This episode of the Tips for Teachers podcast is proudly supported by Arc Maths
You can download an mp3 of the podcast here.
Jo Morgan’s tips:
- Model techniques live [4 minutes 21 seconds]
- Make sure students know whether they are right or wrong, and don’t wait until it’s too late [17 minutes 07 seconds]
- Use calculators with students from the earliest opportunity [23 minutes 43 seconds]
- Use visual aids, including props and online tools to bring explanations alive [41 minutes 28 seconds]
- Don’t forget the “respond” part of responsive teaching [53 minutes 17 seconds]
Links and resources
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Watch the videos of Jo’s tips
Podcast transcript
Craig Barton 0:01
Hello, my name is Craig Barton and welcome to the tips for teachers podcast. The show that helps you supercharge your teaching one idea at a time. Each episode I invited guests from the wonderful world of education to share five tips for teachers to try both inside and outside of the classroom. With each tip, the challenge is always to ask yourself, what would I have to do or change to make this work for me, my situation and my students, experimentation and frustration may follow, but hopefully something good will come out of it. Now remember to check out our website tips for teachers.co.uk, where you’ll find all the podcasts as well as the links, resources and audio transcriptions from each episode. Better still, you’ll also find a selection of video tips, some taken directly from the podcast, and others recorded by me. These video clips can be used to spark discussion between colleagues and departmental meeting, a twilight inset and cellar. Now just before we dive in today’s episode, a quick word of thanks for our sponsor. So this episode of the tips for teachers podcast is proudly supported by Ark maths, though Ark math is an innovative app created by teachers to help students remember all those crucial skills needed to succeed at maths. Art. Math is built around research into the power of retrieval practice and spaced practice on memory. Here’s how it works. Students crack open the artists app and are given a 12 question quiz. With follow up practice questions on anything they got wrong, not just straightaway. But the next day three days later a week later, and so on. Until they have it secure in long term memory. It really is fantastic. Now the more time students spend on the app, the better Ark will get to know them and what they need. With no teacher input required, you can spend more of your time inspiring your students with new ideas. So check out art, maths, and remember, that’s art with a C, not a K. Right back to the show. So let’s get learning with today’s guests. The wonderful Joe Morgan. Now, spoiler alert, here are Joe’s five tips. Number one model techniques live. Number two, make sure students know whether they are right or wrong. And don’t wait until it’s too late. Tip three use calculators with students from the earliest opportunity. Tip Four use visual aids including props and online tools to bring explanations alive. And Tip Five, don’t forget the respond part of responsive teaching. Now Joe is of course a maths teacher but many of these tips will transfer no matter what subject you teach. Now remember if you look at the episode description on your podcast player or visit the episode page on tips for teachers dot Coda UK, you’ll see I’ve timestamps each of these tips, so you can jump straight to anyone that you want to listen to first or real listen. I really hope you enjoyed this one. Enjoy the show.
Well, it gives me great pleasure to welcome Joe Morgan to the tips for teachers podcast. Hello, Joe. How are you?
Jo Morgan 3:11
Hi, Craig. I’m very well. Thank you. How are you?
Craig Barton 3:13
I’m very good. Thank you. Joke for listeners who don’t know, can you tell us about yourself in a sentence?
Jo Morgan 3:19
Oh, so I am a maths teacher and I blog. It was also hollett.com. And I do various other things in the maths world. I messaged him on Twitter.
Craig Barton 3:29
Nice long sentence, but I’ll give you that. All right, let’s dive in. What’s your first tip for his job?
Jo Morgan 3:35
Right. Tip number one is model technics live.
Craig Barton 3:40
Oh, okay, tell me about it.
