Research Project:  Differentiation in Mathematics

Differentiation is a philosophy for effective teaching that attempts to ensure that all students learn well despite their many differences.  It is not new, but throughout the many years since it replaced ‘mixed ability teaching’, its meaning has been analysed and interpreted in many ways, often resulting in common misconceptions about what it is and is not. 

Carol Ann Tomlinson, a leader in the field of differentiation, says teachers can differentiate through four ways:  content, process, product and environment.  

 


In more recent years, especially since the implementation of the new National Curriculum 2014 and specifically the language of the Mathematics curriculum, there has been a significant shift in the way in which differentiation is viewed within our schools.  The Guardian newspaper ran an article on 01st October 2015 by Roy Blatchford, Director of the National Education Trust, with the headline ‘Differentiation is out. Mastery is the new classroom buzzword’.  While the headline may be crude, it is clear that the changes brought about by educational reforms in recent years have offered the opportunity or indeed expectation to reflect upon, refine and improve our teaching practices, including our approach to differentiation. 

 

The Curriculum

The aims of the Mathematics Programme of Study states: ‘The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

The NCETM’s Position

This curriculum has been interpreted by the NCETM as ‘Teaching for Mastery’, the essence of which they say, in their June 2016 paper, includes:

  • Maths teaching for mastery rejects the idea that a large proportion of people ‘just can’t do maths’.
  • All pupils are encouraged by the belief that by working hard at maths they can succeed.
  • Pupils are taught through whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time, as happens in Shanghai and several other regions that teach maths successfully. This ensures that all can master concepts before moving to the next part of the curriculum sequence, allowing no pupil to be left behind.
  • If a pupil fails to grasp a concept or procedure, this is identified quickly and early intervention ensures the pupil is ready to move forward with the whole class in the next lesson.


In an earlier paper (October 2014) they addressed ‘Pupil Support and Differentiation’ specifically, stating:

‘Taking a mastery approach, differentiation occurs in the support and intervention provided to different pupils, not in the topics taught, particularly at earlier stages. There is no differentiation in content taught, but the questioning and scaffolding individual pupils receive in class as they work through problems will differ, with higher attainers challenged through more demanding problems which deepen their knowledge of the same content. Pupils’ difficulties and misconceptions are identified through immediate formative assessment and addressed with rapid intervention – commonly through individual or small group support later the same day: there are very few “closing the gap” strategies, because there are very few gaps to close.’

In a blog post in October 2014, NCETM’s Director, Charlie Stripp discussed differentiation and its link to mindset:

‘I’ll be controversial: I think it may well be the case that one of the most common ways we use differentiation in primary school mathematics, which is intended to help challenge the ‘more able’ pupils and to help the ‘weaker’ pupils to grasp the basics, has had, and continues to have, a very negative effect on the mathematical attainment of our children at primary school and throughout their education, and that this is one of the root causes of our low position in international comparisons of achievement in mathematics education.

If my suspicion about the damage caused by current practice in differentiation in many maths lessons is correct, we should do something about it. However, I do recognise that an individual school’s interpretation of differentiation is rarely as black and white as I paint it below, and I know that many primary teachers put a great deal of thought and effort into developing differentiation models for maths teaching. For that reason, we should examine the evidence very carefully and carry out serious trials to help determine whether a different approach will improve children’s mathematical learning.

Put crudely, standard approaches to differentiation commonly used in our primary school maths lessons involve some children being identified as ‘mathematically weak’ and being taught a reduced curriculum with ‘easier’ work to do, whilst others are identified as ‘mathematically able’ and given extension tasks. This approach is used with the best of intentions: to give extra help to those who are having difficulty with maths, so they can grasp key ideas, and to challenge those who seem to grasp ideas quickly. It sounds like common sense. However, in the light of international evidence from high performing jurisdictions in the Far East, and the ‘mindset’ research I referred to in my last blog, I’m beginning to wonder whether such approaches to differentiation may be very damaging in several ways.

