Closing the gap: differentiation by time

There’s a lot of talk about differentiation by outcome, differentiation of explanations, differentiation of support, differentiation of task, etc. etc. etc.. Heck, there’s eighty purported differentiation strategies here.

I worry sometimes about doing differentiation for its own sake. We don’t talk so much about the goals or the assumptions behind differentiation, when those, to me, seem to be the much bigger questions. In this post I’ll explore some of those questions, and present my view of the conditions when, and how, differentiation makes sense. (The title gives you a hint.)

I remember watching this episode from the Simpsons on BBC2 when I was at school myself. This particular section has lingered in my mind since then, and since becoming a teacher it naturally came back to mind. As I watched it again, it’s even more devastating than I remembered.

While that clip has so much worth commenting on, Bart’s quote says it all:

“Let me get this straight. We’re behind the rest of our class and we’re going to catch up to them by going slower than they are?”

Differentiation via a slower remedial class: clearly a ridiculous idea – or is it?

To me, there are several responses to Bart’s insight. Instinctively we want to laugh with him, because it’s clearly a ridiculous state of affairs. But don’t we subconsciously and unknowingly do something very similar in our daily teaching, as we differentiate? This group of children are the lowest attaining in the class, so they will focus on more basic knowledge and skills. This group are the highest attaining, so they get pushed onto new knowledge and skills or deeper questions. If that’s how we teach – and that IS how I teach and how I was trained to teach – then we are doing exactly what Bart ridicules us for. The students who are furthest behind get even further behind as they are either denied access (whether just by lack of time, as they have to spend their time on more basic questions first, or by explicit lack of teacher permission, or by lack of understanding) harder material. Those who are ahead get even further ahead. There is only one result: a widening of the chasm between the top and the bottom.

Perhaps Bart is wrong. I teach like this because I have to. I teach a subject which is setted and streamed, and even then, no matter which set I teach, there is still a wide range in the speed with which groups of students grasp certain topics. Some students are lightning quick: they require little else than just a few examples and a general rule; others are slower, requiring explicit flagging up of misconceptions, multiple examples, illustrations, non-examples, etc. until the concepts become clearer. On top of that, I differentiate every day because my students literally demand it and like it. I use a strategy like this (featuring the lovely Dani Quinn) in most lessons, where after my main planned explanation I offer a choice: students can either go on to the main task, or volunteer themselves for extra examples and re-explanations (and sometimes I select the students based on AfL). I do this because it’s obvious that some students need that extra explanation whereas others don’t. Yet it is still true: in the time taken to re-explain for these students, the other students in the class have extra time to go onto harder and deeper tasks. This technique may be necessary, but Bart is still right: even if you need to go slower, going slower still leaves you further behind.

This is what I mean by examining the assumptions behind differentiation. While the practice has its benefits, and may even be necessary to be a responsible teacher, most strategies are built on the assumption that some children are only capable of so much. That gaps in attainment can’t be closed. It’s an assumption bolstered by target levels. Yet it’s paradoxical that we then spend so much time teaching about ‘growth mindsets’. At the least, it’s clearly not a straightforward assumption. If we hold to this assumption, then it’s fine to accept that differentiation is good practice, and gets students to where they are able to get to. But as Chris Parsons writes here, there’s also an epistemic problem with this assumption: who are we to judge (or impose?) these limits upon our students?

We don’t know enough about:

  • The past of our pupils
  • The future of our pupils
  • The complex internal state of our pupils
  • The complex dynamics of how learning really works

Back to Bart’s quote. Is there a way forward?

“Let me get this straight. We’re behind the rest of our class and we’re going to catch up to them by going slower than they are?”

As I’ve said, I think that many students benefit from slower teaching. But I don’t like the inevitable consequence that this method enlarges differences between attainment groups – nor the assumption which underlies this consequence.

So, here is the big suggestion: Students who learn slower must catch up by learning for longer. In other words, we should differentiate by time. It’s pretty obvious, really; you can get to any destination at any speed, as long as you’ve got the time. Yet it hasn’t been suggested in any differentiation training that I’ve received.

hare-and-tortoise-300x156

Speed isn’t the only determinant of learning progress. Time and persistence pay off, too.