Jo Morgan 3:44
Right now, this is something that I think all teachers need to model, we know that modelling is part of good teaching whatever subject. And it’s the live bit that I think is really important. And I’ll talk about modelling live in a mass context compared to modelling not live. But before that, I thought I’d mentioned other subjects and when modelling comes in. So I’m thinking back to Lessons I’ve observed and other subjects. And I remember once I observed a drama lesson, where the teacher kept telling the students what she wanted them to do, and at no point showed them what she wanted them to do. And then my feedback to her was that she should get up and model, the sort of technique that she wanted them to show in this drama lesson. And she said, she was a bit embarrassed. And that was like that was a to me a really key part of any teacher’s job is modelling. And I and I’ve really thought about that. I thought it’s funny that she’s embarrassed about doing the thing that she’s an expert at. And then I realised that actually, this applies in lots of other subjects because I think that some teachers and I’m not saying necessarily the word embarrassment is the right word, but some teachers are a bit anxious in the maths classroom, and perhaps in lots of other subjects about modelling live. And then so since then, I’ve sort of been really looking out for examples of good modelling and I’ve seen it in PE lessons that I’ve observed, I’ve seen no way, you could just watch a PE lesson where they’re teaching a technique. And I watched one where there, the PE teacher was teaching in cricket techniques. And he was showing the students kind of five skills that are used in cricket. And what was really good was he had some students get up to kind of do it while he directed them while the rest of the class watched. But the teacher also was modelling them as well. So he was telling the students, right, I want you to go over there, and then you’re going to do this thing. But then also the teacher got involved in in that modelling. Because the teachers, the expert, the teacher, really threw the ball really far and really showed like how to do that really well. And so I’ve seen it brilliantly in PA. And also I’ve seen live modelling really done well in art with a visualizer. But actually, this is what kind of, I guess I was a semi live modelling. Because what I’ve seen is students in art, who are being taught a technique like a very specific technique to do when I come up with it was it might have involved some kind of etchings or rubbings, or something I don’t know. But it was it was really like specific thing that they were being taught. And what the teacher had done was, she’s used the visualizer. in advance, she recorded her hands doing the whole technique. So she sort of started with a blank piece of paper, she’d done the whole thing, and showed all the technique really, really clearly. And you could just see her hands, she had recorded that. And then she left it on the loop while the students did it. And they were so smart. So that meant that the students could see exactly what they were meant to do. And they could see an actual person doing it. So not just hearing explanation, but see what to do. And then while they were working, they could just look up and reference the board and say, Oh, what did she do next? Oh, yeah, that’s what I need to do. Because it was playing on a loop. They could then look again and again. And if you keep checking that they were doing it right, and see what the,
Craig Barton 6:43
you know, the practicalities of what she used to record in Josie.
Jo Morgan 6:47
Yeah, we’ve got those visualizers, the IP ones which have got this like kind of other arm, you know what I mean? They’re kind of angle, the visualizer. So she had then just angled the visualizer, facing down onto her hands, done the work and use the camera function on the computer to record it. So it’s actually pretty straightforward stuff. And it was I think they use it a lot during lockdown, and the art teachers to recall techniques. And now it’s part of their daily practice, which is fantastic. So I know a lot of maths teachers use visualizers in their day to day lessons, and I don’t use a visualizer I use, you know, I write directly onto an interactive whiteboard. But I did use a visualizer, the other day when I was doing constructions. And when I was doing transformations. So these are two topics, which really lend themselves well to visualizers. And particularly with transformations. I wanted to show students the the rotations with tracing paper thing. And no matter how good your animation is on a whiteboard on some slides, that really is better shown with actual tracing paper, where you’re actually, you know, literally doing exactly what the students would do, and they can see your hands doing it. So I think this kind of live modelling under a visualizer is, is such a helpful technique, and particularly in lessons where there’s something practical to do. But also, you know, we know that, for example, editing work in English onto a visualizer, or in any subject with a written elements sort of showing that kind of live editing is really, really powerful. So I think visualizers are a really good tool for that. But I think all live modelling has to be done under a visualizer. Because the other side of it is the writing on the board live. And so for example, wear masks that would be solving a mask question while I’m going through the workings while the students watch, rather than clicking through the PowerPoint that’s got the steps. And I think it’s a huge difference in those two things. So my slides, and I, you know, I’ll use a slide where there’s just a question at the top, and then it’s a blank slide. So I’ve thought in advance about what example I want to model. The slides will just have the question. And then I’ve got a blank slide where I will go through the workings and write it all up. And it should look exactly how it should look in their books. And this again, was where a visualizer really helps because you could actually have an exercise book, but I think it’s so important that they see me do that rather than click, click through the next stage. I don’t think that’s as powerful. What do you think? Right?