For the children identified as ‘mathematically weak’:

They are aware that they are being given less-demanding tasks, and this helps to fix them in a negative ‘I’m no good at maths’ mindset that will blight their mathematical futures.

Because they are missing out on some of the curriculum, their access to the knowledge and understanding they need to make progress is restricted, so they get further and further behind, which reinforces their negative view of maths and their sense of exclusion.

Being challenged (at a level appropriate to the individual) is a vital part of learning. With low challenge, children can get used to not thinking hard about ideas and persevering to achieve success.

For the children identified as ‘mathematically able’:

Extension work, unless very skilfully managed, can encourage the idea that success in maths is like a race, with a constant need to rush ahead, or it can involve unfocused investigative work that contributes little to pupils’ understanding. This means extension work can often result in superficial learning. Secure progress in learning maths is based on developing procedural fluency and a deep understanding of concepts in parallel, enabling connections to be made between mathematical ideas. Without deep learning that develops both of these aspects, progress cannot be sustained.

Being identified as ‘able’ can limit pupils’ future progress by making them unwilling to tackle maths they find demanding because they don’t want to challenge their perception of themselves as being ‘clever’ and therefore finding maths easy. A key finding from Carol Dweck’s work on mindsets is that you should not praise children for being clever when they succeed at something, but instead should praise them for working hard. That way, they will learn to associate achievement with effort (which is something they can influence themselves – by working hard!), not ‘cleverness’ (a trait perceived as absolute and that they cannot change).

 

In a further blog in April 2015, Charlie Stripp posed the question ‘How can we meet the needs of all pupils without differentiation of lesson content?’  His answer relates to ‘depth’.

Meeting the needs of all pupils without differentiation of lesson content requires ensuring that both

(i)                  when a pupil is slow to grasp an aspect of the curriculum, he or she is supported to master it and

(ii)                all pupils should be challenged to understand more deeply.

This can be achieved by:

(i)    Ensuring that any pupils having more difficulty in grasping any particular aspect of curriculum content are identified very rapidly and provided with extra support to help them master that content before moving on to new material. 

Same day intervention can provide the necessary support to secure learning before the next lesson. This requires rapid formative assessment and mechanisms for enabling pupils to access support as soon as the need has been identified. Some of the primary schools involved in the China-England Mathematics Teacher Exchange programme are already piloting ways to achieve this and are reporting immediate significant benefits for their pupils. The NCETM, working with the Maths Hubs, will publish case studies of how schools are doing this during the summer term.

(ii)    Incorporating skilful questioning within whole class teaching.

The success of teaching for mastery in the Far East (and in the schools employing such teaching here in England) suggests that all pupils benefit more from deeper understanding than from acceleration to new material. Deeper understanding can be achieved for all pupils by questioning that asks them to articulate HOW and WHY different mathematical techniques work, and to make deep mathematical connections. These questions can be accessed by pupils at different depths and we have seen the Shanghai teachers, and many English primary teachers who are adopting a teaching for mastery approach, use them very skilfully to really challenge even the highest attaining pupils. As pupils’ mathematical education continues, they experience deep, sustainable learning of increasingly sophisticated mathematical ideas. Shanghai teachers sometimes emphasise challenging questions by saying “dong nao qing”, meaning (I think!) “Please use your head!”, to make it very clear that deep thinking is expected. Evidence from the exchange visits suggests that pupils really enjoy such questions and are inspired by them - when discussing the Chinese lessons, one higher attaining child commented “I like the Chinese lessons, I need to think very hard because I know Miss Lu will ask me to explain why and I will need to have a good answer!”

