SLOP for declarative knowledge resources here
Starting with a very brief history – this time three years ago, -I liked my job-. I got good observations by getting my students really engaged in practical work, and I got results by secretly telling my groups what they needed to know when no-one was watching. I was happy, but I wasn’t thinking. I was never bored, but I was never fascinated either.
This time two years ago, I had just read Daisy Christodoulou’s book “Seven Myths About Education” – and nothing would ever be the same again.
This time one year ago I came to my first ResearchED, at Ashlawn School here in Rugby, and I spoke about how I’d been trying to apply what I’d learned about cognitive science to teaching in my classroom.
When you start learning about cognitive science, so much opens up. So much makes sense – and at the same time so many of your assumptions are challenged. Your brain feels like it’s being made to work and it feels wonderful.
What I’m proposing today is that philosophy can play a similarly important and rewarding role in education. In fact I’d go further and say that philosophy is necessary in order to apply cognitive science well. In education we’re seeking to build knowledge in our students, but knowledge is complicated. Philosophers have been thinking about knowledge for thousands of years and we need to draw on their wisdom, their conceptual frameworks, their language in order to get to grips with this thing called knowledge.
So back to my own journey with researchED :
One of the main things that came out of my reading around cognitive science was the benefits of lots and lots of similar questions for students to practise on: Shed Loads Of Practice, or SLOP. I’d seen this kind of questions for maths but for some reason we didn’t seem to have them in science – so I started making my own.
Here’s an example:
SLIDE 3 (pause)
Now this kind of work for our students has several cognitive benefits:
• “Memory is the residue of thought” as Dan Willingham tells us, and so if our students are spending time thinking about answering these questions, they are building strong memory of the area.
• Cognitive Load Theory: This model of cognition tells us that space in working memory, where we process new problems , is very limited. By repeatedly practising similar questions, we automate the process as it is encoded into our long-term memory. This frees up space in our working memory, allowing us to successfully tackle challenging problems.
• The value of feedback is one of the most well-evidenced things in education I think, and with SLOP, we can actually make feedback work for our subject. If students are getting something wrong, we can show them their mistake, or “reteach” and then there are lots more questions for them to practise on in light of this feedback. They can even do it in purple pen if you like…
There are some other observations about SLOP that I think it’s interesting to make:
• It’s easy to make – it might not be quick, but once you have one question it’s easy to make lots of different versions of it for practice. In fact some amazing people are writing code to generate questions –have a look at Gary Davies’ brilliant work on this.
• SLOP’s easy to give feedback on – Almost all SLOP questions have a single, right-or-wrong answer. One thing I felt we’d been getting wrong in science was focussing on questions but not answers, I don’t know if that’s down to assuming that teachers can just work them out themselves – obviously we can but it takes time – or possibly the focus we had for so long on activity (answering questions) rather than knowledge (what answers do they need to be able to give). Anyway, I’m a big fan of writing answers to go with all SLOP questions, so we can read them out or project them in lessons, and students can quickly self-mark and we can see where any problems arise.
• Quite easy to atomise – I think it’s Kris Boulton who coined this term, what I mean is it’s quite easy to break a process down into constituent steps, practising one at a time in order to allow students to master very challenging work.
• And linked with this is the possibility with SLOP of making questions with increasing level of difficulty, beginning for example with values for quantities already identified along with the formula, and ending with a worded question where students have to pick out the values for themselves and choose the right equation, maybe convert a few units, that kind of thing.
• Renewable and transferable – we’re obsessed with sensible workload at my school and what we’ve noticed is this: I can’t teach a lesson using someone else’s slides. Or lesson plan. Or “activity.” I can’t even make much use of a lesson plan of my own a year after I’ve made it. But if a colleague has made a load of SLOP for a topic, it’s easy to pick up and use – and likewise if I’ve made some SLOP myself a while ago, it’s really easy to use later on. This is a very interesting phenomenon, I feel like it tells us something deep but I don’t know what it is yet – but for now I’m happy because teacher time is precious, and SLOP saves teacher time.
So it’s fair to say I love SLOP. But, as I was working with this model, I kept running into a problem. As I was writing SLOP, working my way through a unit, this sort of thing would happen:
Properties of waves – yay SLOP
The wave equation– mmm SLOP
Ray diagrams – SLOP SLOP lovely SLOP
Production and absorption of electromagnetic waves?? ______ ______ ???