Craig Barton 9:16
Yeah, a couple of things to say about that. So the first is on that one on the NOC clicking through, I see this a lot. Yeah. You see this whenever because there’s so many good resources. We’re obviously we’re mathematicians, so we speak about maths. There’s so many good pre prepared math resources, whether it’s white rose or whatever, where it’s all fully worked out for you all the all the examples or the working out. And if you download something off tears, often the author’s put so much time in and done all the working out for you because they want to communicate, you know, how they’re thinking and so on that there’s almost too much on the slide. And I watch a lot of lessons these days where exactly the teacher clicks, clicks, clicks, and there’s a couple of problems with that. One is if the if the child’s thinking of a slightly different method, or even if they suggest a different method, and it’s not exactly the same one that’s written on the slide, the teacher almost ends up saying, Oh, you’re absolutely right. But we’re just going to do it slightly different here. What’s going on here? I like the mantra, I’m going to get this tattooed on myself, do the maths don’t reveal the maths, I think that’s really feeling the maths is the problem. The other thing I want to say about that is, and this ties into the visualizer thing, I remember, I don’t know if you were the same job. When I first started teaching, I was PowerPoint obsessed in the sense that I wanted everything on my slides. So when you said those transformations, I used to spend hours getting the animation of the rotating tracing paper around. And so I’m thinking that that’s, that was the proper way to do it, because it looked nice on the thing, but you’re absolutely right. Like, it’s, you want to replicate as much as you can, what the kids are doing so that they can follow you doing it, and so on and so forth. And I was just thinking back to what you said about the art teacher, this, I really love this idea of recording what’s still on the visualizer and playing it back on the loop. And I guess you can certainly do that before the lesson, which is really nice, because it shows you that a go at the example yourself and so on. But you could if you are more technical than we are, or certainly you are Joe, no offence, but what you could definitely definitely do is you could record it as you’re doing it live in the class, right, and I’m sure then with a bit of button press, and you could then get that up on the screen going, you know, going on that loop so the kids could could refer to even then get a bit fancier upload it to VLE, or Google classroom or whatever. And then the kids could access that whenever they whenever they want to.
Jo Morgan 11:38
Yeah. And for people that aren’t kind of confident enough with the tech to kind of record live and then immediately get it on the screen. There are ways you can use things alongside each other like you could have, I’m gonna model it live under the visualizer. And then, while you’re doing it, I’ve got like a GIF, because you can just Google these things, you know, I got a GIF running on the screen where it’s just you know, which might not necessarily be my hands doing it, but it’s just, you know, showing it so while they’re practising, they can see it. But I just Yeah, I do think like, that’s, you’re right about that kind of, we shouldn’t just reveal step by step. Sometimes what I do, like, I download, and normally write my own stuff, but I sometimes I will download someone else’s slides. And then I want to use their examples. And I just delete all the answer bit. So I’ve now got my blank slide, I’ve got the question at the top that I want to show. But I delete all the animated examples, because I just don’t think it’s, and I know it’s really, really common practice to click through slides with the, the answers, but it’s just not as powerful as teaching themselves. And I think there is sometimes a lot of anxiety, I remember when I first started teaching a level. And I’d have worked out the questions in advance, I had them on a bit of paper in the room. And it was and I used to like I’ve been modelling on the board, and I knew how to do it. But I’d still occasion look at this paper. And I always thought that the students were judging me when I did that. And they were thinking she doesn’t know what to do next, she’s having to take a note. So I very quickly stopped doing that. Because I thought I don’t want them to think that I need that. But for a while I you know, I just lacked that confidence. I thought, well, what if I mess this up in front of them. But now I’m at the stage. And you know, it’s like when you get more experience, you kind of get that confidence where it’s like, if I mess it up in front of them, that’s actually sometimes quite a good thing, isn’t it? Because they can say, Oh, if they’re paying attention, it’s a really good way to check in and pay attention. They can say, Miss, actually, you’ve made a mistake there. And then you can go back and fix it and say, Yeah, everyone makes mistakes, and well done for spotting that. And hopefully you can all see why right? wrong there. And I’m gonna fix it. So you just need to sort of get to the point where you’re comfortable with the fact that you will occasionally make a mistake on the board. But the live modelling is a really powerful thing for students.
