Podcast series two now available
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Teacher Craig Barton is back with series two of Inside Exams, the podcast that gives you an access all areas pass to snoop around behind the scenes at AQA.
He’ll be meeting the people who write and mark your students’ exams, as well as pioneering teachers, to get answers to all the questions you ponder throughout the school day.
© AQA 2019
Writing questions: setting the setting
Episode four | 9 December 2019
Why are some exam questions written in context? Mike, AQA’s Lead Assessment Writer for GCSE Physics, tells Craig Barton how he comes up with interesting contexts, and Laurie Luscombe, a maths teacher at The Blue Coat School in Oldham, explains how he teaches them in the classroom.
Featured in this podcast
Craig Barton – Maths teacher, podcaster and author
Mike – AQA’s Lead Assessment Writer for GCSE Physics
Laurie Luscombe – maths teacher at The Blue Coat School, Oldham
Here are some useful links to resources to use in the classroom when teaching contexts:
- The British Library teaching resources
- 20 ideas for enriching students' cultural capital [Teachit]
- The National Theatre teaching resources
- The National Portrait Gallery learning resources
- Science Museum learning resources
Craig Barton: Hello, and welcome to Inside Exams. I’m Craig Barton, and I’ve been teaching maths for 15 years now. I’m pretty confident in my teaching ability, but I think we all have those moments when we wish we could quickly clarify something about the spec with the people who wrote it.
Well, that’s exactly what we’re doing on this podcast. I’m putting your questions to the exam experts, so what insights would it be useful for me to gather?
Bridget: My name’s Bridget, I teach psychology, I teach students for a variety of backgrounds, so how do you ensure all contexts are fair for all students, and how do you reduce the risk of introducing bias.
Craig Barton: Do you know what, Back to the Future, aside from being a brilliant film is a great example of the confusion that develops when you're catapulted into a cultural context you don’t understand. 1955 Doc can’t fathom that in 1985 the President of the USA is an actor. That’s unthinkable. All he knows is a world where only a lucky few have recently got 1 tiny TV. His understanding of celebrity is long term because his own life experience means he hasn’t got the whole context.
So, what do exam boards do to make sure that, like you said, Bridget, no student is disadvantaged because they don’t understand the context?
I’m going to meet Mike. He’s AQA’s Lead Assessment Writer for GCSE Physics, and I’m hoping he’ll be able to explain exactly how exam writers ensure it’s the content rather than the context that’s ultimately being tested.
Okay, Mike, thank you very much for the kind invite to come and speak to you at AQA today. I want to start with a question that’s come in on Twitter by @DRoseMaths. He says: How much content must be contextualised? What are the rules here with this?
Mike: From a physics exam point of view, there is no real limit to how much should be contextualised and how much shouldn't be. As a question writer, you sort of decide about whether it would be appropriate to have a context or whether it wouldn't. If it’s a question about electricity, you might choose not to have a context because the electrical circuit might be quite complicated, whereas if it was a question about energy transfers and a context was appropriate, you would build that into the question.
It generally depends on whether the question that’s going to be asked fits in with the everyday context that students would probably appreciate, something that they might have experienced in their everyday life. This recent exam series I’d written a question about a zip wire in a park, but fundamentally it was simply testing whether the student understood how to work out gravitational potential energy. So while it hopefully is something that students at some point in their playground days might have actually had experience of, it didn't fundamentally alter the question that was actually being tested.
So they are designed really to be relatively simple context.
Craig Barton: How does it fit into the assessment objectives? Because we’ve heard a lot about those in the past two seasons of this podcast. I know there are requirements to have a certain amount of AO2 and AO3 questions. Is that where context feeds in?
Mike: It does, but I think it probably depends a fair bit on the subject. I was talking to a colleague earlier today about chemistry, and a previous conversation that I had with the chair of chemistry who rules ultimately on the level of the chemistry and the accuracy of the chemistry.