 

In October 2015 Jane Jones HMI, OFSTED, responded to those questioning the NCETM’s position, specifically the way in which OFSTED would evaluate maths teaching in schools going forward.  She affirmed, in her guest blog on the NCETM site, that although

The word mastery is not used in the programmes of study, the principles cited by Charlie are at one with them. Likewise, the messages from Ofsted’s report, Mathematics: Made to Measure, emphasise the importance of developing conceptual understanding (not just procedural proficiency on its own) and giving all pupils the chance to solve problems and reason about their work. So, there’s synergy in what we are all aiming for.’ 

She went on to say:

‘Differentiation should therefore be about how the teacher helps all pupils in the class to understand new concepts and techniques. The blend of practical apparatus, images and representations (like the Singaporean model of concrete-pictorial-abstract) may be different for different groups of pupils, or pupils might move from one to the next with more or less speed than their classmates. Skilful questioning is key, as is creating an environment in which pupils are unafraid to grapple with the mathematics. Challenge comes through more complex problem solving, not a rush to new mathematical content. Good consolidation revisits underpinning ideas and/or structures through carefully selected exercises or activities. Mastery calls this ‘intelligent practice’.

The notion that headteachers might encourage their staff to retain previous ways of working because they fear criticism from an Ofsted inspector is a concern but one that everyone can play a part to dispel. While the curriculum is new, leaders whose schools are being inspected may want to take the opportunity to explain to inspectors how mathematics is organised in the school, what an inspector might typically see in a mathematics lesson or a support/challenge session including how differentiation works, and how pupils’ attainment and progress are assessed.’

 

In December 2015 Debbie Morgan, NCETM Director for Primary, referred during a presentation to teachers to the anomaly of ‘slowing down the lower attaining/struggling learners, in order to catch them up.’  She goes on to say that while we should be proud of our commitment to inclusion, we need to think differently about it under the new approach to teaching mathematics. 


Carol Dweck

Dweck’s research and theories of intelligence have featured heavily in education in recent years.  Her mindset work suggests that when we focus on ability-related feedback/conversations/behaviours in our classrooms, we are limiting the growth mindset of our students.  This is further compounded when the curriculum is ‘dumbed down’.  Instead, having high expectations for all students, coupled with valuable feedback, will increase achievement.  Following this line of thinking, we should therefore avoid the temptation to make the curriculum easier for the ‘less able’ students and instead differentiate up from the core.

 
Professor Jo Boaler

In her book, ‘The Elephant in the Classroom:  Helping Children Learn and Love Maths’, Professor Boaler summarises the extensive research she has conducted studying what successful maths classrooms look like in both the UK and the USA.  She cites the statistic that 88% of children placed in ability groups at age 4 remain in the same groupings until they leave school.  To summarise her work in short, she explains how evidence suggests that setting is counterproductive for learning and that mixed ability classes that have a problem solving focus through the use of rich tasks lead to faster rates of progress as well as higher levels of motivation and engagement.  More specifically, when considering the concern that you can’t both stretch the top and support at the bottom, she explains that the research and evidence says that high attainers achieve just as high in mixed ability class, but the lower attainers achieve much higher in a mixed ability environment. 


Geoff Petty

Geoff Petty, a leading expert on teaching methods, believes that there a number of common misconceptions about differentiation.  He says:

Some believe that it is something ‘added on’ to normal teaching and that it just requires a few discrete extra activities in the lesson. In fact, differentiation permeates everything a good teacher does and it is often impossible to ‘point’ to a discrete event that achieves it.  It is not what is done often, but the way it is done that achieves differentiation. For this reason differentiation may not show up on a lesson plan or in the Scheme of Work.  However some teachers try to show their intentions to differentiate by setting objectives in the following format:

            All must….

Some may…

A few might…

This may help novice teachers to think about the diversity of their learners, but having such objectives does not guarantee differentiation.  It is the strategies, not the objectives that achieve differentiation, and this should be the focus of our interests.’