And a similar thing here:
Fleming’s left hand rule SLOP
Explain how a DC motor works…. ???? HOW DO YOU WRITE SLOP FOR THESE THINGS?
Right? Some things are easy to write SLOP for, and some are really hard.
List A here shows some things I think are easy to write SLOP for, and list B is some things for which writing SLOP is a struggle. I’m going to call them SLOP-amenable and SLOP-resistant.
So – this is really interesting, and quite mysterious. There’s something in the nature of these areas that make SLOP difficult to make, while other areas are much easier.
So it’s the difference between these two lists that I want to talk about today.
I want to give my students Shed Loads Of Practice on all of their curriculum. But is this possible? Or is there a fundamental principle meaning that you can’t write SLOP for these topics in list B? Is SLOP forbidden for these areas, by some law of nature? Is it senseless to pursue SLOP for these areas, in the same way that it is senseless to try and staple water, or sculpt air?
At first I thought the SLOP-amenable areas were all calculations, but that’s not quite right, punnet squares, products of reactions and dot and cross diagrams are all in there and they don’t involve any calculations.
What all these questions do have in common is that the student should carry out a procedure, a method or algorithm if you like, and the person writing the question changes the initial conditions. The initial conditions can be numerical values, but they can also be things like reactants, parental alleles, or constituent elements. The fact that people have written programmes to generate these questions is a big clue to this procedural nature of SLOP-amenable topics. The procedural nature of the knowledge means that many similar questions can be generated because the procedure can be applied to many different sets of initial conditions.
So if these SLOP-amenable topics are procedural, are SLOP-resistant topics are the opposite of procedural? I have to know this because I need to know if SLOP is possible for these topics.
Knowledge is characterised by philosophers as falling into two groups: There’s procedural knowledge, or knowing how, and this is when you know how to carry out a process. And then there’s declarative knowledge, or knowing that, and this is when you know something to be the case. Could our answer lie in this distinction? Are SLOP-resistant topics declarative knowledge?
Looking back at these two lists, they do look like they represent these two categories.
Know-how to calculate velocity. Know-how to draw dot-and-cross diagrams. Know-that electromagnetic radiation interacts with matter in this way. Know-that the National Grid is designed how it is because… And so on.
So: Procedural knowledge, declarative knowledge. Knowing-how, and knowing-that.
Are these declarative knowledge topics, then, “just recall”?
This is interesting.
I like the way that sounds like the bitterest of insults.
If students are just remembering some facts, rather than applying a procedure, then surely it must be the case that these SLOP-resistant topics are easy while the SLOP-amenable ones are hard?
If you’re planning a lesson and you know you’re going to be observed, it’s ace if you’re due to do one of these SLOP-amenable topics. You can show expert modelling of a worked example, AfL with your mini-whiteboards, students completing increasingly challenging work and probably the observer (a non-specialist of course) will be wowed by all the snazzy symbols and maths and will recognise that the work your students are doing is really challenging.
But if you’re due to do a SLOP-resistant topic, it’s like, oh god, how can I plan a great lesson, there’s nothing for them to do, they just need to know it. I’ve said this myself and heard colleagues say it too, countless times and it is a perfect example of knowing-how contrasted against knowing-that. “There’s nothing for them to do, they just need to know it.”
It’s interesting about being observed here. There are a couple of areas that you feel sad about teaching whether or not you’re being observed. These are the little, annoying, not-very-interesting things like “what is peer review” and that Resources unit out of the chemistry. They don’t really have much explanatory power and they don’t illustrate fundamental principles. These things are SLOP-resistant but they’re also just a bit shit, I mean I can see why someone might want to include them, to help our students grow into good citizens, but they’re just not pleasing or interesting to the specialist.
But that’s not what we’ve got with this list.
I like teaching these proper things, because they’re cool. I just don’t want to be observed teaching them because of this problem: “there’s nothing for them to do, they just have to know it.”
It’s a short jump from this idea to thinking that these SLOP-resistant topics are not challenging while the SLOP-amenable ones are. This idea is lent weight by the pernicious denigration of knowledge that we are fighting every day in our schools. But this idea is wrong, wrong, wrong. Are your students getting loads of marks on -these topics but not on -these? Mine aren’t.
