Are they really learning, or have you (accidentally) planned for a 1000 inequalities?

WARNING: the content in this blog post is probably going to irk you (a bit).

This little piece of edu-thought is what happens when you read something like this and then are given the amazing opportunity to implement a direct instruction program of mathematics across most year groups in a primary school. I crudely crunched some year 5 PUMA data on Friday, during a pupil progress meeting, and even though I knew of the evidence base for direct instruction, I was truly shocked to see the increase in average standardised score across the cohort – from around 95 to over 100 in just a TERM. This is in a school situated in one of the most deprived estates in the country. The visual of all those reds and orange cells turning into green – massive, massive thanks to the hard working teachers, utter professionals who bought in to the vision and this project, trusted the evidence-base and then made sure that other aspects of the curriculum (the program intent is fluency in number, something that all secondary maths teachers would be on board with) were adequately covered as well. The privilege of overseeing such a dramatic reduction in inequality really got me thinking about the curricular and (somewhat unusual) pedagogical features of the program and how they contrast with what is generally considered ‘best practice’.

It is these features of best practice that I would like to highlight to you now and ask you to think about whether they are genuinely as good as is commonly perceived, but first you must choose to abandon the whole concept of ‘naturally good at….’ and consider that perhaps ‘not being good at…..’ is not so much about natural ability, but really a manifestation of a lack of: decent instruction, adequate practice and opportunities to reheat that knowledge at frequent intervals. Also, I need you to have the courage to question (you can do it quietly inside your head, no need to raise this in a staff meeting and make a pariah of yourself) what you have been told MUST happen in every lesson, whether it be for Ofsted, or because a consultant has told you, for example. I give you permission to think for yourself! In case you’re not aware, I should probably let you know that the features of the program are:

  • Carefully, oh so carefully, sequenced delivery of core knowledge, both ‘know that’ and ‘know how’, including how to solve word problems
  • Systematic retrieval practice that constitutes the majority of the calculations practice in a lesson: understanding is developed during that practice (connections are made) and core knowledge is transferred to all long term memories in the class
  • A script that cuts out the waffle, uses common words and phrases to dial down cognitive load and is so carefully thought out, that, if followed properly, misconceptions don’t arise in the first place. The teacher gives the children everything they need to know and at no time are children expected to discover for themselves
  • A lesson structure that is pretty much the same every lesson, thus eliminating the need for dead-time where the teacher would be explaining (over and over) what needs to be done
  • Via the script, interactions with children are more likely to be choral response (rehearsal for the many, not the few) and individual questioning uses cold-calling rather than ‘hands up if you’re the most confident and already know everything’. The script is planned at the level of children’s thoughts at any one time. This makes every lesson almost like a scene from the film Inception.
  • Throughout the lesson, the class stays on that learning bus together and no child is allowed to opt out or fall behind. The ‘practice’, to onlookers, seems ‘too easy’, but the program is designed for success now and transference of core knowledge to long term memory in order to ensure that each child can access those harder problem solving questions later on
  • Frequent whole-class marking and direct feedback to shimmy everyone along with pace and rigour

So, now you know the main features (yup, it’s very different, weird even), let’s look at just a few features of ‘best practice’ and really think about whether they’re as good as everyone says. What I’d like you to do is think not so much about what children are doing and feeling at any one point in lesson time, but about what they are thinking. Seriously, it’s only when you imagine yourself inside that child’s head that the full realisation of how we as a profession are not only entrenching, but possibly augmenting, inequality is revealed.

Choice:

Surely this is a good thing, right? Children know what’s best for them and being given choice makes them feel empowered and confident – everyone knows that! OK. So let’s get inside the children’s heads. You’ve just given children some carefully sequenced knowledge and now they’re ready to go practise, so you give them a choice of what to do, a ‘chili challenge’, perhaps. You might be the best teacher in the world that causes all children to automatically choose the best thing for them, but while you’re explaining the different challenges (and pleasing the inspector because differentiation), what are they thinking? They’re thinking about what chili challenge their friend is going to choose so that they can pick the same one. Whatever they’re thinking at that point, it’s not going to be about the little piece of knowledge you’ve just given them – it’s going to be anything but the knowledge.  For those disadvantaged children who have gaps in their learning and are struggling to hold on to what they’ve just been taught, being asked to choose what to do will cause that knowledge to fall out of their heads. This is one of the reasons why so many children, when finally sat down at their tables, end up sticking up their hands and saying ‘I don’t get it.’ The other thing to consider is the psychology of that situation: when we constantly give children choices like that we’re also teaching them to think the following:

  • That there is such a thing as natural ability – great for the (currently) high attainers*, but terrible for low attainers (who are over represented by the disadvantaged) who gradually give up
  • That natural ability also extends to ‘capacity to work hard’
  • That one should be expected to be given choices all the time that suit what one is feeling at the time (think about what happens when the child has to sit their exams)

Deviation from the ‘script’ via general conversation:

You’ve all heard of the Mathew Effect, right? Good. But have you thought about it in terms of conversations with various individuals in the class while the rest of the class is listening? This tends to happen when, during the main input, a high attaining child throws up their hand and the teacher momentarily deviates from her own plan of instruction (where she might have sort of made her own script in her head before the lesson) in order to answer a really interesting question, one that takes those involved in the conversation off on a joyous tangent of discovery and realisation where that warm, fuzzy feeling and ‘love of learning/maths’ is demonstrated to the person with the clipboard. Frequently, a few other children will also be able to join in with that thought process and will start calling out in an attempt to join in and feel the love because children are like that. But what are the other children thinking? These are children who already struggle and are just about clinging on to what the teacher is giving them and who then have all those thoughts blown out of their heads and replaced with various permutations of ‘Shit, how…..what……..eh? Why is Hermione so good? I’m so shit at maths. Oooh, Jamie is pulling a face at me, ha ha, yeah I’m going to pull a funny face right back at him! I am the king of funny faces and the teacher isn’t even looking at me!’

A typical reply to my highlighting this kind of inequality is that teachers feel really sorry for the higher attainers if they’re not challenging them enough. They worry that higher attainers will be ‘held back’, bored and feel thwarted if they’re not continuously given opportunities to race ahead, shine, do more and trickier practice, engage in higher level conversation with the teacher. The fact remains that the price of giving bespoke opportunities to higher attainers is at the expense of lower attainers, particularly when it comes to differentiated conversation and as a profession we seem to be OK with that. Or are we? I will return to that question at the end of the blog post.

Working walls:

For many teachers, there will still be an expectation that they will either overtly refer to a working wall during the main teaching input, or that children will refer to them when they’re working by themselves. The person with the clipboard will have a box on the observation proforma called ‘working wall’. The thing about working walls is that some children come to rely on them and if we go back to our ‘think about what the children are thinking’ challenge, what are those children who are more likely to rely on a working wall going to be thinking? Well, they will think ‘I don’t know, so where is the answer to X so that I can then do Y that the teacher has asked me to do?’ Far better to have retrieval practice for all, surely?

Open-ended tasks (as the main form of rehearsal/practice and particularly if discovery based or designed for group work):

In some schools where all the children are able to focus and who also bring in an ocean of knowledge from home, all the children will be thinking about what you want them to think about, maybe making new and correct connections too. However, in a typical lesson where children are real children and not learning vector quantization automabots, how are we ever sure that all the children are thinking about the knowledge we have just given them? At any one point in time, some children will not be thinking about what has just been taught to them. You can tell me that that is not the case because your class does growth mindset now, but statistically speaking, there will be some children who are thinking about other things like lunch or honing their knowledge of how to make others laugh, or perhaps thinking about what you want them to think about, but still drawing the wrong conclusions – as a profession, we seem OK with taking that chance, even though we know that such a situation is more likely to hold the disadvantaged child back in their learning and perpetuate inequality.

Schematic of a machine learning algorithm (taken from John Salatas’ ICT researchblog)

There are probably a few more examples of ‘best practice’ that when looked at through the prism of ‘what are children thinking’, might seem somewhat dubious. Please do feel free to add to this post by commenting below on examples you can think of and that you are now questioning. For me, this whole journey has actually shifted the way I teach. I’ve always been a trad, but I now use so much more choral response in my teaching practice, and I plan for what children are thinking at any one point in the lesson, being keen to ensure that everyone is thinking about the knowledge. Frequently, this means my doing one question and their then doing a similar question in turn, all the way through the lesson. I do whatever I can to ensure that nothing is left to chance.