 

Of course, there is always much debate over different education and learning theories.  For me, David Didau (The Learning Spy – an influential education blogger in the UK) sums up the position when he says:

‘I’ve written before about both my concerns with differentiation and also some of the critique of the growth mindset trope – these to me seem almost like competing, opposing forces in education – on the one hand, children should be treated differently depending on their ability and on the other, everyone can improve if they have the right set of beliefs. I’m not sure of the truth of these statements, but I do know that no one rises to low expectations.’

He is a firm believer in ‘teach to the top, support at the bottom’, where there is an expectation that everyone can accomplish something challenging. 

So, what does this mean for us at Parkside Community Primary School?

As a school we are focused on our students’ self-esteem and are taking action to foster growth mindsets in them.  The growth mindset itself will give the students the appropriate attitude and self-belief, but meta-cognition will give them the tools to be able to talk about and understand their learning, giving them a shared language and understanding.  It is not enough, however, to talk to our students about effort without making it clear what it means to put effort into a task.  Hence we need to discuss and develop their learning skills in the same way that we would develop their academic skills, and we are seeking to do this through building their ‘learning powers’ following Guy Claxton’s work on learning dispositions. 


In terms of differentiation itself, it seems to me that the biggest change in thinking concerns differentiation through content.  The tendency in years gone to plan ‘three ability groups, three activities’ was an attempt to find a standardised approach to differentiation, thereby turning what is a philosophy of effective teaching in to a teaching strategy.  Going back to the earliest research and writings by Carol Ann Tomlinson, the philosophy starts with knowing your students – know where they are before you start – which is why differentiation is so closely connected to formative assessment.  You then aim high and support those who need it – a process of know, challenge, support.  Rather than differentiation by task therefore, differentiation lies in the skillfulness and agility of the teacher to respond to both the anticipated and unanticipated difficulties the students encounter during the learning process.  Differentiation should cease to be viewed as a ‘thing’, but rather melt in to the practice of a teacher as they develop, adjust and refine their delivery in real time response to the students. 

 

So what might differentiation look like going forward in our mathematics lessons? 

 

·   Mixed ability classes/groups – no ability setting or pre-determined ability groupings (groupings are used fluidly and with an element of student choice - as appropriate to age/maturity of the cohort and subject to focused group time used in EY and Y1 - which allows students to pitch in at their own level of understanding and confidence).

·  Teaching whole class to year group expectations – objectives/concepts are not differentiated down for individuals by perceived student readiness; making work easier, or setting work from a younger year group’s objectives, will not result in those students that are ‘behind their peers’ catching up.

·         Clear, high expectations of all students.

·         Quality formative assessment that enables teachers to use the evidence of student learning to respond to and adapt teaching         and learning, or instruction, to meet student needs. 

·         A learning environment where students know how and are motivated to deepen their learning to extend themselves, with the         majority of children learning within the ‘zone of proximal development’.

·         Self-differentiation – through tiered instruction and challenge by choice.

·         Regular (daily) challenges to be available to and experienced by all students.

·         Provision of depth of learning through rich, more complex problem solving and questioning that takes those most ready                 students forward. 

·         Provision of process support, scaffolding, coaching and clarification for those less ready – greater use of manipulatives, visuals,       further practice and consolidation; guided groups working with teacher and TA.

 

We are all, to a certain extent, playing ‘catch up’ due to the raised expectations in curriculum content brought about by the new National Curriculum.  However, beyond this, there are some students who have significant gaps in their knowledge and understanding and have considerably more ‘catching up’ to do before we can even think of them ‘keeping up’ with age-related expectations.  But if they are removed from lessons to carry out this catch up work, then everything will always be new to them – they will miss seeing and hearing how their peers are expected to think and work.  It is better for them to be part of the daily mathematics lessons, helping them to remain with their peers as much as possible, experiencing what they experience.  But it is vital that they also have the additional support they need to catch up through precise teaching and regular practice of the concepts that are not yet internalised; hence a targeted intervention programme is necessary alongside quality first teaching.


                                                                                                                                                     By Kate Robertson (March 2017)