I said some years ago that chemistry questions with context lose students in the context rather than just assessing them on the chemistry, whereas biology and physics questions are usually enhanced by having a context because it’s something that the students can actually relate to from their everyday life.
Craig Barton: Why the difference?
Mike: I guess it’s shaped by my world view that ultimately everything we do in life there is some aspect of physics behind it. This sound booth that we’re in now with the microphones that we’re speaking into, the computer recording the sounds coming out of our mouths, all of that is physics. The fact that we’re sitting on a planet hurtling around the sun is physics.
So I think the student’s experience of physics in a classroom is shaped by those contexts and so it is normal within the subject to have the context added to the questions, whereas perhaps a student’s experience of perhaps chemistry is more to do with the practical aspect of the chemical reactions that they study. Similarly, biology is driven by the interactions of biological organisms which again is part of your real world experience as opposed to just something that’s very abstract. I think maybe that is part of the answer.
Craig Barton: I’ve never thought of that before that different subjects lend themselves better to context because of students’ real world experience. That’s absolutely fascinating.
What I want to dive into next, Mike, is writing questions involving context. Let’s imagine that you sit down and you're wanting to write a physics question and you're wanting to have a contextual element to it. Can you just talk us through the process from start to finish, what’s in your mind first?
Mike: I think probably the genesis for most context based questions that have worked well has been an observation that I’ve made that I’ve come across in everyday life. Some years ago I went on a Year 9 residential where we went on a bushcraft camp, and the bushcraft people who ran the camp were spending pretty much about 3 or 4 hours heating up an outdoor pizza oven by putting small twigs and leaves and branches in it ready so that at lunchtime the 200 students that we’d brought with us for the Year 9 camp could then in very rapid succession took their pizzas in this extremely hot outdoor pizza oven.
It just occurred to me that here is quite an important thing and an interesting way of cooking 200 pizzas in half an hour. So then I thought I’ll remember that and save that for an instance when I can actually write a question about it, which became a question then that students will have sat a few years ago and will probably still exist on Exampro having to do with the specific heat capacity of the pizza oven itself, the colour of the pizza oven.
One of the questions which didn't work so well for this one was to suggest the name of one solid biofuel that the students could have used to heat up the inside of the oven. This overlapped a little bit with chemistry, so there were all sorts of answers that were incorrect. Some students suggested that you could put some shells in it and burn the shells because they were thinking shells are organisms and therefore that will be a biofuel, but you can’t burn shells.
All I really wanted them to say was sticks, twigs, charcoal would have done, but as it was some students wrote banana skins, some students even wrote manure. Now why do you want to stick manure into your own pizza oven to cook food on? But at the same time those students would have scored a mark because it is a solid biofuel. So in the context of the question, the context worked well except that one little part of it which passed students by I think because I think they were overthinking it from a chemistry perspective because the content with biofuel is common content.
Craig Barton: I’m picturing you almost like a poet or a songwriter here wandering around in your day-to-day existence getting inspiration for writing questions, and that’s not what I’m picturing exam writers as. No offence here but I’ve not seen them as artists but in a sense that’s what it is, right?
Mike: Yes, I guess. The pizza oven is my muse –
Craig Barton: [Laughter] I like it.
Mike: – I think you're suggesting. I suppose it is part that. I’m sure artists when they see something that’s beautiful they think oh, I’d like to paint that and I do feel that that is the way I go about writing a large number of the questions that are context driven, as I said earlier.
Some of them will inevitably lack context because of what’s on the specification and it’s difficult to frame a context around it, but yes, certainly, the zip wire question is based on my experience. I have two young children and they spend a lot of time on zip wires. Those sorts of interesting things are generally how I start the process. Finding then the bit of the specification to hang it on is then sometimes a bit more difficult because sometimes the specification doesn't go far enough or you decide that it’s something you've seen that’s interesting in your everyday life but you just can’t do much with. That is the problem with being an exam writer in that you see a lot of interesting context and perhaps only a quarter of them make it to the end of the process.