To understand and be able to answer questions on these SLOP-resistant topics is absolutely not “lower order thinking”.
D.C. motors: First of all remember which way current moves relative to the power supply. Now actually apply Fleming’s left hand rule to this side of the coil – now flip your mind around please because the wire is coming out of the page, kindly apply Fleming’s left-hand rule again here, or just remember that the force will be reversed because the direction of current has reversed, it’s up to you. Or of course you could do this whole bit using maths, but I’m going to say that’s probably felt by most people to be pretty hard as well. Now we’ve explained one half-turn and you have to repeat the last two steps in order to show that the coil will not turn any further… enter the commutator! And so on.
And it’s the same for all these topics. They’re not easy, they’re hard.
If anything I’ve proved to myself here that SLOP is very much needed for these areas, because they are hard, but I haven’t got much closer to finding out how it can be done, or if it’s even possible. To answer this, I turned again to philosophy.
Most philosophers in this area see procedural knowledge as a subset of declarative knowledge. They say all you have to do in order to carry out a procedure, is know-that step 1 is X, know-that step 2 is Y, and so on.
But the philosopher Gilbert Ryle says it’s the other way round: that declarative knowledge necessarily requires some procedural knowledge. Hasok Chang, a philosopher of science from the University of Cambridge illustrates this: when as a child we first learn that this is a table, and that this is a chair, we must first have learned-how – to play the pointing game.
Here’s another way of looking at it. If the human race was wiped out, but all our textbooks remained, what would be the nature of what remained? I don’t think we could call it knowledge – for me knowledge needs a knower, and a knower is a living person, a being in time.
So what I’m following Ryle and Chang in saying is that declarative knowledge is really a special type of procedural knowledge. This is important because if it’s true then it should mean that we can break declarative knowledge into steps, and create practice for each step. Shedloads, in fact, of practice.
One of the most powerful models I’ve come across in cognitive science is the idea of knowledge existing as a schema – a web of connected pieces that we move through when we think.
SLIDE 13 – schema and subset web
I think that when we understand a declarative knowledge topic, we move through the web, from one relevant node to another. Maybe it’s like a musician reaching for notes where he knows they will be, or maybe it’s like a butterfly going from flower to flower, drinking nectar. We move through all the associated knowledge, gathering things we know to be useful and disregarding those we know to be irrelevant at this time. So in my explanation of my DC motor, I move from my Fleming’s Left Hand Rule, to my knowledge of rotating effect of a force, , I’ll double back and take another branch towards my knowledge of current flow, I arrive at my knowledge about the problem of the continuous rotation, and then that neat solution, the commutator…
SLIDE 14– lists A and B
So going back to our two lists – the difference here is not that
these topics (B) do not involve processes. It’s that the processes for B are much more…. Untidy, less predictable, less explicit, less linear. Less of an algorithm, more of a dance.
I wonder if some of the progressive opprobrium of knowledge comes from seeing it as just “information”- maybe if we can show it to be such a very human experience it could go some way to bridging the gap and convincing people that knowledge is wonderful?
Maybe and maybe not. But what I’m really interested in is this: if understanding these SLOP-resistant concepts, and answering questions on them, are processes that take place in time, then we should be able to break them down into steps. And if we can do that, we should be able to create SLOP for them.
So I’ve been thinking about what this SLOP might look like.
I feel like whenever you move in the web, a relationship is involved. So it could just be “this leads to that” or “this is an example of that”. Or sometimes we’ve got “this forbids that” and very often of course, “this explains that”. So relationships between propositions are critical to this dance through the web.
If we can be explicit about propositions and their relationships, and get students to practise them, then we will have gone a long way to achieving Shed Loads Of Practice.
So I’ve been experimenting with this model:
Reading, comprehension, graphic organiser, sophisticated sentences, extended answer.
So I thought it might be useful to talk a bit about each of the stages in the model.
Reading – quality text, with diagrams, to start the unit and refer to during practice, with the aim of “fading” reliance on the text as we move through the practice.
Bog-standard comprehension: What is a gene? Which way does the current flow? Where will the ion move to? These are absolutely critical foundations – but they are only foundations. Previously I’ve stopped here and moved on, and my pupils have not had the practice they need. So.