To some extents all schools already do this: it’s exam season, and across the country certain groups of students are currently being showered with intervention classes and extra teaching time. Yet it’s very limited, based more on pushing for borderline exam results than on helping students flourish over their entire education. And by the time students reach year 11, the gap is already huge, and the impact of these sessions limited. Far better to close it earlier on, when it’s smaller and there’s less to cover, but it seems to me that focused interventions in year 7 aren’t anywhere near as common.

What might it look like in practice? Shanghai success-story maths teachers use same-day intervention sessions, based on same-day homework assessment. It’s easy to see similar systems put in place without the burden of extra marking – perhaps by using exit tickets. Every lesson, every student is checked for their ability to perform the lesson’s learning objective successfully. Those who don’t nail it get extra teaching time to nail it after school. If teaching time is stretched already, link it to an online maths package or software, with explanations and tasks to try. Alternatively, free up some teaching time by making class sizes bigger; any drop off in class focus should be caught up by the very same interventions. This way, classes can go at various speeds, suiting various groups of learners, whilst extra teaching time for those who need it ensures everyone gets to the same point of mastery in the end.

In summary, there are all sorts of attainment gaps in education. I believe that much of my day-to-day teaching practice of differentiation, while necessary, doesn’t address these core gaps: students who are behind can’t catch up by going slower (even though they need to go slower). The only way to close the gap for such students is to give them more teaching time.

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22 thoughts on “Closing the gap: differentiation by time

  1. I completely agree with the logic of this proposal and have often thought the same myself. I try to practise ‘mastery’ style catch ups, but only have lunchtimes and breaktimes to do this. In upper KS2 it seems like an impossible task because the cumulative effect of your bottom table not doing as much as the rest of the class over about half a decade is that they lack the fluency and efficiency to access the current material. So, they need extra time to master the new material as well as extra time to master the old stuff that never got enough practice to go into long term memory; a double whammy that apparently is solved by my always helping them in class, giving them less to do and personalised, easier worksheets? Madness!

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    • Thanks for the comment, and your perspective from primary. It’s sad to hear how big the gap is already by the end of KS2 – instead of saying focused interventions should start at year 7, I should probably change it to year 1/ reception.

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  2. I’ve always thought this. Back in the day, in another country, when we made our ‘o’ level choices, some opted for the 2-year course and some for the 3. It was understood that the exam showed (hah!) mastery and therefore it wasn’t about a rite of passage. In fact, we knew that you could take the 98-year course if you wanted. In the mastery materials from a maths publisher this year, it states the belief that all pupils can attain, some just need more time. Well hooray! But what have we not got in primary school? Different amounts of time. Not only are pupils all expected to meet the arbitrary attainment standards for their academic year, they’re not even the same age! The gap/SEN quotient of summer born children is the stuff of legend but it’s a bit of a no-brainer isn’t it? Some children have been alive for almost a year less than their year group partners. In KS1 this is a massive % of their life. I’m having a good time with the ‘mastery’ notion in my maths class, because I’ve always held to that belief about attainment myself. I could just do with twice as long with my group and we’d get there – possibly with greater understanding than the fast-trackers.

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  3. Differentation is “a process to approach teaching and learning for students of differing abilities in the same class. The intent is to maximize each student’s growth and individual success by meeting each student where he or she is . . . rather than expecting students to modify themselves for the curriculum. ” (Hall, 2002).
    From this definition and my understanding differentation is not meant to close the gap? Is the aim of teachers to get all students to the exact same point at the end of their education?
    In a similar vain is Growth Mindset about closing the gap?
    Damian

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    • Hi Damian. Thanks for the comment. I appreciate the referenced definition, but what’s interesting is that I don’t recall going over such clear definitions in most discussions on differentiating. Here it’s helpful because it makes explicit one of those assumptions: that of differing abilities.

      This is something I accept as given – that all of us have different abilities – but I can find it problematic when this fact is used as the basis of a teaching philosophy. One big reason is the epistemic problem, mentioned in the blog – how can we really know or judge what students are truly capable of, when learning is composed of so much more than mere cognitive ability? Some examples of this include some of my AS-level students scoring much higher marks in their mock exams than I would ever have predicted, if I had just based it on their homework/classwork and the amount of support and help I need to give them. Others include several students I have taught over several years, making leaps and bounds that I couldn’t have predicted the first time I taught them.