Craig Barton: Gee, and again, going back, I’m dragging this analogy out as much as possible, but the songwriter or the artist, not all these ideas make it to the final cut of the album. This is fascinating.
So you've got the idea, you've mapped it up to the specification and you've got a question, how do you know if that question works? What are you looking for? You’ve mentioned earlier on that some questions work well, some questions don’t work as well, what does that actually mean?
Mike: As part of the creation process for a question, I would write an initial draft which the reviser, who’s another experienced examiner, would see and they would offer comment on it. They might say this question works, this question doesn't work, it might be slightly beyond a typical student experience. You’d ask the question that you thought the students ought to know the answer from based on the content that they’d been learning about.
Often, the answer to the mark scheme, is what you’d write first and then think, right, how do I elicit the mark scheme response, and the style of the question you choose from a list. Is it something they're supposed to know, in which case you might say: Describe or explain or give one reason. If it’s something that’s slightly beyond their experience you might say, “Suggest,” giving them a hint, a clue that actually this might be beyond your experience but we’re asking you to suggest a possible reason.
Craig Barton: Wow, so the command word becomes super important.
Mike: Oh, yes, definitely, we’re very careful about which command word matches which mark scheme style, and so “suggest” can also be a clue as to: this might not be something that you have been taught about in class, it might be something that you're using your knowledge and understanding but in an unusual context or in a way that is beyond your everyday experience. So those questions would have been more open and inevitably the mark schemes are a little less prescriptive.
Craig Barton: Have you got any examples of questions that you have written yourself that with the benefit of hindsight you think that didn't actually work as well as I intended?
Mike: Some years ago I wrote about a, it was called a camping stove, I won’t name drop the name of the company that saw advertise it but it was a bespoke camping stove that you took away with you, put some twigs in, not the same as the pizza oven, honest, you set fire to them, and in addition to providing you with heat to cook food on, you could also charge your phone because it had a USB connection, so it was quite a novel device. But this question didn't work so well because the artwork for the camping stove had a mesh on the side of it and a number of students thought the mesh was to help you prepare your food. The question I’d asked was: Give another advantage of using this camping stove. Simply put, it was you could charge your portable devices with it, but some students thought the mesh on the side was a cheese grater, so in addition to cooking your food they said you could grate some cheese as well.
Craig Barton: That’s not a bad idea though for a patent, I like that.
Mike: It isn’t but unfortunately that wasn’t quite what the side of the camping stove was for.
Craig Barton: How do you ensure that these contexts are accessible to all students?
Mike: I think being a relatively young person with young kids, I would say that my life experience is pretty typical of someone who lives in the UK. The way in which AQA sets out the introductory statements to questions making sure that the sentences are short, so we try to have no more than 20 words in a sentence, breaking up the page so that there's some white space and helpful artwork that contextualises the question. My question from last summer about the zip line for example had a diagram of someone going down a zip line, and the change in vertical height was what they were trying to calculate given all the relevant information, I would like to think that someone who’d never been on the zip line ever should have been able to answer that question and therefore you wouldn't get a student looking at it going, “I’m not even sure where to start here,” because the information was so set out in an easy to access way.
Craig Barton: It’s fascinating, isn't it, because I think bias is the big thing, certainly from a teacher perspective, running through my head. I can only speak from a maths perspective, when I see some of the context, I think is that favouring some of my students over others, because as soon as that kind of bias comes into play, all of a sudden we’re assessing something else other than the actual, in your case, physics content. Does that make sense?
Mike: Yes, completely. There have been contexts that I’ve thought would make a good question in the past, and at some point in the question-writing process someone’s gone, “I don’t actually think this adds anything to the question, and therefore I think we should probably change it to something that is more accessible.”