Craig Barton 13:37
Yeah, it’s really good. Just a couple more things on that. Yeah, I was exactly the same. When I first started particularly further maths a little bit of a bloody clue what I was doing. And that’s when if there was pre prepared slides, I was using those left, right and centre because I had much more confidence, the fact that I could then show a line and then explain the line, but it was nowhere near as powerful as me actually kind of kind of hand doing it. And, and the other thing, Joe is a you as well, you’re doing your live modelling, are you doing some kind of explaining your thinking as well, I always think that’s important. What what kind of things you do in there?
Jo Morgan 14:12
I guess. So sometimes I’ll sometimes I’ll stop between each line and ask for their ideas. And there’s sort of pros and cons of that, isn’t it? So sometimes I’ll say, right, this one, I’m going to just I’m going to model and you’re going to watch and you’re going to try and follow my thinking. And it Yeah, each day. So I won’t necessarily be I could suppose if you think about something like your techniques of silent teacher and stuff, I might just be writing down each step. Whereas then there are, there’s, you know, because we can use all these things, you know, you don’t have to just show one technique. So another way you might do it is narrating each line. So now I’m going to subtract 2x from each side, you know, that kind of thing. So there’s that. And then and then there’s the sort of technique of any ideas what I should do next. And then someone might suggest something you say, right, so now I’m going to subtract, you’re extremely excited. So yeah, there’s a kind of combination of stuff and I don’t think I stick exclusively to one side of modelling and then one lesson I might have for examples. And I might do, I might use those, like all those different techniques. In my four different examples, there might be one where I take a bit more input from the class and one where I write each step and one where I’m just writing it down. Yeah, so but I think, yeah, the, I think the thing, there’s what you said about the different methods is really interesting, because actually, on the few occasions where I have clicked through slides, sometimes I’ll say, Oh, they’ve done it differently. Do it. And and it was confusing people that so you know, and then actually, and yeah, it’s nice to, or sometimes I’ll say, right, how would how any ideas and how we do this question, someone might suggest something. And they’ll say, oh, that’s different times gonna do it. So I draw a line down the middle the board, and I say, right, so this is one method. And I write that one up. And I say, No, I’ve got another method. Now. Okay, so let me show you how I was thinking of doing it. And I’ll put it side by side. And I’ll say, look, here’s two different ways. And I don’t mind which way you do it. But it’s you can see two different perspectives. And all that stuff, you lose, if you just got a load of pre filled texts and a PowerPoint that you’re clicking through.
Craig Barton 15:57
I’ll end on this step. I was in a school the other day, I won’t say where I was watching a very experienced teacher. And they were using some pre prepared slides from a well known resource provider. And they, you could tell that I looked at him beforehand, because they were genuinely surprised when the methods were coming up on the board. They were like clicking through like, Oh, right. Okay. And then they were trying to explain, I was like, oh, okay, yeah. There we go. Right joke. Tip number two, please.
Jo Morgan 16:27
Okay, tip number two, make sure students know whether they’re right or wrong. And don’t wait until it’s too late.
Craig Barton 16:34
Oh, I like it. God, tell me more.
