**The problem of Juxtaposition Prompting**

In sum:

1)Theproblem of Juxtaposition Promptingis endemic in our classrooms. It prevents generalisation and transfer, and therefore what we consider ‘deep understanding’ or ‘deep thinking.’

2)To overcome it, we must reconsider old lesson and curriculum structures, to carefully introduce greater variation into lessons, which will require us toremove lesson objectivesas we know them.

Give this a go, if you like.

**From brilliant.org**

When I tried it three thoughts came to mind. First, this can definitely be solved using **trig**. Second, I wonder if there’s a simpler way to solve it using **ratio**. Third, I wonder if there are **other ways** to solve it that haven’t occurred to me.

Now let’s think about where this can fit into a lesson.

If we include it in a lesson about trig, pupils will automatically think they have to use trigonometry to solve it, and try that.

If we put it into a lesson in ratio, they’ll think they need to use ratio to solve it, and try that.

If we put it into a lesson on cumulative frequency diagrams, they’ll be deeply confused and refuse to engage.

This is the problem of **Juxtaposition Prompting **^{1}. We narrow pupils’ thinking, constrain their ability to **generalise** and **prevent transfer** by teaching pupils that they can use some feature of the *lesson* to figure out how to respond to our questions: ‘This is a ‘*Pythagoras lesson*,’ so there must be some way of using Pythagoras’ Theorem to solve this problem.’

In principle, the solution is to very, very carefully introduce greater variation into each lesson. In one moment I’m asking you to calculate an unknown angle, in the next I’m asking you to calculate the missing numbers in a set, having given you the set’s mean and range, and in the next I’m asking you to add three fractions together.

This is the same as what Bjork calls the Desirable Difficulty of Interleaving ^{2} (though I personally tend to prefer using that word to mean something related, but different,) and it’s noted as the Variability Effect by Sweller ^{3}.

Although messy and confusing language, the concept of **Juxtaposition Prompting** helps us to understand why interleaving in this way can be useful, and why the Variability Effect manifests.

I used to run daily negative addition / subtraction drills with children in Year 9. The sheets always looked like this (credit to Bruno Reddy for creating the auto-generator in Excel)

Now, they *were* very effective, perhaps because I added in a few other bits and pieces around the edges (e.g. talking about what to do for each section and why, over time) and spent so very long on them – but it would have been more effective if they weren’t always arranged so neatly into the same columns. The **problem of Juxtaposition Prompting** rears its ugly head here because pupils can, and did, quickly learn that ‘in column 2 I just add the numbers’ rather than ‘when subtracting a negative I can add it as a positive.’ They were able to respond correctly to the questions by attending to something extraneous to what I wanted them to learn. I was intuitively aware of this problem and wanted to change the sheets to avoid it, but it’s a nightmare to create that kind of flexibility when you only have Excel available to program with; likewise, while it didn’t have a name before now, I’m sure most teachers reading this will have realised this problem before.

So we need to design worksheets and even whole lessons to remove pupils’ ability to preempt how to respond on the basis of ‘the lesson objective;’ the greater the variation in question type for any one lesson, the more we tear into this problem. But I noted above that this must be done very, very carefully. At the other end of the scale lies **cognitive overload: **too much variation, of the wrong kind, and pupils have no idea what’s happening or how to respond to any questions. The trick is in successfully manoeuvring pupils to attend to the right things – to kick **System 2 thinking **^{4 }into gear, if you like – without leaving them frustrated and feeling overwhelmed / overloaded.

Ultimately, pulling this off requires completely rethinking how we plan for learning over time. It requires us to abandon ‘lesson planning’ as we know it, with its objectives and careful **A leads to B leads to C** structures, and instead have many micro-objectives being studied and revised in every lesson. Engelmann’s curricula work much like this – referred to here as a ‘**Strand Curriculum**‘ design ^{5}.

**The black is a traditional Spiral Curriculum Design. The grey shows a Strand Design**

**Scheduling the lessons in which a given objective will appear, over time**

In these curricula objectives are not covered in a lesson, but over 50 or 100 lessons or more, simultaneously alongside other objectives.

**In sum:**

**1)** The **problem of Juxtaposition Prompting** is endemic in our classrooms. It prevents generalisation and transfer, and therefore what we consider ‘deep understanding’ or ‘deep thinking.’

**2)** To overcome it, we must reconsider old lesson and curriculum structures, to carefully introduce greater variation into lessons, which will require us to **remove lesson objectives** as we know them.

^{1 }Engelmann, S., & Carnine, D. (1982). *Theory of instruction: Principles and applications*. New York: Irvington Publishers.

^{2 }https://bjorklab.psych.ucla.edu/research/#interleaving accessed 17/04/17

^{3 }Sweller, J., Van Merrienboer, J. J., & Paas, F. G. (1998). Cognitive architecture and instructional design. *Educational psychology review*, *10*(3), 251-296.

^{4 }Kahneman, D. (2011). *Thinking, fast and slow*. Macmillan.

^{5 }Snider, Vicki E. “A Comparison of Spiral versus Strand Curriculum.” *Journal of Direct Instruction* 4.1 (2004): 29-39.

Might an alternative middle way be that each lesson has a single learning objective for new content to be learnt, but what’s practiced in a lesson is more interleaved, with anything goes? So there’s certainty of what new concept is being introduced, and there will be some practice of that, but it’s always clear that anything else might come up in practice questions, leveraging the interleaving effect.

Almost certainly, but it still depends on what the ‘LO’ looks like, for different reasons.

I think their current form is largely a misinterpretation of Dylan Wiliam’s earlier work; I’m also struck by how much I learn from something like Michel Thomas without the need for learning objectives per se to be stated at any point. On the other hand, when introducing something they can’t do yet / haven’t seen before, I’m imagine there’s scope to do something that ‘sets the scene’ or ‘introduces new learning,’ etc. much as you suggested.