A question I can think of, again, never made it, my grandmother had some Victorian bed warming pans on the wall of her house which I’m not sure if they were ever used for bed warming pans, but the idea is you stick some coals in them, they heat up the bed warming pans and you smooth them over the sheets and that warms up the bed.
Craig Barton: Wow, okay.
Mike: So it’s an interesting physics context, but at the end of the day all I wanted to know was can the students describe conduction in metals, which was a process that was on the old GCSE physics spec, so that gives you a view of how long ago I’m talking about, it was about five years ago. So the context didn't really work. It didn't have to be a bed warming pan, I was just looking for something that was different to every other way that had been asked prior to that.
So the question changed, and I did feel a little bit sad about my grandmother’s bed warming pans not getting a mention, but at the same time it probably, well, no, it wasn’t probably, it was the right decision for that question. So you draw on the experience of everyone involved in the process, and sometimes, as I’ve just said in that example, the context didn't work, and so it comes out and the question might become a little bit less interesting as a result, but also perhaps more accessible and that’s the important thing, I think, as you said.
Craig Barton: It’s fascinating, isn't it, because there is this kind of trade-off between interest and accessibility.
Mike: We talk about this quite a lot in meetings because both I and other question-paper writers, some of the meetings that we have in the development process, inevitably I might comment on the context of another examiner’s paper and say I don't think this adds anything to the question. You've got to be able to deal with the criticisms and be ultimately very thick skinned about it and not be precious about your particular context or your particular question, which is something you learn pretty fast in the question-writing process. You don’t say around very long if you're thin skinned, you just wouldn't be able to deal with the criminal.
Craig Barton: Mike, once again, I’ve been blown away by the thought that goes into this question-writing process. That happens every single time I speak to somebody from AQA as part of this series.
Thank you so much for your time. It’s been an absolute pleasure.
Mike: Thank you.
Craig Barton: Okay. Whether we like it or not, we do have to prepare our kids to answer questions in unfamiliar context. What’s the best way to do that in lesson time while also making sure we’re teaching all the content on the spec?
Laurie Luscombe is a maths teacher at the Blue Coat School, Oldham. He’s got a bit of a reputation for coming up with impressive context in class, so I’m looking forward to nicking some of this ideas.
Laurie, first off, thank you so much for inviting us to your school today. Very few things in life make me happier than speaking with a maths teacher so I’m very much looking forward to this. But we’re talking about something I’ve got a bit of a problem with, and that’s context.
My first question is: how do you feel about context? Do you enjoy teaching with them?
Laurie Luscombe: I think it’s part of the parcel of teaching any subject. The questions are going to contextualised whichever way we look at it. I think the first point to make is not to see it as a necessary evil. You hear that word –
Craig Barton: That’s how I see it, I can tell you that.
Laurie Luscombe: What we need to do is think it’s part of the package, perhaps we’ve been led down this road in some of the old style GCSEs, A-levels of we’ve almost been proceduralised ourselves, and we just need to take a step back and go no, there's a bit more to it than just following these procedures. It’s almost that enjoyment factor, you know, when people are doing maths and solving problems or they're really stuck into their own subject area, a little bit of that’s required to get through these contexts and see the other side, if you like.
Craig Barton: Jeez, because I’m going to put my cards on the table here, and as a teacher I struggle to teach questions involved context. This must come through to my kids because I don't think my kids particularly enjoy them either. What are your students’ take on, do you think they enjoy these kind of contextual questions?
Laurie Luscombe: Yes, I think students and teachers alike really. I think they get put off by them. It’s a bit of a sweeping generalisation but I think it may be fair to say if you see a great big whopping contextual question and maybe you don’t select them if you're doing some retrieval practice or whatever it may be. You go for the smaller, snappier questions, or just when it comes to actually you've got to the stage where you've got a question that’s contextualised and we’ve got this habit as students, and sometimes as teachers, of not really wanting to sift through the problem. We want to just get, in the maths case, to the maths.
