (The quote that Mike was thinking about which is followed by a blank page in the book, was...  

'Suppose all the syllabi and curricula and textbooks in the schools disappeared.  Suppose all of the standardized tests - city wide, state-wide and national were lost.  In other words, suppose that the common material impeding innovation in the schools simply did not exist.  Then suppose that you decided to turn this 'catastrophe' into an opportunity to increase the relevance of schools.  What would you do?'

Must go back and read it again. Published 1969.

Next, off to an Inquiry lesson with Andrew Blair. A simple but challenging “prompt” about matchsticks forming rectangles. What do we notice, what questions do we want to ask? Now, the pivotal moment for the teacher: which way do we take the lesson? Let the participants nominate their preferred route from a given structure of enquiring mathematically; how to take the whole class forward is the question. We are guided to look for more examples, my colleague from Bratislava notices triangle numbers are popping up, we conjecture, we play with some algebra, someone graphs a couple of equations on her phone using Desmos (“this app is changing my life”, she lets us know in an aside), we start to see what’s happening, we run out of time. There must be a nice proof lurking behind this surprising result...
 
Lunch in the Peace Gardens in Sheffield city centre. A cosmopolitan community enjoying the sunshine and splashing around in the fountains. Conversation about the Mastery programme and its relationship with mixed attainment teaching.
 
Post-lunch, grid algebra with Tom Francome. Trepidation at having to take my turn and do some simple arithmetic on the screen; so this is how my students feel when I invite them to the front of the class! Not as easy as I thought… Memorably, Tom says, the biggest benefit from mixed attainment teaching is teachers working together. And he recommends reading Dave Hewitt’s paper “Arbitrary and Necessary” – it will change the way you view what you do.
 
Final session: Helen Hindle runs a lesson her way, us evaluating the resources.  Learning journeys, starter tasks, self-assessment. When do you do your teaching, how do students respond to this style of learning, how do you change the culture of the classroom? Lots of interesting discussion with those doing mixed attainment teaching, those implementing, and those like me wanting to believe and trying to find ways to make it happen.
 
An uplifting day, a reassuring day, lots of good people doing lots of good things. As Hilary Povey said  in the opening session (I paraphrase): Hope, in an era of change; imagine… a world in which mathematicians are made not born.

Thoughts on the conference by Laura Brown

​I started the day thinking 'but we're expecting weaker students to be part of a conversation where they won't even understand half the words', and left thinking 'but if we don't expose them to those conversations how do we expect them to develop that vocabulary and understanding?'.
I came looking for ideas for one class and left to do more research into mixed ability teaching with an idea to introduce it in Year 7 in 2018. I've got a lot of work to do...
We've tried some mixed(ish) groups before - it didn't go well. This weekend I learned why:
- staff need to be on board
- there needs to be a high level of collaboration
- we didn't have a bank of rich learning / low floor, high ceiling tasks which are obviously key to making this style of teaching a success.
Mark Horley's session in particular gave me such an insight into what mixed ability teaching can and should be like.
I'm even going to join twitter so I can follow the updates on the #mixedattainmentmaths feed!
Many thanks to all the team for such an inspiring, thought provoking day!
Now to convince my team....

Gareth Evans, Mathematics Teacher at Tarleton Academy, attended the first Mixed Attainment Maths Conference at Birmingham University on the 28th Jan 2017.

The images below show how Gareth has been using Learning Journeys with his classes,  alongside the GCSE questions activity which Zebedee shared in her workshop.

 "I have used the learning journeys with a number of classes at the start of a unit, along with a selection of GCSE questions taken from http://www.mathedup.co.uk/ or https://corbettmaths.com/. The feedback from students is that they found value in seeing the range of outcomes and types of question related to the unit for two reasons 1) it helped establish the things they were already good at and 2) it gave them a clear idea of what they potentially would be able to achieve by the end of the unit.

Student also have a learning journey stuck in their books that they can highlight as we progress through lessons, and at the end of the unit they return to the GCSE questions and make any changes/additions. It is still a learning curve for me and I'm sure I could make it even more effective but I have found them really valuable.

I have particularly noticed with my Year 10 class the effects of 'mixed attainment teaching approaches' at both ends of the class - I am seeing the 'less able' students flourishing and the 'more able' students making even more progress. We currently set our students and I will be leading the transition to mixed attainment in Year 7 from September."

Gareth is hoping to visit a schools that is currently teaching mixed attainment classes. If you are able to welcome a visit from Gareth please contact him via twitter @tarletonmaths

The conference is a chance to open a philosophical debate that has long been shut: What is the point of maths education? We find ourselves in an impoverished system that focuses exclusively on outcomes and, specifically, measurable achievement in public examinations. As Professor Roy Lowe describes in his book The Death of Progressive Education, students have become ‘victims’ of education. They are labelled and ‘set’ in classes depending on someone’s notion of how well they will perform in the final exam. There is an alternative in which children value the experience of education. They learn to see mathematics as a way of understanding and communicating about the world; they learn how to do mathematics, rather than have it done to them. At the heart of this vision lies mixed attainment classes engaged in inquiry. Such a vision invokes a conception of social justice that is, unfortunately, alien to our times of inequality, greed and deprivation. The conference shines a light on an alternative way for maths education and, dare I claim, a more just way for our society
Andrew Blair - @inquirymaths

If you love mathematics and respect young people it can be very tough working in an English school. Mathematics lessons may be subject to extraordinary constraints and young people reduced to a set of colour codes on a spreadsheet. The conference on Saturday was a supportive and uplifting gathering of people with many shared values who work in very different contexts. Those who are blazing new trails, or have years of experience of mixed attainment teaching were an inspiration for those who would like to do things differently. We have a shortage of maths teachers in England or rather we have a diminishing number of qualified teachers prepared to stay in the system. Given the space and trust to work in the inclusive and mathematically rich ways that were shared on Saturday I like to think that many would be happy to return.  
Corinne Angier - Corrinne is on the General Council of ATM

On Saturday I felt to be in the company of many people, (slightly over 100) who were keen to discuss and work on the many issues concerning teaching and learning in mixed-attainment mathematics groups at KS3 and KS4. I felt there was much sharing of practice and ideas and pedagogical implications for looking at the alternative to creating ‘ability’ sets. Something that was important was the fact the presenters gave up their own time for this non-profit making conference.  Nobody was selling published resources or schemes of work created with profit motives in mind.
I was aware some people took photos and wondered if they might like to send any of them to either myself or Helen so they can be posted on the mixed-attainment website. For example I know a couple of folk took photos of the whiteboard which showed a spider diagram based upon all the different mathematical concepts and skills which are accessible through the use of a 9-pin square Geoboard together with a simple grid of nine dots.
I hope this conference becomes the embryo of a community of practice involving teachers who are keen to develop their own schemes of work for use in mixed-attainment classrooms.
To finish, I am aware my first two sentences contain the words “I felt”. I invite others who attended the conference, therefore, to write a short piece for the website about what you felt the day was all about.
Mike Ollerton

Sam Hoggard, one of the workshop presenters has written an interesting blog about tasks that provide students with the opportunity to shift their relationship with mathematical objects and ideas. You can find Sam's blog using the link below.