Jo Morgan 16:37
Okay, so, again, I’m gonna I’m gonna reference mass, but I think this probably applies in, in all subjects, most subjects, is this idea of having students do an entire chunk of practice or exercise, and they’re getting it all wrong, and they don’t know till the end. And then it’s just kind of a waste of time. So you know, there are various different ways that you can kind of deal with this. And when I, in my first job in teaching, I used to work at a Girls Grammar School, where very much me and all my colleagues had this, this technique of just putting the answers up for an exercise at the beginning, you know, so, so you could hand out your exercise, and you’d have all the answers on the board. And the students would just work it out, check. Oh, yeah, I got that one. Right. And, and that sort of works quite well, a level as well. And then I moved to a school, where immediately, I found that the students would just copy down the answers from the board. So I had to have to think more carefully about how to make sure that students were able to know immediately whether they had the understanding to carry on with the exercise. So what I tend to do now is I’ll put a task up on the board. And I’ll give them say, a minute or so to get that first question going a bit depends on the topic and how long each question takes. But say, I’ll give them a minute to get started. And I might have a little circulate around to make sure everyone’s on task. And then what I’d normally do is I’ll then return to the board, like my whiteboard. So I might have a task up on the screen. And I’ll go and I’ll go back to the whiteboard. And I might do the first question on the board. And so again, that’s me doing it live, they should be getting on with their work at that stage, but some of them might be stuck, and they might watch me do it. And then I’ll work all that out. And then I’ll have an answer at the end. And then I’ll say to them, I don’t like to interrupt them much while they’re working. So I think it’s really important for teachers to not constantly talk over students when they’re doing exercise. But I will say, right, everyone, the first answer is on the board, can you make sure you’ve got that one? Right, before you carry on with the rest of exercise, some of them might already be on Question Three by that stage. And if you’ve got it wrong, put up your hand, I’ll come and help you. And so there’s a few things there. First of all, I’ve got that whole thing modelled on the board. So what that might be is that they look at it and nice. They think, oh, actually, I can see what she has done. And I can see why I’ve got the different answer. And they might immediately be able to self correct and then go on, move on get the next one, right, oh, they might look and say, Oh, my answer is totally wrong. And I have no idea why. And then they put their hands up and I go and help them. But if you don’t do this kind of thing, if you’re not providing them with one or two early answers, then it could be that they get the first one wrong, it’s like I’m on December, we’re all gonna do the whole lot wrong. And then you’ve lost your opportunity to do the what your job is, which is to go round and help them improve. So they’re not going to make any progress. So um, so I think it’s just, you know, there are various techniques, you can provide the answers up front. Another technique is, you quite often get worksheets, where they have the answers jumbled up at the bottom or something. So students can you know, they know if they’re getting an answer that’s not at the bottom, then they know that something’s
Craig Barton 19:21
wrong. So like Question three, the answers this, it’s just as, for example,
Jo Morgan 19:25
MasterCard, have quite a lot of resources where they’ve got a whole load of questions, and then sort of, they’ll have a big chunk of answers all jumbled up. And I say to the students, it’s not a matchup activity, really, it’s an activity where they’re working out the answer, and then just check that your answers at the bottom if it is you can cross it off. And if it’s not down there, you’ve done something wrong. So that’s just another way of kind of making that letting them check as they go. But it’s just so important, isn’t it that that you that you give them the opportunity to know early on, whether they’re on the right track because otherwise you’re just wasting sort of X Sighs 1015 minutes, were getting them all wrong. Imagine they get them all wrong. And at the end, you put the answers up, you say, right, we’re going to babble pen, our answers everyone mark your answers. And then someone might cross cross, cross, cross cross, and say, right, what’s next? So what a waste of time. So I just think it’s really important to find a way of providing answers early on, which will depend on your class to have the way you do it, to make sure that they then get the help they need at the right time.