Yes, so I can understand the issues with that, and having given it a lot of thought, one of the things that I’ve come to the conclusion of is subject knowledge.
I think the more I read around it, the more I understand and appreciate that a strong subject knowledge allows you to make those connections within a topic. It allows you to see them, in our case, the maths running through the problem and almost not getting away by the context itself.
Craig Barton: I can really relate to this because I reckon a mistake I made, I reckon I made this for about 12.5 years, and I’d be fascinated for your view on this, Laurie. I came in with a context too soon, so I’d be almost using the context to introduce a topic.
Let’s take something like the lowest common multiple or something like that, instead of just focusing straight in on the maths, I’m coming in on the context: so here’s an interesting scenario which requires students to use lowest common multiple. But to go back to your point, my kids weren’t at the stage yet where they have the knowledge to fully appreciate that, so I found that they were actually focusing too much on the context and not actually on the maths itself. Is that something you can relate to?
Laurie Luscombe: Yes, absolutely. In some areas I’ve come to a bit of a halfway house whereby I completely agree, if they don’t have the subject knowledge, how can they access the arguably trickier conceptual questions. I think that’s fairly well appreciated.
The way I’ve looking at it and when I was really thinking about what I’ve done over the last couple of years in particular with context, I thought, do you know what, when we talk about context, we often think about lobbing a story of some kind on, you know, you don’t just give a ratio question, you start talking about Anne and Bev who’ve got some random marbles, for whatever reason. It’s superfluous, it’s kind of white noise, it’s faff, it’s redundant, right?
Craig Barton: Yes.
Laurie Luscombe: There's a skill in that. I think that’s part of our job is we have to work with the students and get them to be able to decipher information, thinking about context in a different way, not just the throwing the story on the top like a cloak. I’ve come to realise that it can be done, perhaps this is a different sense of context, but how we set out the maths and how we set the context in that sense can be a bit of, well, I’m going to argue it can be a bit of a game changer, we’ll see what people think.
Craig Barton: Okay. Can you give me an example?
Laurie Luscombe: For example, I’ve got through the deep thinking of subject knowledge and I’ve gone away and I’ve picked a topic and I’ve thought maybe volume. I’ve thought how can we make sure that we ensure a consistency so that what we teach doesn't change and the facts don’t alter and we don’t say, “Oh, by the way, what you learnt in Year 7, forget that, now it’s this.” I thought ah, prisms and cones and that area of volume, that’s an absolute beauty of a topic because any pyramid, what’s the consistent fact there, it’s always one-third of the related cylinder or cuboid or prism that it forms.
So, I thought right, okay, a few years back I thought what can I do that hangs on this really principal factor that is consistent when they get further down the line to trickier shapes it’s still consistent but maybe isn’t so dry. How can I put the context around this? That is one of the topics where I go for it with an experiment. I get water jugs –
Craig Barton: Wow, and this is at the start, right –
Laurie Luscombe: – start, so I’ve got the full works, I’ve got 3D cones, I’ve got 3D cylinders, although you can have a 2D one, and I’ve got jugs of water. In a nutshell, we’re filling them up and the class, I’m trying to generate a bit of excitement, you know, science have got it all with their experiments, I’m trying to get the class around.
Craig Barton: Yes, I like it.
Laurie Luscombe: I’m getting predictions: how many cones are going to fill this cuboid, and similar with the other related shapes? The kids love it. They've got these predictions, it’s not taking up a huge deal of time and they're convinced it’s going to be 2, or is it going to be 2.7, or will there be 7 of these cones, 8 of these cones or pyramids. And of course we don’t get to see what it is.
Craig Barton: Do you know what, Laurie, you've hit upon something here that I’ve been getting wrong because you're really drawing a distinction between different types of context here. We have the redundancy on the one hand, so I’m thinking about how I’ve introduced volume in the past and I’m cringing already here because I’m telling stories, I’ve got those fake set up things where there's characters involved, it’s some scenario that would never happen at all. That’s redundant because again kids can’t get to the deep maths. To me that needs to come later one once they've learnt the maths, then they need to develop this skill to filter out what’s relevant and not.
