Tips for Teachers by Craig Barton

MathsConf30 takeaways with Jo Morgan

You can download an mp3 of the podcast here.

Jo Morgan’s tips:

  1. Assess pre-requisites
  2. Use a variety of techniques for differentiation
  3. Plan a curriculum suitable for the group you’re teaching
  4. Explore boundary examples to deepen understanding of a concept
  5. Pay attention to how students write their answers (we need a reciprocal symbol!).

Craig Barton’s tips:

  1. Make sure students are good at units
  2. Don’t forget the old classics
  3. Adapt off-the-shelf resources
  4. Make use of the power of interweaving
  5. Interweave out by using questions that all have the same underlying concept

Links and resources

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Podcast transcript

Craig Barton 0:00
Hello and welcome to the tips for teachers podcast with me Craig Barton. Now you may be noticing some background noise because in a tips for teachers are world exclusive. I am here live in Piccadilly station Manchester in the great northwest of England, but I’m not on my own. I am joined by my longtime podcast co host conference takeaway resource queen, Joe Morgan. Hello, Joe. Hello, Craig. How are you?

Jo Morgan 0:26
I’m good. Thank you great conference today and looking forward to a nightmare journey home later because the trains are not in a good way. No, it’s

Craig Barton 0:32
not good. But it doesn’t matter because we’re here we’re doing a podcast is all wet coats. So this is one of our conference takeaway podcasts. Now longtime listeners of the Mr. Barton mas podcast will know all about these we’ve done from everywhere driver, we were saying we’ve done him from Alton Towers,

Jo Morgan 0:45
that was the best it was like 30 degrees sitting out in front of a roller coaster. Yeah,

Craig Barton 0:49
we’ve done him from hotels where we’ve had a bit to drink.

Jo Morgan 0:52
We did remember University of Warwick can we did it in the student halls. Yeah.

Craig Barton 0:56
We’re gonna do one in a spa. But that was

Jo Morgan 0:59
unfortunate. COVID cancelled the spark or

Craig Barton 1:01
now we’re in the glamorous location of Piccadilly station in Manchester. So you may hear some announcements, rail announcements, we’ll just go with that. So the way we’re going to structure this a bit different to fit in with the tips for teachers theme is we’ve been to the LaSalle Mass Comm 30. We’ve seen where we’ve run a session, and we’ve seen four sessions in addition to that. And we’ve I’ve tasked Joe with trying to come up with five tips tips for teachers, from all the sessions that she’s seen. I’ve come up with five I’ve no idea what Josie is Joe doesn’t know where mine is. So we’re just gonna tell each other our tips and see where we go. So Joe Morgan, let’s start with you. What’s tip number one, please.

Jo Morgan 1:36
Okay, so tip number one is assess prerequisites. And this is something that was talked about in Stuart Welch’s session, which was called Think fast the art of responding in the moment. And it was really about responsive teaching. And there was a point in it where he said, I he doesn’t like end of topic tests. Now, I love my end of topic tests. And what we do at my school, is we have a thing called a learning snapshot, which is another topic test that’s done. So all the subjects do them. And they all have them they will on yellow paper. And that sounds like enough. Like who cares what kind of paper they’re on? Actually, the students take them really seriously. Because they know that they’re sitting in the lesson with something that’s a whole across the school, every subject does it the same. And our snapshots in maths have. They have the topic we’ve just learned. So for example, my attends did one last week on trigonometry, sine and cosine rule. And then at the end, they have some retrieval questions on stuff that they that isn’t in that topic we’ve just learned. But normally, it’s stuff that they’ve been doing and they’re less than warmups. So say for example, I’ve recently been doing expanded double brackets and the lesson warm up, then there’ll be a question in the snapshot on that. And that helps increase engagement in the warm ups because they know they’ll be tested on that stuff. And so it’s interesting when, when she said he doesn’t like ended up with tests, but he said, I tell you, what’s more important is testing prerequisites. And that’s that was really interesting as it links to something I learned another conference I went to. So last week, I went to the pixel conference where I was speaking. And there was an excellent speaker called Tom, and I can’t remember their name, but he was very good. And he said, he talked about assessment. And he said that assessments in maths and of topic assessments should have three things in them. They should have retrieval questions. Yes, they should have the topic you’ve just done, because you do want it you know, even though yes, they might forget it in a few weeks, it is helpful to see. And then he said, they should also have a couple of questions on the prerequisites for the next topic. Why have I never thought about? So just like after half term, I’m doing quadratics with my year 10. So I could have asked some questions that would help me understand the starting point for quadratics, or with my year elevens. I’ve just given them a snapshot on histograms. And I could have put a couple of questions on angles, because we’re doing circles there. And it would have helped me assess my starting point. So I thought this was a nice link between the two conferences I’ve been to this week. And it’s really just a very sensible and kind of almost obvious thing to do that some somehow i i haven’t quite picked up on. I know some people do give pre tests. And we don’t do that in my school. But including prerequisite questions, prerequisite skill questions in end of unit tests, I thought very sensible. I like that would