In order to practise the movement through the web, to spend time thinking about the relationships between the knowledge, I have been getting students to work on graphic organisers for their declarative knowledge. I’ve been through and tried to list all the relationships I could see in these declarative knowledge topics.
And then I’ve tried to find or create a graphic organiser for each type of relationship, so that students can think explicitly about the relationships in the knowledge. All this will go on my blog after this talk, so if you’re following me you should be able to find it so please use it if it’s helpful. I won’t go through them all now, lots of them of course are very familiar, like the flow chart for sequential relationships, but I’ll just explain the thinking behind a few of them.
For systems, I’ve been using this “Label and counterfactuals” graphic. The system goes in the middle and then students label the parts and functions. Then I’m putting questions around the outside ring, about effects of changing the parts. What would happen if the current was reversed here? What would happen if the commutator was broken? What would happen if the coil was twice as heavy?
This is the graphic I’ve been using for misconceptions. Research says we never really lose our misconceptions: we just learn how to stifle them. So it seems to me that this is a relationship in our schema, a relationship where we sort of arrive at the misconception, remember it’s wrong, and then turn round and go the other way, arriving at the correct understanding. So to get students to practise this relationship I’m getting them to fill in the wrong idea here, write a little warning note to themselves here (“Stop! No resultant force does not necessarily mean no motion!”), and then write the correct understanding here.
I’ve called this one the manifestations grid, what I’ve been getting students to do is to fill in the underlying principle here, so that might be “conservation of momentum”, and then the manifestations in these boxes, I’ve found it best to just put the question in there so it might be a diagram of a cannon and cannonball, two ice skaters, exploding trolleys. Then in these faded boxes I get them to write about the surface features, what’s different about them: it’s a cannon firing a cannonball, it’s two ice skaters pushing off each other. And then here is where they fill in what links it to the principle, so – the cannon and cannonball are two bodies in an explosion. Momentum before = momentum after. And so on.
Using a decision tree to show the outcomes of a set of initial conditions is an idea I got from Pritesh Raichura, so I’ve been giving students partially completed trees and getting them to fill in the rest…
And then finally another idea from Pritesh, a proportion map. There is an important declarative element to all formulas, and showing the relationships using arrows like this I think helps to make them explicit. So again I’ve been giving students a partially completed map and asking them to fill it in.
So my students have had a decent bit of practice now. But we want even more – so here I’ve been heavily influenced by the book “The Writing Revolution”, in particular about training students to craft excellent sentences in order to think deeply about a subject. So the next stage in my model I’ve called “sophisticated sentences” just because I wanted it to be a bit catchy – I’ve tried to begin to create a bank of sentence structures, stems and conjunctions that match the types of relationships we’ve just been looking at.
SLIDES 29 – 33
Again this is all going on my blog so please use it you think it could help. These sentences are amazing. I mean it’s lovely to see the students writing sentences like this, especially when they spontaneously recreate them in later work, but that’s just a happy accident, a free gift. The reason for doing it is to get them practising thinking deeply with the knowledge, and I think that it’s a really powerful tool.
Finally I ask students to put it all together in an extended answer, to build resilience and force them to think about the whole thing all at once, whilst balancing the challenge of writing a longer piece. And after all that, they’ve had a decent amount of practice.
Going back to this then, what I’m trying to get them to do is to build and strengthen these deep, detailed and well-organised schema, by practising moving through the web using the model Reading, bog-standard comprehension, graphic organiser, sophisticated sentences, extended answers.
So that’s what I’ve been doing really, I wanted SLOP and I got it in the end, none of the parts on their own were original but putting them together in this way was new for me at least, and I’ve loved working with it.
In education we are trying to transfer something that is in our head into the heads of our learners. But there is no direct route, there is no plug and play, no copy and paste. We have to translate what’s in our heads into a medium that can cross the gap, and then help our students to build their own schema. This is our explanations, and practice and feedback respectively.
It’s clear that we must try and apply the principles of cognitive science to our teaching because learning is a cognitive process. What I’m suggesting further to this is that we need philosophy as well – because not all knowledge is the same, and philosophy helps us to understand why. If we can understand the nature of the knowledge, then we’re better informed about how to cross the gap, how to build the web, how to teach our students, really really well.