But you're talking about something different here, aren’t you? This context here and the volume thing you're describing is integral to understanding the concept of volume in a way, if that makes sense?
Laurie Luscombe: Yes, and I referred to it earlier. I’m going to come back to it about subject knowledge. It’s the sitting down and thinking about subject knowledge that then can determine how am I going to conceptualise this in the first instance, as you referred to.
Craig Barton: Yes, because again, you've hit upon something else there because Dan Willingham talks about the problems with these surface features is that kids remember those. I’ll never forget, this was a low point in my teaching career where the kids came out of an exam and there was a question on lowest common multiple involving parrots, how many times does a parrot squawk and the next person squawk at the same time. The kid came out and said, “Sir, you never taught us parrots,” and I’m thinking are you winding me up here or not.
This is the problem, the kids had latched on to that surface feature and not remembered, or not been able to establish what the deeps maths is. But when you're talking about context in the volume lesson, kids are going to remember the third thing because that’s the memorable part of that demonstration.
So my next question is, now we have listeners from all subjects listen to this, they’ll have been loving our chat about that, everybody loves talking about mathematics of course. But if they're sitting there thinking what’s in this for me here, I like the sound of this approach but is this going to work in my subject, do you have any experience or any kind of insight about whether this kind of thinking translates across other subjects?
Laurie Luscombe: I tell you what, I’d like to draw on something that again, I am biased, it’s come from a mathematical background, but I’ve got a book here that stems from the STEP examination, for people who don’t know that’s the Sixth Term Examination Paper that some sixth formers may attempt to help get a place in Cambridge and Warwick.
Now this chap, he’s talking from a maths background, but this is the kind of thing that I do think’s applicable elsewhere and I think it’s for students and teachers alike. The book is called Advanced Problems in Mathematics: Preparing for University, and it’s by Stephen Siklos. Reread the question, check you understood what it wanted.
Craig Barton: Okay. Simplie, or so it sounds.
Laurie Luscombe: “Reread the questions to look for clues, the way it’s phrased, maybe the way a formula might be written, or just other relevant parts of the question. You may think that the question setters are trying to catch you out, but usually nothing could be further from the truth. They're probably doing all in their power to make it easier for you by trying to tell you what to do. Try to work out exactly what it is that you don’t understand.” How hard is that? That’s one that could get overlooked.
Really, I mean be specific. One of the things we need to do is talk to the kids about this. What do they do when they can’t – I like to say, the phrase is: what do they do when they can’t see the light?
Then he says, “Can you simplify it?” So maths, you know, can you put a more simple problem ahead of yourself and try that first, reduce the complexity? Again, I suppose with a different subject, can you just write out a little bit to get you started? Can you not take the entire big question as a whole? Break it down and just focus on a little bit to get you started. Can you look at special cases? Is there anything that you remember that is a real key fact about this topic, be it a key fact about a certain event that happened in whichever other subject we’re referring to?
Then it’s fine when it’s just write down your thoughts, okay, write them down, and in particular try to express the exact reason why you get stuck.
Craig Barton: We’ve spoken Season One to AQA examiners who write these questions, they're obliged to make them unpredictable, so kids are going to be surprised almost by definition in these exams. And that’s what freaks kids out, isn't it? And the frustrating, I don't know if you see this too, Laurie, one of the most frustrating things for me as a teacher is whenever you say to a student, “Come on, that question was about lowest common multiple.” Then they go, “Oh, right, I can do it now.” Or, “That question was about trigonometry.” “Oh, if I’d have known that I could have done it.”
Laurie Luscombe: And you've provided the cue.