Craig Barton 20:24
I completely agree, Joe. So three, three things on this. Again, if I go back earlier on in my career, I thought the key thing was that the kids didn’t copy that that was kind of the top thing in my head. So I would always do what you described there, leave the answers till the end. And it’s only when you kind of gain in experience that you realise now, the most important thing here is that the kids are practising the right thing and developing that right fluency. And there is that trade offs of Sure some kids might try and take advantage of it, and just wait till you’ve done it on the board, and so on and so forth. But you’re gonna get far more benefit from the kids who are taking it seriously and practising it practising correctly because they’ve got access to the answers. And my second mantra of our conversation, I like the practice doesn’t make perfect practice makes permanent, I think that’s a really, really good one to to bear in mind, because it’s whatever they can to practice. And that’s what they’re going to remember, we want to make sure that’s that’s the right thing. And final thing, Joe, just on a practical sense. I love your idea that the kids kind of crack on with their work. And then after a minute or so you bang up the answer and the method of question one, two, the board making check, do you would you then if it’s let’s say a 10. Question exercise? Would you then like do the same for kind of question three, or question five a bit later on? How How would you manage that as as the exercise progresses, I
Jo Morgan 21:37
think that it really depends on how they’re getting on. So obviously, I think circulating around the room is just such a vital part of teaching. And that’s why during COVID, we really struggled with our teaching, because we couldn’t get around the room. But I think if I’m circulating around the room, and I can just see there’s like a really high level of success with the with the task, and they all kind of know what they’re doing, then I might just actually wait till the end, put all the answers at the end. But then what I always do when I put the answers up, is I say something like, so here are the answers. But I’m not 100% sure they’re all right, because you know, quite often you get to say, especially if you’ve downloaded the results. So what I want you to do is if your answer doesn’t match while on the board, just challenge it. Just say to me what you’ve got, and then after and actually it’s a really nice technique, because you’ll get some someone who’s like, they’ll put up a hand and say, I got a different answer for Question five. And I’m pretty sure mine’s right. And I’ll say right, so we’re going to do question five on the board now. And then often there’ll be other people who have got that one wrong as well. So even if I’m pretty sure the answers are all right, I’ll often say to them, if you’ve got one that differs to mine, put your hand up, and we’ll go through that one. So I’m not having to go through every single question, but I am going through one or two at the end. So I will do that in an activity if when I’m circulating, I can see a high level success. If I’m circulating around saying that there’s students that are genuinely finding, some of them will say half the cost of doing well and half the cost of making a bit of a mess of it, then I might say, I’m actually going to put up the first five answers halfway through. And if you’re getting them all wrong, I’ll come to you directly or I might gather a little group together or something. But yeah, so that really depends on how they’re getting on, I think.
Craig Barton 23:03
Perfect. Love it. Right, Joe? Tip number three, please.
Jo Morgan 23:09
Right? This is very much a maths tip. Okay, so this is used calculators, from the earliest opportunity. So day one of year seven, get your students using calculators?
Craig Barton 23:18
I’ll tell you what, let’s broaden this out a bit. Right. So I science will be loving this as well. Right? Yeah, but a geography they’ve not ruled it out.