*Returning, as promised, to the issue of what to do with higher attainers in these kinds of lessons, I do understand that if there is compromise, then it is their learning potential, erm, potentially. These are children who are what I call ‘super-focusers’ and they tend to be prolific readers in and outside of school such that for any unit of time, they are gaining more knowledge and making more and more connections than anyone else. However, allowing them to do and learn something different also risks their internalising that they’re naturally good at, say, maths – this can lead to a sloppiness of working out, lack of systematic approach to problem solving, a poor attitude to wisdom and expertise and the risk that further down the line, a learned laziness embeds that eventually curtails their potential. I know this happened to me because when I went to a mad private school, I was accelerated to a year group above my chronological age and then when I went back into the state system (and you’re about to sense some serious sour grapes on this), I was told ‘We are not elitist and Hannah will be returned to learning with peers her own age’. It was all way too easy and I switched off. I’d actually be in favour of accelerating children up year groups and then when they get to year 6 they’d be in a small group of super-mathematicians, rather than have the current scenario where we let lower attainers fall further behind and never really catch up (even with interventions).

This has probably been the most enjoyable blog post I have ever written and, regardless of which maths (or history, or geography etc) program you are using, I hope the content has caused you to look again at your short term planning and think about what the children are thinking.

Who’s with me?

 

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7 thoughts on “Are they really learning, or have you (accidentally) planned for a 1000 inequalities?

  1. I particularly liked this one:
    “Systematic retrieval practice that constitutes the majority of the calculations practice in a lesson: understanding is developed during that practice (connections are made) and core knowledge is transferred to all long term memories in the class”.

    in England’s National Curriculum, lessons designed to instill conceptual knowledge precede the teaching of procedures. Recommendations produced by the NCETM closely track the progression in the NC, and of course this informs the guidance dispensed by our Maths Hubs. As an example of how this works, this conceptual knowledge is specified in the NC for Year 2:

    “Pupils use fractions as ‘fractions of’ discrete and continuous quantities by solving problems using shapes, objects and quantities. They connect unit fractions to equal sharing and grouping, to numbers when they can be calculated, and to measures, finding fractions of lengths, quantities, sets of objects or shapes. They meet 3/4 as the first example of a non-unit fraction.”

    However, pupils don’t learn to add fractions with different denominators–such as 1/3 + 1/2 –until Year 6.

    The Far East is the only area where procedures are taught before concepts. These nations outperform the UK and other Western nations on both PISA and TIMSS–usually by very substantial margins. In a 1999 article in The American Educator, Wu argued that

    “in mathematics, skills and understanding are completely intertwined. In most cases, the precision and fluency in the execution of the skills are the requisite vehicles to convey the conceptual understanding. ..Conceptual advances are invariably built on the bedrock of technique. Without the quadratic formula, for example, the theoretical development of polynomial equations and hence of algebra as a whole would have been very different.”

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  2. A lot to think about here. I feel that many educators *think* they are considering what the children are thinking, but are (although very well-intentioned), off base a tad (myself included!) and posts like this really make us take a step back and re-evaluate. Thanks so much for sharing 🙂

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  3. I’m not irked or surprised either. Most teachers know that direct instruction works, but have been led to believe it is wrong. Given permission to teach properly, results are usually quite quick.

    It will be interesting to see if there’s any back-sliding. I’ve seen teachers who have seen that the pupils at a school are doing well — because the teachers before them taught explicitly — instigate inquiry techniques because they had the luxury of doing so with students who were well prepared. Not realising that the reason they think can is precisely because the people before them haven’t.

    My bet is that if your school continues on its improvements, that there’ll be pressure from some quarters to get even better — by advancing the previously used techniques that didn’t work.

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  4. […] Explicit instruction is growing in popularity, particularly more extreme script-based approaches based on Engelmann’s direct instruction. Its advocates suggest that the evidence warrants it; however, the evidence seems largely based on the premise that guided instruction is better than unguided. By definition, it is hard to disagree, but socially constructing a definition to debunk decades of scholarship does not constitute evidence. […]

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