Craig Barton: That’s the thing, because the skill is knowing what it’s about right. When we’ve got all these unpredictable questions, it’s really challenging for the kids and challenging for the teacher to empower them to be able to spot which structure.
Laurie Luscombe: Which makes you think, and I thought this before, you could run a similar task where it’s a bunch of questions, total mix, and you ask the students to label, “Read through it. What topic is it?” But I’m cautious with that because –
Craig Barton: Tell me why.
Laurie Luscombe: Because it somewhat suggests one topic per question, so it’s predefined, and there can be so many areas of maths that come into it. Then you can say get them to write down all the topics, but sometimes you need to work your way through the questions to see what they're going to be so I prefer the other one of describing the steps.
One of the things I have done in the past is working in pairs with one expert who’s got a model solution, or preferably model solutions if it can be done more than one way. They've had a chance to read them and get their head around it, and when the student says the first line of what they would do, the expert reveals that line so the student can see where they're up to.
Again, you're saving time, you're involving communication, and every time they say the next line, the expert can reveal it slightly.
Craig Barton: It’s this idea with the expert of talking through their thinking, how do they know what’s coming next, how do they spot it. It’s so important. Let me pitch this to you, Laurie. You’ll probably be aware but listeners may not. One of my approaches for dealing with this is the idea of these SSDD problems, these Same Surface Different Deep problems. This is to address a lot of the issues we’ve talking about today, the fact that when kids are taught things compartmentalised, they don't have to think about what topic it is. If every question for five lessons is on Pythagoras, where’s the need to think about what it’s about?
So it doesn't matter what context you throw at kids, oh, it’s Pythagoras, or it’s volume, because every other thing is. So the idea of SSDD is to present kids with problems that on the surface look the same, same surface, but actually, the depth, the deep structure is different, same surface, different deep structure.
I don't know if you dabble with these, Laurie, but god almighty, the kids find these hard. Let’s take parrots, I’ll give you four questions, each involving a parrot, but I’ll tell you what, they're four different areas of maths. And the kids are like, “What? I thought parrots was the lowest common multiple.” Well, no, and again it helps in the exam because in the exam kids are going to get these questions in isolation. They're not going to be signposted as to what the topic’s about and they've got to find this deep structure themselves.
Have you dabbled with something similar and how have your kids found this kind of approach?
Laurie Luscombe: I’ve jotted down an idea actually which I had the back end of last year, by my own admission I’ve not got around to trialling out yet. It was sort of, maybe you call it a dead steal from the SSDDs, I don't know –
Craig Barton: I’ll get the legal team –
Laurie Luscombe: No, no, it was along the same sort of lines I think really to complement it rather than replace it, I don't think it’s one or the other. It was the idea of spinning it around the other way around so that instead of having different areas of maths with surface content, surface structure looking very similar, having it switched around so that you've got a very similar deep structure but actually the surfaces look very different. You could have a straight line equation of some form, you could have something to do with ratio.
Craig Barton: Yes, tables of values –
Laurie Luscombe: All of which could have a relatively similar, they could all look completely different. One’s about parrots, something else is about cakes, all sorts, right, but actually the mathematics underneath it is really quite similar. So you've got kids are finding out the gradient and they realise oh, right, that’s linked to the other term, and then -
Craig Barton: Yes.
Laurie Luscombe: So actually, the calculations are really much the same, but I wonder about having an odd one out in the...
Craig Barton: To throw them.
Laurie Luscombe: So all four look very different, but three of them the maths is really similar, and one of them is not.
Craig Barton: That’s interesting.
Laurie Luscombe: I don't know, it’s not doing I’ve really dabbled with.
Craig Barton: You need a catchy name, that’s the key to this –
Laurie Luscombe: I did. I came up with a catchy name for something else but you're right, yes. Is it like DDSD, SSDs, I don't know.