      This also explains my reference to growth mindsets – Dweck talks about the limiting effect that a fixed mindset imposes upon students’ attainment. It seems to me that applying the philosophy of differentiation that you mention, has the effect of limiting students’ attainment – exactly what Dweck’s research warns us against.

      Another way I might respond to your questions: Hall’s def of differentiation assumes that there will be a gap. I agree that there will. However, instead of taking it as a given and adjusting ourselves to that gap, I believe that a different approach and a different mindset – that of differentiation by teaching time – can do much to narrow that gap, even if it’s impossible to close. I worry that by working on such premises as ‘the intent is to maximize each student’s growth and individual success’ we can inadvertently impose limits on students, as we then make too much of individual differences. If we don’t ‘expect students to modify themselves for the curriculum’, then we are in danger of not expecting enough of their capabilities. At least let all students try to reach the whole curriculum in all its riches, rather than impose upon them our [limited and flawed] beliefs about what they are capable of.

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      • I agree we cannot truly know what all students are capable of, but I struggle to see that I would inadvertently set limits on my students?
        The intention of your post is great – closing the gap – but the tortoise and hare imply that it is a race – which clearly education should not be?
        Do we adjust for the gap?
        Do we impose our beliefs of what they are capable of?
        I agree with you dedicating more time is a great approach, but education is not a race and comparing students by gaps is not profitable. One of the mastery approaches is to measure the improvement made not to point out that they are behind x students.
        Thanks again interesting comments.
        Damian

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      • Thanks for the comment. Here’s my take. One practical way to see it might be on a lesson by lesson basis. Each lesson we are trying to teach something. If a student doesn’t quite get it, they should instantly be given more time, so that they can keep learning and not fall behind on successive lessons which build on that lesson’s learning.
        The alternative is to ‘differentiate’ in the standard way, but that increases the gap between the top and the bottom. Sure, all might still be making progress. But if it’s mainly a matter of the bottom end needing more time, why not just give them more time there and then, rather than inadvertantly cut off their ability to access deeper and more complicated material?

        Progress/improvement is important, but progress for progress’ sake isn’t. Progress is important only if we’re progressing towards an important goal. The use of thinking in terms of gaps, to me, is that it requires clarity on what the end goal is, and then doesn’t accept anything less than the end goal.

        To me, in maths, when I first became a teacher I was shocked at how easy (in terms of %) it was to get grade C in maths. I was even shocked (as are my current year 11s) at how easy it is to get a B. And I was then shocked to realise how many fail to achieve this. I think it’s a realistic goal for all students to achieve a C in GCSE maths (notwithstanding what the new GCSE is going to look like…), and for me, that’s one of these goals where the gap is really important to know, define, and then work towards closing.

        Sorry if the hare and tortoise were confusing – I wasn’t trying to imply it’s a race, just more that speed (of learning) isn’t the defining factor.

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  4. One definition of differentation is “a process to approach teaching and learning for students of differing abilities in the same class. The intent is to maximize each student’s growth and individual success by meeting each student where he or she is . . . rather than expecting students to modify themselves for the curriculum.” (Hall, 2002).
    So is differentation meant to close the gap? The same goes for Growth Mindset, this is about maximising pupil progress regardless of where the student currently is?
    Is education a race where students have to catch up and finish the race at the same time?
    A very interesting read though, I would be interested in your thoughts.
    Damian

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  5. Hi, interesting thoughts. Is there research to suggest that differentiation widens the gap? Is there research to suggest more time closes the gap? It would be interesting to know if there is any material out there regarding this.
    After reading the above comments, I am still concerned that differentiation is not really understood the definition by Hall implies maximising progress – this does not mention that the teacher is setting this target. I understand that thus probably does happen that many teachers sets limits and assumes progress, like you mentioned with you a-level students where they exceeded expectations.
    Halls definition clearly needs to be built upon and perhaps explained better in training sessions,
    Differentiation is clearly a powerful technique that needs to be talked about more because it is something too many avoid talking about, so thanks for sharing a very very interesting read, and something which us getting people talking about.
    Thanks George

    Liked by 1 person

    • Hi George, thanks for the comment. Interesting thoughts about research on differentiation – I haven’t looked! Just had a quick scan of the 2014 Sutton Report on Great Teaching and differentiation isn’t mentioned once.
      That said, given how most schools routinely add on a lot of extra teaching time in year 11 for targeted learners, this strategy clearly has some success (or schools wouldn’t keep on doing it). Another way of looking at my suggestion is – if it works so well in the last few months of students’ educations, why not incorporate this principle throughout their education instead?