Craig Barton 4:05
no reason it can work for homeworks as well. Right. Like, as long as the kids do the homework and take it seriously.

Jo Morgan 4:10
Yeah, I guess the thing is, you know, so I school we do Haggerty homework and and that means that we’re not really apart from monitoring that they’re doing it we’re not really looking at it. But yeah, I suppose what we’ve and the other the other challenge would be like I’m a bit of a obsessed with. If I give a test, I like to mark it that evening and return at the next lesson. So it was it’s always better to give it on like the last lesson you seen that week and it gives you a few days extra sewer. I like sounds like a market because I just really want to give it back to them next lesson. Whereas some of my colleagues who’ve got more classes than me might take a bit longer to market and then that’s then not going to work. So I think this might have been David suggestion. David ferrum suggested that you could put in, say, you could just mark the three prerequisite questions. So if you haven’t got time to mark the entire test, at least you can go through and mark those prerequisite questions before you start your next lesson. And that’s quite smart. I think so good idea from David

Craig Barton 5:00
Good tip that I like that one. Very, very good. Okay, right one for me very quick one. So I went to Andrew Taylor’s session where he was reviewing AQa summer exams, blah, blah, blah. And I put a Twitter thread out on this, and I’ll link to it in the show notes of questions where kids did worse than you would expect them to them and questions where they did better than you’d expect them to do. And they were really interested was any kind of delve into the reasons why a one recurring theme was units, as soon as any question needs kids to do anything with a unit, they do crap on it, basically. So he shared a really interesting one where it was fascinating. It was a triangle to the sides were marked in maybe centimetres and one of them in millimetres. And all they had to do was write as a fraction, the like, shorter side, angle side. And they couldn’t do it

Jo Morgan 5:52
because they had to convert the unit. But they can’t do it, or they’re not spotting the units are different. Well, either

Craig Barton 5:56
way, either way. Units, I think need a big focus from

Jo Morgan 6:01
because that’s a city that’s carelessness and rushing, which because actually, last night, last week, I did a question on the board, I was going through a question where there were different units that I didn’t spot. And then one of my students said, that one says mitigators. And it’s not that I don’t know how to do it. So it’s actually you have to sort of figure out is it that they don’t know how is it that they’re rushing? But that’s interesting isn’t you know, isn’t it, I tell you something about units that interests me is that when they’re in as far as I know, in case they choose SATs, they never have to write the unit. And it’s always written there for them. So we when we used to do baseline tests in year seven, and we would write include units with your answer on an area question. They didn’t know what that instruction men, like they literally didn’t know, what does this mean, include units of your answer? So that’s something that you know, seven teachers need to be aware of that that instruction is something they’ll need to explain.

Craig Barton 6:47
That’s good. That’s good. Yep. So my tip is just make sure either we’ll cover units more basically make sure we can do the conversions and practice. And again, it’s the classic thing, either right, the unit sin before you do the working out of the answer, or whatever it takes the units or a point. Yes, right, Joe tip to

Jo Morgan 7:05
use a variety of techniques for differentiation. So this was from a session I was sitting with you and which was from two excellent speakers involved in White Rose. So this was Ian once again, surname. And Davis, and it was Matt and I, this is one I don’t know how to pronounce his last name. So apologies, Ames cough, I think or something like that. Um, so brilliant session, I’ve really enjoyed it, I really enjoyed it. In fact, you were laughing at me because I was literally opened up my my scheme of work and editors in the session based on what they were saying. But so the thing about differentiation was they were talking about how you adapt your lesson to the class in front of you. And they said, there’s a whole load of techniques you can do. So if you’re taking an off the shelf PowerPoint, and you want to edit it for your class, they talked about choice of numbers, whether you let them use calculators, you know, if you’re doing angles with a weaker cast, just let me use calculator with anyone let me use a calculator and choice of questions, removing elements, providing elements rewording things, and basically adapting the level of support that you’re you’re providing, but there’s all these lovely techniques to make an off the shelf lesson suitable for your particular group in front of you. So you know, it’s, it’s nice to think about, like different ways that you can decrease or increase level of challenge.