Craig Barton: If you call it that, as I say, the legal team will be onto you there. If we’ve got teachers from other subjects or from mathematics listening to this and they want to start doing something similar to your approach, is there any kind of generic advice you could give? How do you start thinking about these kind of activities? Where does the thought process start when you're putting something like this together to start with the context but in a useful way?
Laurie Luscombe: I’m going to have to come back to, Craig, on subject knowledge.
Craig Barton: Well, it’s the key to it, isn't it?
Laurie Luscombe: I think it has the wrong connotations occasionally for people that you get this idea of the geeky professor who can’t empathise, and clearly that’s not what’s meant. Having the whereabouts to appreciate the connections across topics means that you are then better placed to deliver that and to provide opportunities for the students to make those connections which all in all means that in these conceptual problems that are going to vary from bit to bit, students are much quicker at honing in on what is the crux of the problem, what is the mathematics in our case.
But that’s where talking to teachers and collaboration comes in. I don't think it has to be about the wordy scenario, the wordy context, it can be the context that you've set up the lesson in. Then it’s a case of when you come to more exam prep in that point in time, it’s, as I’m sure many teachers –
Teachers all the time are talking about this, explaining your thoughts as to why you stop. I think it’s just useful. I find it a useful reminder myself. Get on the visualiser, have the guts, will you have the guts to try a question that you're not looked at before the lesson.
Craig Barton: Wow, that’s interesting. It’s making me a bit nervous here.
Laurie Luscombe: It’s one of those, isn't it? Then you kind of think oh, god.
Craig Barton: That’s really interesting because, ooh, I’m thinking about this, whereas if you've never seen that question before, that is watching a mathematician live out of their comfort zone trying to talk through it. Oh. Now that isn’t math-specific advice either, is it, right? I could imagine an English teacher being chucked a curve ball, a random question. A history teacher. You could even get the kids to pick one out at random from a past exam paper, just add a bit of a lottery style to it, “I’ll have Question 4 from 2016, Paper 3,” and so on.
My heart’s going like mad here thinking because again –
Laurie Luscombe: It makes me a bit uncomfortable too. It does.
Craig Barton: It is interesting, isn't it? I’ll tell you what, Laurie, we’re going to have to bring this to a – I could speak to you for hours and hours and hours about this, but just to wrap things up, you've really made me think hard about context. I came into this conversation, I hate context, you know, because I see it as redundant. I know why it’s got to be in there because we want kids to be able to filter out redundancy, but it annoys me. And crucially, I always leave it until the end of my teaching. I teach the kids the mathematics, the deep maths, and then once they've got that, now we’ll focus on I’ll add in some context, can we whittle it out, get around it and then get back to the maths.
But what I’m picking up here is that there's a different type of context. That’s one type, the story type, but there's this different type of context that you can hang these mathematical ideas on to actually make them make more sense to kids, and perhaps that’s the type of context that I, as a teacher, need to be thinking a little bit more of.
Laurie Luscombe: I like that. I think that’s a nice way, how to hang the maths from it.
Craig Barton: I’ve just come up with that, I’m going to copyright that. That’s good to know.
Laurie Luscombe: Yes, and I’m going to work on a catchy title.
Craig Barton: Perfect. I’ve learnt absolutely loads here, Laurie, so thanks so much for inviting us into your classroom today, it’s been absolutely fantastic.
Laurie Luscombe: You're welcome, and thank you. If anybody does try the water jug lesson, just please make sure the lid’s on carefully.
Craig Barton: Good advice.
Laurie Luscombe: It is. Wet pants halfway through a lesson...
Craig Barton: If your appetite for conversations about context has been whetted, go back to your podcast feed and find the first bonus episode of series one where you can hear about cultural capital in exams.
There are plenty of articles to get stuck into in this episode’s show notes as well.
I’ll be back after the Christmas break putting more of your questions to the experts, but in the meantime, make sure you rate, review and subscribe to the podcast. You can also join the conversation on Twitter using #insideexams.
Until next time, goodbye.