Most of us are into our second week of teaching with our new class which means we’re starting to get some understanding of where our students are at, what their needs are and how we are going to make sure this is a successful year.
The word that comes to every teacher’s mind at this point is of course: differentiation. Even schools which use streaming for Maths or English will still, to a certain extent, have differentiation present. It is of course a mainstay of teaching; our understanding that not every learner is the same. It is our obligation as teachers to make sure that every student gets the most out of every lesson to the best of our ability. What I had my eyes really opened to though last year (no thanks in part to the White Rose Hub Maths scheme, which I’ll mention throughout this post, but not go into too much detail on) is that there is no right or set way to differentiate.
In some schools I’m sure there is still the planning template with the 3 (or sometimes more) columns of LA, MA and HA, perhaps with a little G + T box on the end, with an SEN one somewhere. This is the plannings’ way of showing that it has differentiated; that we have taken into account that the needs of our students are not all the same. In these columns the work, scaffolding or support that each ‘group’ will have in the lesson might be briefly referred to and so the differentiation is very visible. But is it always effective?
The New Curriculum introduced in 2014 was designed, in my opinion and I’m sure others’, to somewhat do away with the grouping of children into categories such as LA, MA and HA etc. The idea being that every child should reach the expected level in subjects, and once reached, broaden their understanding of the subject matters they’ve learnt. In principle a lovely idea; in reality – more difficult.
Of course we as teachers still group the children (maybe just mentally, lesson by lesson) to make sure they can access work, it perhaps seems scary, or even lazy to give out the same work for all children to tackle. LA children might struggle, HA become bored and our MA (our the children we want to push that little more) may simply coast along silently under our radar. Is there though another other way to differentiate? Can we give all children the same objective, the same work even, yet still differentiate? I argue YES.
Last year, I was teaching year 6 and felt I had my best year of teaching mathematics. I really felt the children were engaged and challenged in my lessons. To support this, it turned out to be our highest attaining year for year 6 in maths for several years. I put this down to my own re-thinking of the way I differentiated for maths and this was where the White Rose Hub stepped in.
A free scheme, with an overview for the teaching for the subject and resrouces. Last year, was its launch year, and although resources were not yet overflowing, it really helped me to re-think and evolve the way I differentiated. Differentiating in the way I interpreted it last year did not only have to be differentiating of work difficulty and outcomes, but it could also be support by teachers and TAs, how the same work could be tackled in a number of ways and by giving activities that could be accessed and expanded by all to whatever extent their mathematical ability allowed. Thus, taking away the opportunity for HA to become bored, or LA to feel overwhelmed and for MA to coast along. The most effective way I felt the white rose helped with differentiation though was breaking down mathematical skills to really help children understand what they were doing, using a manipulative/pictorial (equipment and drawings) representation to an abstract one (I.E 1/4 + 1/2 = 3/4).
To exemplify I’ll discuss the way we taught adding fractions, something that we did successfully in the Autumn term to the extent that our students still remembered the methods and more importantly the mathematical process in the summer term (meaning I didn’t have to use revision time before the SATs going over a skill taught in the first two terms).
I am going to first put a ‘more-traditional’ approach to teaching this skill that I might have used before last year as my differentiation. You may even recognise this type of thing from some of your own planning and I want to note it’s not necessarily wrong, but in my opinion is not the most effective differentiation:
Lesson – Adding fractions:
LA – add with same denominator, move on to different ones if able
MA – start with 2-3 same denominators, move onto different ones, using common multiples to help add fractions
HA – Different denominators, use common multiples to add
You may or may not recognise this type of thing. What’s important is that it shows differentiation by entering the students at a different difficulty and differentiates what the children are expected to do. It does cater for ability and so is differentiation. It’s also normally taught using an abstract representation from the off.
However, when I taught the skill I modelled it to all students, but used a pictorial representation of the fractions. My students knew the denominator showed the total parts, and the numerator showed the amount of parts (this had been thoroughly pre-taught in other fraction units). So the visual of two fractions say 1/4 and 1/8 being added together immediately showed them they needed to change something. You draw the fact that the 1/4 becomes 2/8, then bingo, you can add them. Showing this again visually.
Now I know some may read this and think, yes that’s ok but aren’t your higher abilities going to be bored? Well you engage them in a different way, get them to show how to draw the pictures of the fractions being added, let them take over, talk through what they are doing; talk mathematically. This shows their greater understanding of what they are doing; they’re not just robotically getting them to find the common multiples and answer adding fraction questions in an abstract way (which I argue doesn’t really allow them to understand the actual maths).
Once independent working started, you have your differentiation. Students not as confident will continue with the use of pictorial representations, and (as I often found) your HA students will still do one or two (I used to insist they did 2 pictorially) as this ensures that can not only do the skill, but understand what, and more importantly, why they are doing it. I, at this point would also always have fractions boards and other physical manipulative that the students could use to help solve questions on their tables. They then get a ‘choice’ of self-differentiation of how to tackle the problems. This I found to be really beneficial as it really gives the students confidence, and as all are tackling the same work, does not lead to any feeling deflated that they’re doing ‘easier’ work to others. I would note that even some of my HA students continued to use the pictorial representation (drawing out the fractions) to help them for more than my obligatory 2 questions by choice.
Step one of your differentiation is here then. In the way that you have differentiated how to solve the problem. Given them the real mathematics behind the skill, and got them to think about other ways to show it and then the way that they continue to do so – they have the choice though.
Your challenge (further differentiation) then comes through expanding. I used a lot of extensions where students used the skills in a real-life context: The bottle was a quarter full, and Matt added a third more water to it, how full was it? Not particularly difficult you’d argue, but then you tell them to visually show the question – draw the bottles before and after perhaps. Again, showing them and you as the teacher that they have understand the mathematics behind the skill. But, giving them the choice to show how they do it. This type of thing, because you’ve modelled it to all, is then accessible to all. But will allow more able students to express, and ‘show off’ their understanding.
Ideally yes, you would want your students to be able to solve an abstract problem like: 1/25 +13/50 using a more traditional method as drawing it would be time consuming. But for those first few lessons, give the students the same ways in, let them discover the real mathematics behind it, using the methods that allow them to do it at the beginning, and then you will find the understanding sticks much more.
This idea of ‘choice’ in self-differentiation is, I know, not groundbreaking. You can give students ‘choice’ in the work they do, perhaps say in its level of difficulty. But, what I’m suggesting here though is why not give them choice in the method? Why not take into account more that learners learn in different ways and we should perhaps give them different ways to tackle the same problem? At the end of the day, if they’re achieving the objective and learning, then you’ve done your job.
Differentiation does not just mean different work, or worksheets. Why can’t it mean different methods; different styles of learning? I challenge you to take the same activity for a whole class, but teach them a visual way of doing it, or one using manipulatives before you start showing it as an abstract maths problem. Of course it takes time, it’s not easy to get them, or teachers even on board (I know as I was sceptical at the beginning of the year), but see what a difference it can make to the students’ confidence and engagement: I did.
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