Craig Barton 8:29
Yeah, well, I had a related one on there. So let’s, let’s box this off now. So I got I’ve got adapt off the shelf resources from the same session, but specifically, so I’m very lucky these days, I get to visit tonnes of schools. And I see one of two things happening with lessons quite a lot. So I see off the shelf lessons being used exactly as they’re presented. And the teachers are clicking through slide after slide after slide. And it’s really problematic. There’s no no flexibility to it, there’s no chance to adapt if either the kids are struggling or the kids are going quicker than you think. Or you see others where you’ve got novice teachers trying to do everything from scratch, and they really struggle. So it seems to me like the perfect balances. Let’s have an off the shelf thing available, whether it’s similar wires or whether like you were talking about how you have your lessons that you plan out available for your staff. Yeah. And then spend the time adapting as opposed to starting from scratch. I mean, it’s quite hard for a lot of teachers. So start with some a decent Yeah, then do exactly what you’re saying. Yeah.

Jo Morgan 9:32
Yeah. And it was interesting that Matt was acknowledging that he said that he can have to set to your nine classes where he wants he thinks he can use the same lesson. And he can’t use the same lesson because different classes. So it’s it’s interesting, because we’re told to not that we should use off the shelf lessons because it reduces our workload, but they were acknowledging and they and they did a really good job of explaining why you have to look at those lessons in advance and you have to kind of fix them so they’re right for you that we have in front of you They acknowledged that.

Craig Barton 10:01
Yeah, yeah, really good, really good. Okay, so I’ll do Tip two, because this was from your session Josie, you did one on area in depth one of your classic in depth sessions, award winning in depth. So this way you do all the classics, you go through what they should know from primary misconceptions and saunas, and then you get to your favourite, where you do all the resources. Yeah, so my tip was very, very simple. And just for math teachers, don’t forget the old classics, because you show a shed? Well, one resource I completely forgotten about that I love from the standard, you know, yeah, that’s a great one, which is a brilliant one. And I’ll link to that in the show notes. I took a photo from all the resources from your session on Twitter. But then also, I always forget the smile resources and you share them. They just, yeah, they’re really good. They’re almost kind of like the precursors to a lot of dumb Stuart’s tasks. And yeah,

Jo Morgan 10:45
absolutely. And that’s, it was, yeah, the one that I showed where there is that boxing in method where you want to find an area of an awkward shape, you can draw a box around it and subtract the bits around the outside. Like, it’s interesting that I saw the Don Stewart task on it. And I thought that reminds me of a smile task. And then I found it in the old haling textbook, and they there, that’s where I got the word the phrase boxing in. But yeah, I think a lot of John Stuart stuff is kind of, because it’s all reasoning based. And that’s what smile well, but again, new teachers can go to stem centre and look for the smile resources. And the only problem is the files are scan. So they’re not great quality, but they’re totally usable. Yeah, pretty good, Sally

Craig Barton 11:23
good. And just a little bonus one on that. Now boxing and you made a really good point. So for listeners who don’t know boxing is if you’ve got, like a weird looking shape with like diagonal lines. And so on Squared paper, you essentially kind of draw a rectangle around it through through all the vertices and then subtract triangles. And you made the point, Joe, that we issue that’s actually harder than Well, kids find it hard to imagine to find it, but it’s good practice of area of a triangle, identifying perpendicular lengths and all that. Yeah.

Jo Morgan 11:53
And and it’s good to sort of, it kind of reinforces the concept of area being the number of squares covered. And, and there’s lots of reasoning in there. And then, you know, sometimes I’ll do groups, we’ve got two questions where they have to subtract something, or they try and find an area of a shape in a really long winded way. And I say, well, can’t you just, you know, subtract this. And it’s a really useful skill. So it’s good to sort of do that kind of thing in year seven, where we shouldn’t just say, Well, it’s an area before, so let’s just skip over it. We’ll just say, well, they’ve done it before. So let’s go into greater depth by doing that kind of thing.