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  6. Differentiation comes in several forms: adjusting the content, adjusting the way we teach the content, adjusting the way we assess mastery. Here we are focusing on differentiating content, but perhaps thinking of the other two would help in closing “gaps.” For example some students might learn faster through different teaching methods, and we might realize students are gaining skills we didn’t notice if we adjust the way we assess.
    I’d also not that a “gap” in learning or achievement is really a symptom of the misguided concept that all students should learn the same thing. In my classes, I aim for a 50/50 balance between leveled work and project-based learning. Some students are destined to be rocket scientists while others will be painters. No reason they need to be acquiring math expertise at the same level or same pace.
    I recently did a 3 per blog entry on how I use blended learning platforms to differentiate in a way that opens up possibilities for students who are behind to “catch up,” but also allows advanced students to move even farther ahead.

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  7. Great point. Differentiation by time.
    Very useful to throw in the next time a manager reels off all the different types…”ah you’re using differentiation by outcome”.
    “Am I? I had no idea. Is this good or bad”

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  8. My understanding is that this “same day intervention” principle is used in Finland as well, sometimes by the teacher after school, sometimes by a pupil spending time in the “special education” classroom that all schools have, in order to get one to one attention.

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  9. I am sorry but this post has so many misconceptions.
    1. Differentiations purpose is for all students to make some progress not close a gap.
    2. Time alone does not solve the problem, our lower achieving students get an extra lesson every week they do not catch up. Some students could get double the time and still not catch up. Again this goes back to differentiation is not about closing the gap.
    3. Your focus seems to be getting all the pupils to the same position – really? Focus on students making progress not on closing a gap.

    Perhaps the training you got in Differentiation was not clear – it is not about closing the gap.

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    • Hi Geoff, thanks for the comment. No need for the apology, disagree away!
      1) I agree that that is the purpose of much differentiation as it is practised in schools today. Part of my post, via the Simpsons, is to point out that this method of differentiation leads to a chasm between rapid-graspers and those who take more time and practise to ‘get’ things. This isn’t widely acknowledged, and when it’s brought out in the open (as is my aim), it starts to feel problematic. Perhaps it is – perhaps it isn’t. My purpose is really to start examining the assumptions behind ‘making progress’ as the ultimate aim.
      2. Time alone might not get a low-attaining student an A*, but it undoubtedly helps raise standards enormously – why else do schools across the country throw in extra lessons for their borderline y11s at this time? Saying that time doesn’t _completely_ solve the problem doesn’t mean that that extra time is useless. It might go a very long way.
      3. I think closing gaps is far more clear (and thus more helpful) a concept than ‘making progress’. The reason most students fail to access higher level material is not because they are cognitively unable to get it. It is because they have gaps in lower level foundational material. Therefore, closing gaps is critical for students to make long term, meaningful progress in maths. The idea that pupils should all get to the same position is also a big part of the recent thrust towards teaching for mastery. https://www.ncetm.org.uk/resources/45776 This article makes a lot of similar points about this idea that you may find interesting.