I agree with jdapayne. I don’t think it has to be one or the other. The experienced and good teacher can (and I believe must) have a lesson objective (or more than one, ideally differentiated) shown on the board but allow for higher level questioning that will enter other concepts and areas. The teacher should also create a culture and environment whereby students do this. Again, this is what an experienced and/or excellent teacher does naturally.

I agree with Steve (next comment) too.

The actual title is misleading because I don’t think the article actually pushes for removing objectives but more to allow connections with other concepts. There is nothing to say we cannot do this without clear objectives as per my comment above.

Personally, I think the research (including Hattie) is pretty clear and significant on using lesson objectives (as you point out – if done correctly). This in itself is rare for educational research!

Thank you for putting a thought-provoking article.

Reblogged this on The Echo Chamber.

I’ve taught classes who, in the midst of learning about Pythagoras’ Theorem, can solve the most complex of problems and who can, similarly when learning trig, solve hideously complex trig problems in 3D.

The problem comes when the face a problem which isn’t clearly flagged as trig or pythag in an exam, for example. They so often went down the wrong route having “just gussed” one way or the other.

As I developed as a teacher I started to give serious exam revision time to activities where students had big piles of questions and their only task was to sort into ‘trig’, ‘Pythag’ or ‘either’ piles and explain why. It was effective but felt like an ‘exam prep fix’.

Nowadays I still teach Pythag as a discrete chunk of work and ditto trig (although my LOs, in so much as I share them, are much more ‘over the next X lessons we will be learning about …. and you will need to be able to do ….” Compared to the lesson by lesson LOs in my early career) but my weekly home works are a “glorious pick and mix” of this, that and everything we have studied to date.

That’s proved very effective at keeping learning fresh (which was my initial aim) but, as an unintended (but very welcome) side effect, has really sharpened students’ decision making process.

Agree! Thanks! My response is above

Interesting post Kris, and it’s great to see this aspect of inflexible knowledge/situated cognition named. The thing that always strikes me about variability of practice is that it works much better in some subjects than in others. In maths and language learning, if we are going to do lots of practice at some point in the lesson, we can vary the types of sums/sentences requested: (I go to the beach, you went to the beach, they are going to the cinema) and accrue significant benefits.

I think these benefits come with significant costs in subjects like history. To take your example, if we are teaching a unit on the French Revolution, we may want a lesson (or more) in which to teach the Terror. There are a lot of separate things to understand, and they have to hang together to understand the phenomenon as a whole. What we might benefit from varying the topics (ten minutes on the Terror, then five minutes going back to the Storming of the Bastille), we will lose from abandoning the story structure the lesson could otherwise follow (and, I suspect, from students’ righteous indignation about such a lesson approach, which can’t be totally overlooked).

The solution I’ve proposed for a subject like history is maintaining a narrative structure and a focused lesson objective, but planning in advance what previous topics to recap and what future topics to foreshadow – I’ve described this here: https://improvingteaching.co.uk/2017/04/23/better-planning-better-teaching-better-learning-a-template/ We can also ask a variety of questions about the same thing (Why was the Bastille stormed? What effect did this have? How have historians disagreed about the event?) to vary the practice about the same topic. I think this allows us to get closer to what you’re advocating with jettisoning having a main idea for a lesson.

Sorry it took so long for me to reply this this, Harry.

You’re absolutely right about how this changes from subject to subject. I think you’re probably right – restructuring a curriculum the way I’ve suggested probably isn’t appropriate for the kind of teaching that happens in history lessons. I suspect this is a combination of *what* we try to teach in history, and how it’s distinct from maths/languages etc. and potentially how the subject is assessed as well…

One of the interesting things I find about history cf. maths is that it is heavily fact dependent, whereas maths isn’t. I think people expect maths to be all about facts, but the more and more I think about it the more I become convinced that very light on facts, and super-heavy on concepts and processes, whereas history perhaps has no processes at all, relatively few concepts (sorta…) and a super-abundance of facts.

The concepts thing in history *can* get messy, for example ‘Russian’ is arguably a concept, and ‘Russian in the 1960s’ is another concept, and perhaps they both depend on concepts of ‘citizen,’ ‘nation,’ and ‘identity’… but then how deeply do history teachers strive to fully map out what those concepts mean, and do they even have limits \ clear boundaries, the way that concepts in mathematics tend to, or are they forever subject to extensive debate and disagreement…?

My working-hypothesis is that the importance of variation becomes dominant in subjects whose content is very heavy on process-chains and transformation-concepts in particular… but that’s just a starting position. I could be way off. Fascinating to keep thinking about, though.

An interesting post. I will go back and read several times as well as re-referring to th evarious texts.

I have to be honest and say that I was a little confused by the post, in that I wasn’t sure quite what you are advocating. You talked about “getting rid of learning objectives” but then went on to talk about “learning objectives as we know them”.

The vast majority of the points you make I have seen before, and Harry above described the “naming of the issue” .

I have an initial feeling that you are describing something that is very particular to your own teaching style as I do not recognise the processes raised in my teaching. I will read Engelmann again with a focus on Juxtoposition prompting.

A really nice post.

Thanks Brian.

I think with objectives it’s about how they’re used – of course *we* need to be clear on precisely what we’re teaching, when, how and why, but if we look at how the concept of ‘sharing learning objectives’ is used in teaching – especially maths teaching – it allows for spurious prompting: “I know I need to use Method X because that’s what today’s lesson is about,” rather than recognising the need to use Method X because of features of the problem / question.

Which processes did you not recognise from your teaching? Which subject do you teach, as well?