Craig Barton 12:25
Exactly, exactly. So I’ll put links to the images I shared in the show notes. So I’ve been three tips. Now. Just that must be your your Tip three, maybe my

Jo Morgan 12:32
Tip three, yes. So this is a plan a curriculum that’s suitable for the classes you teach. Now, obviously, we have told the curriculum to teach by it. So we’ve got the national curriculum, and then our schools that we work in interpret that into a scheme of work. But then the against in the same session by in a map from White Rose, they were they they did this wonderful example of congruence and similarity. And they said, here’s all the Susan the steps or the things you need to cover. And then figure out if you were teaching a group in year 10, a working at a grade three or four, which bits would you teach if your work had a grade eight or nine group which bits and then and then there’s sort of trickier, the five, six group. And obviously the if you’ve got the foundation, people have to teach only the highest stuff. And that gives you more time for the kind of, say more time to focus on the things they really need, like, say, starting with a refresher on enlargement. Whereas with your higher group, you might say, Well, they probably know how to do enlargement from Key Stage Three, obviously, you check that, but then you can spend some time on negative enlargement. And then it was like, you know, with your higher group, you’re going to do those congruency proofs, you’re going to do those, those volume and error scale factors, and look at foundation group, what like they were talking about where you might want to focus your time. And it just it again, it’s similar to the thing they were saying about adapting the lessons themselves. And they’re talking about that skill of adapting that curriculum. Because you know, every teacher needs to do that, like, you know, unless you’re in a school where the sequence you teach is canned. And you’re not allowed to deviate from that, then we’re all kind of responding to our class and changing things as we go. In terms of the sequence of lessons. And it was a really good example of that, because it is a it’s a topic that kind of spans a lot of difficulty level. Yes.

Craig Barton 14:13
And just related to that this isn’t a tip. But I always think it’s worth thinking. If the order that this your schema work at the object is within a unit is the right order to tell the story you want to tell? Yeah, I’m going deep here, right? So obviously, like you have a certain amount of objects, if you’ve got a cover and as you say, you want to think for your class, which ones am I going to get to and blah, blah, blah. But then also, if you leave in some out, it might make sense just to reject the order just to tell a more coherent narrative, how you introduce them. So I often find teachers are quite rigid in terms of sticking to the order but you don’t need to write you know, you choose the order you do things. Yes.

Jo Morgan 14:50
Yeah.

Craig Barton 14:52
Roger Morgan. Well, my last two are from the final session. So you might as well do your tip for now then because I think your last one will be from that So, yeah, so

Jo Morgan 15:00
um, so my tip is to deepen understanding of a topic by looking at boundary example. And, and this is from your session, which was very, very good, I got a lot of ideas from it. I don’t like to flatter you, but it was very good. And this is all about learner generated examples, which I spoke at a conference yesterday where I was talking about how you can get a lot of challenge out of learner generated examples. And I show and there’s an I showed you our maths fans website, which is a really good example of how that works. But then there’s the three different models you show today, I thought were particularly powerful. And, and obviously, perhaps you can put in the in the show notes and links to some pictures that I took and share with those. But they were the one example that I wanted to mention was this one about quadratics. So you had to sort of fit the page into four, and this will be done maybe on a mini whiteboard. And then it was like right in one in one in the top left corner, write a quadratic that can be factorised, then write another quadratic can be factorised. And the thing is, that’s so simple for us. Not going to be simple for my students. And I’m teaching quadratics to 10, straight after halftime, and I’ve got a class that are working around a grade four. Yeah. And I know that they won’t just immediately think, Oh, I could just drop it out, put some brackets and expand them and say like, they will have to think about that. Or they might think, Oh, I can I think of a number were watching, like, Well, are they gonna think about it in that way? And then you said, like, come up with another one. And then it’s like, well, that’s an interesting one. And we had some, we had some really nice, different examples in that. So like, Paul Rodriguez was sitting with, he did a trigger, create a trigger expression there. So he had like sine squared plus, it was really good. And then we talked about like, interesting examples. We had like a difference of two squares and stuff like that. Oh, like a mnemonic. And then you said, right, and so that’s your kind of boundary example. Because you said that’s like, how far can you push this concept. And then in the bottom right box, we’re writing something that can’t be factorised. But someone might think it can be. So this is basically they’re like the common mistakes or the like the non example of an expression that can be factorised. And that was really interesting, because that talking about what could go down there. And it could be something where, you know, there is no, so I had x squared minus two there. And you could factorise that if you put a bracket, but then when the you know, David had one, which was, I think, like x squared plus five plus 10, or something where the numbers just don’t work. But it was, it was it was, we had good discussions about it. And so so much students, and I think that was a really accessible task, and one that would just create a lot of thinking, which is just what we want to do. But if we can get them thinking, then we’re doing the right thing. And I thought it was a really nice format. And then you show to other formats, which was sort of sort of similar ideas. They’re generating examples. And they’re doing this thing where they’re discussing them in pairs to discuss them as a class. And there’s a whole load of drawing out misconceptions. And also like that, like the bit we said about how the kind of boundary example then chips over into a non example. And then understanding that point means I got a really deep understanding of the concepts. So I really, really enjoyed that was fantastic. Thanks,