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      • I think it is important to acknowledge challenges with leveled groupings, but to discount them because “all students won’t reach the same end-point” misses the most important concept behind differentiation, which is that students are individuals who will learn in different ways and different paces, but also will ultimately learn different things. You and I have learned quite a bit about educational best practices, while some of our peers have focused on pharmaceuticals, botany, or crafting legal briefs.
        The problem with teaching some students at a remedial pace so they can ‘catch up’ is a bit of a straw man argument, as it obviously will not work. In order to differentiate effectively, we need to start letting go of the idea that schools are factories that will produce ‘products’ (i.e. students) with the same skill set, and we will produce such products at a uniform pace.
        I have worked with students who are in 5th grade (US) for whom the appropriate material comes from a 2nd or 3rd grade curriculum. When considering how they got so far behind, it usually seems that they missed some foundational concept many years ago, and have had trouble ‘keeping up’ with the rest of the class. As a result, they’ve become frustrated, bored, and have lost confidence in their math abilities. When I can identify the foundational concept that is missing, they often will fly forward through multiple years of math content in just one year: it is actually quite simple for a ten-year old to learn material designed for 8 year-olds when s/he has the proper foundations. So I do agree with your premise that a student who is ‘behind’ should not be tracked in such a way that they will always be stuck in a lower level.
        At the same time, when some of my students have an advanced understanding of math, it would be absurd to slow down the entire class so the others can ‘catch up.’ By doing so, we cause accelerated students to become bored and disengaged, and we may achieve equity (I believe this is the term you are looking for regarding closing ‘gaps’ in student learning), but we do so by making the top worse, rather than making the bottom better.
        I actually just tackled this topic in my most recent blog entry: http://www.blendedlearners.com/?p=269
        My contention is that when we put students in charge of their own learning, we have less control over their pace and path, but ultimately, the outcomes are vastly improved – one big caveat is that when we are putting students in leveled groups, the groups need to be dynamic (students can switch between levels as appropriate), and we need to ensure that the work assigned to each group is truly targeted at giving them the best instruction for their individual needs (at least as much as is practical).

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      • Hi Jeff, thanks for the comment. Whilst it is true that students will ultimately learn different levels of maths, in the UK it is compulsory till the age of 16, and pupils’ maths grades are highly correlated with their future prospects – I would guess that most successful pharmacists, botanists or lawyers here have an above average grade in their GCSE maths. So, there is a high degree to which your suggestion about letting students study different things is untenable, at least here in the UK. To get the grades they need they must learn the same wide spread of maths. Whether that is an ideal situation is a different debate!

        As you say, I completely agree about the impact of missing foundational concepts, and that’s what my suggestion has in mind. And as I mention, the best way to ensure everyone’s foundations are solid, in my mind, is to give those who need it the extra time to solidify them.

        Yet this doesn’t imply slowing down the rest of the class. My suggestions focus on intervention strategies like giving extra time outside of the normal school schedule. This would keep lessons moving sustainably at a faster pace so no one don’t get disengaged. I would prefer this to your suggestion because it requires so much more work from the teacher. Here’s a metaphor using journeys. Under my suggestion, every student has the same destination (at least a grade C in GCSE maths, of course with the expectation that others will go far beyond this); they progress at different speeds, so to ensure excellent outcomes the slower students simply need to be given more time. Under your suggestion, every student has not only a different speed, but also a different route, a different journey and a different destination. The only thing that’s the same is the time. The workload implications to keep track of all of this are huge!

        To me, it doesn’t seem to make sense that we keep time the same and modify everything else, when we could keep the destination and outcomes and journey the same and simply modify time. On the contrary, when the destination (grade C and above) is so important, make sure everyone gets there in the most efficient way (as planned by an expert teacher) with enough time to get there.

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      • Hin-Tai, I appreciate that you are taking so much time to reflect on your practice. When I began my teaching career 16 years ago, I would have said the same thing – there is no way one teacher can provide individual learning plans for every student! I actually tried many of the plans you suggest, thinking that if we only had some extra time outside of class, we can get everyone to the same place. Over time, I’ve come to realize a few things – 1) If we fix a destination for all students, there are always winners and losers – the “winners” are the middle kids who are challenged just the right amount. The losers are everyone else (the vast majority of the class) who have to slow down or try to keep up with somethng beyond their current capacity. 2) The things that seem impossible become possible with experience and technology – I currently work with teachers just like you, who can’t imagine truly differentiating, and when we work with good tools (like Khan Academy), I see teachers eyes opening to the possibilities every day. Of course, this change doesn’t happen overnight, so I hope you will keep reflecting and reinventing your practice – if you have the opportunity to work with a skilled coach, it will also make the growth journey quicker and more enjoyable. Best of luck to you and your students!

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  10. Roger Penrose (Stephen Hawking’s boss, as you know) used to voluntarily stay back during break time to finish his maths questions in primary school in Canada, while the other kids went out to play. I believe he was also held back to repeat a year. He did quite well in the end.

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  11. Pingback: Starting at Michaela | mathagogy

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