Craig Barton 18:04
Joe’s very, very code. Yeah. And what I will say is, it’s the it’s you’ve got to be, you’ve got to know I didn’t mention this in the session, but your subject knowledge has got to be pretty, because and for a lot of non specialists, it’s problematic there speak. So even I’ll give you an example here. So what I did in a school, where there was some non specialists, and people who had never taught a level, or even taught high at GCSE, so one of the ones I did was fractured equivalent to two thirds. Yeah. So give me an example of some forces fine. Yeah. 20 over 30. Fine. Then he got to the interesting one. Yeah. So somebody had put down one over 1.5. Okay, so then we had the discussion, because is that a fraction equivalent to two thirds or not? And then like some teachers want yeah, it is, and some to just Well, no, it’s not. So then it really makes you think very carefully about your definition of the concept. So if you’re going to do something like like, it’s very, it’s a lot easier to ask kids questions where you know, the Yeah, it’s a risky game. Yeah. What a worthwhile game to throw it out to the kids because they could come back with something. Yeah.

Jo Morgan 19:12
It is. No, it doesn’t feel good as a teacher when when they when when you don’t know. And you say, actually, I’m not sure that it’s fun. And it’s a bit like it’s a bit of a horrible moment. But so do what was your conclusion on that? Do you think that isn’t equivalent fraction?

Craig Barton 19:27
No, I think it’s equivalent, but not a fraction would have been was my Yeah, that would be

Jo Morgan 19:33
a fraction as a integer. Yeah, I

Craig Barton 19:34
was. Yeah, yeah. But the thing is, with these boundaries, some of them are like going to be clearly wrong. Some of those kinds of edge cases you can say, because look, this is an interesting one. You’ll never be asked, you’ll never have to make this decision or like in an exam, but it’s just worth having this Eddie always draws out these problems.

Jo Morgan 19:52
Your first example I love the way it links so perfectly to my area. I have spoken about finding areas of triangles and how and the common misconception there, and then you said right draw a triangle or an area of 12 square centimetres. Sure, number one, draw an interesting one and then draw one where there’s a common mistake that people make. And then so I suppose maybe not everyone did this, but my one was where they use the non perpendicular. But yeah, really nice link. It’s almost like we found it.

Craig Barton 20:16
Yeah, we get there we go. Joe, right. Okay, so now I’ve got Tip four and five are both from Nathan days sessions. Nathan did one arm into weaving with a focus on reciprocals, but then branched off into other stuff. So I’ll do one first. Yeah, so I just had a make sure you do interweaving was my simple one. It’s very powerful. So for those of you not aware interweaving, I get the sense it only really works in maths or certainly works a lot easier. So it’s this notion that you mix in concepts that kids have experienced in the past in the current one. But what’s good about Nathan, he doesn’t just do the obvious does. He’s not just like, trick a decimal into an answer question. It’s very creative. Yeah. And if you haven’t been on his website, what is it?

Jo Morgan 20:57
Is it Andover mass,

Craig Barton 21:00
exactly what it is. And he’s got some lovely examples. So the reasons he gave for why you should mix in place stuff is good for retrieval. It allows kids to swap connections. And it’s almost by definition, good for multi step problem solving. Because you’re dealing with two different concepts. It’s never just straightforward questions. So if you’re not a regular into Weaver as part of your normal teaching practice, the tip will be dropping in the mix.

Jo Morgan 21:24
Yeah. And some of the some of the examples he showed were incredibly challenging. We were like, Ah, I can’t do this, you know, really, really hard. Isn’t wasn’t it? It was interesting. reciprocals of standard form, like, that really got us thinking. But yeah, so because he was focused a lot on reciprocals. We were our slightly silly tip was, say, think about, think about how you get students to write their answer. So that’s a nonlinear way of saying it, because I found this before. So you’re doing a question on a reciprocal on the board news. And you say, what’s the reciprocal of five? Yeah. Then you write down, there’s not a symbol, or symbol to write for this reciprocal just didn’t represent you just so you can write. And then they will put equals. And they always use this equal sign. So I was sitting next to David and I said, I want a symbol, which I decided was an upside down R, but he didn’t really like that. So we’re going to get something better. So I’m saying it’s like, I want them to write upside down r equals just we need some kind of symbol there, because students will write equally well. And so it was initially because we were trying loads of wonderful reciprocal questions. And every time I was just had this the frustration that there’s not a simple to represent reciprocal. So so that is not a really a tip other than keep an eye on how your students write their answers, and don’t accept them writing and equals when they shouldn’t have written equals. So I’ve turned that into a tip. I’m just saying you that I’m making up a new symbol.

Craig Barton 22:51
That’s very good. My final one again, from Nathan session. I like the bit he did at the end. And this is almost, you know, obviously I do ssdd problems, same service, different depth, Nathan does a lot of help. Constantine is good at this as well of doing questions that have this have the same deep structure, but on the surface look different. So Helen does a really good selection of Pythagoras questions where, even if you know it’s Pythagoras, yeah, it’s still challenging, as opposed to a ladder leaning against a wall. Once you know, it’s by Congress, there’s no challenge. And I really like Nathan’s ID equals the interweaving out where he had six questions, all from different areas of math. So I wrote these down here he had, there was like, solving simultaneous equations, there was there was like,

Jo Morgan 23:36
given a point on the line, what’s the equation of the line

Craig Barton 23:40
term of a linear sequence, so completely different areas of mathematics, but his point was, they all require kids to correct something, adapt the correct the cancel out something from the simultaneous equations with the term corrective from a times table to the term so on. Again, I just want the thought of doing that drawing, like almost kind of picking a big idea and explicitly drawing the connections by presenting you can imagine it like GCSE revision once the kids have done all those areas. Yeah, put that together as like almost like a retrieval starter. And the kids get all the retrieval but then say, look, there’s a connection between Yeah, I just thought was really,

Jo Morgan 24:22
I wouldn’t have spotted it. I couldn’t see what he meant when he was saying there was a connection. Yes, I really liked the way he explained, you know that where it said, a line goes through the point 440 What’s the equation of the line? No, there must have been Oh, I had that it was parallel something. So we knew the gradient was four. And I thought it was just like the way he explained it where he said, so we know it’s y equals 4x. But if it was y equals 4x, then you get you get four but you want to have 40. So what do you have to add to that? And it was, it was quite a nice explanation like even the way he explained the completing the square one isn’t the way we typically explained. So it was quite a nice way of looking at But yeah, I agree the it was interesting to find these common threads, which is something that Watson was looking at with some Don Stewart’s while she was trying to look at it. Loaded John Stewart tartan she found threads that went through them in a kind of similar way when they seem like they’re unrelated tasks, but they’ve got something some deep masks and comments. Yes,

Craig Barton 25:17
yes. Yes. He’s good. Yeah. He’s a good way about him as well. I like his style. I think he’s good. He’s good as well. Joe, there we go. That was a good format. Wasn’t that was quick, snappy. Yeah. What do you think about so now let’s just tell the listeners you’re going to try and get back back home down south.

Jo Morgan 25:31
We’re going to attempt to get a train that’s running tonight. Who knows we’ll have a go. Well, Joe

Craig Barton 25:36
Morgan as ever, pleasure catching up with you. And thank you for joining us on the tips for teachers podcast.

Unknown Speaker 25:40
Thanks very much. Great.