Jo Morgan 23:26
Yeah. And that it’s interesting in science, because it’s, you know, I felt like the maths department takes spot responsibility for calculators and the school were the ones who make sure I’m in my school, perhaps not, you know, were the ones who make sure that every student has a calculator. And then that’s very different ways of doing that, depending on what kind of context your scores in. But we make sure everyone has a calculator, we make sure they bring it every day. And then science kind of piggyback off that, because I use them quite a lot. But you know, we really, we really have to ensure that calculator usage becomes really fluent, because what you end up with is and I think we’ve all seen it, if you’ve if you’ve got some experience in teaching maths, you would have seen that quite sometimes they get to their GCSE exam, and they’ve got to calculate two papers, one on calculator. So we have majority calculator work going on. And they’ll have a question like, fine. Oh, increase 210 pounds by 35% or something. And you’ll see them do like a build up method for signed funding, that’s 85%. And I got a calculator in front of them. And I could do it in a second. Because I know how to use a multiplier and they got a calculator, but they’re not reaching for their calculator. Because they’re not they’ve not they haven’t got the habit of doing that in schools where it’s not been built up as a habit since year seven. And actually, it’s something I really, I really work hard on. So in my school, every student is constant using a calculator and occasionally we’ll have a lesson where I’ll say, Look, we’re doing fractions today to calculators away, because this will normally be on the non calculator people. I need you to know how to do this without a calculator. So I won’t say if it’s the way I’ll just say you’re not using a calculator today. But other than that, like 95% of less than say Got the calculator on the desk and they’re just using it fluently. They’re picking it up to check things, they’re picking it up when they need it. And it’s and it’s just, it’s, I just think it’s my students, I’m hoping when they get to their year 11 exams will not forget, they can use their calculator, because they’re so used to using it. And obviously, they’re, they don’t use it a primary school anymore. That changed on the on the national curriculum. So now, calculators come in, in year seven, it’s massively engaging to get them using them, they love using calculators. And I get that there are really good reasons why schools can’t do or think they can’t do it. You know, there are you got people, lots of people, premium students, and you’re saying that they you know, they can’t afford calculators, in which case, there’s, you know, the head of maths needs to be going to SLT and saying, I need a big chunk of that Pupil Premium budget that has been assigned to those students exactly for this sort of thing. So I can buy a calculator, a set of calculators for every class, and they can use them in the lessons, if not at home, I think it’s really important that we our heads of maths are making sure that that people premium budget is being used appropriately. And buying calculators is a brilliant use of that budget. And there’ll be some schools where it’s not so much they can’t afford them. But the behaviour is not good enough, or they’re just there isn’t a system in place to make sure they bring them. And in which case, you just need to tackle these problems rather than ignore them that you just need to find a way of making sure that every student has a calculator at every lesson.
Craig Barton 26:24
Movie Joe have five things to say about m by COVID. That’s been scribbling them down. So the first thing is, I don’t if you find this, I find it’s the lowest achieving students who are the worst at using their calculator, and they’re the ones who need it most. So to use your example, there have a finding 35% of 200, you’ll get a student who, mentally that’s going to be a real challenge for for them to do it kind of on paper and stuff. But they’re the ones who will do it on paper, whereas they’re the ones who benefit most from using their calculator. And it always does matter when you mark a non calculator like foundation paper, the sorry, a calculator foundation paper, the amount of mental methods that have been written methods that have been used, it’s just mind. I mean,
Jo Morgan 27:07
sometimes you’ll see in a calculator paper they’ve done like long multiplication or long division at the side and got it wrong. So you think, why are you doing that? And I’d get, I’m like, I really use a calculator. But you know, and it’s like, there’s people, I think some people who have little bit precious about, well know, if they use a calculator too much they’re not going to get they’re not going to practice their arithmetic. But there’s plenty of opportunities for them to practice technique, and they do a lot of arithmetic practice at primary school. And there’s been some research recently that does show that using calculator secondary school can really assessed the broad range of maths skills, so it’s not hindering them in any way. And I think there’s a, there’s a little bit of a, it’s almost like people think that students can’t become over reliant on calculators, because then they’ll stop using their brain, but absolutely not like the calculator helps them to Oh, no, it doesn’t help them. It opens up a whole new load of maths to them. So they get to actually do the important maths and not be bogged down in all this arithmetic. That’s, you know, we we will it gets into focus on the right things if they got a calculator to hand.
Craig Barton 28:12
That’s good. Right. So that’s point 1.2. Again, just a very quick and obviously, it’s important that kids use the same calculator, right? We’ve all we’ve all seen this kids coming in with bizarre models of calculator that they’ve Grammy’s lent them or wiped out. Yeah. And then the one they get given in the exam, if they don’t have it, it’s just a completely different model. They don’t have a clue how to do it. That’s that’s obviously, it goes without saying, but this is what you’ve changed my opinion on this, Joe. I know you’re out. Calculate Trump sass. And as a result, I’m about calculate Trump Sass now. So to use, I think your fractions examples are a really interesting one. So in the past, I would never like for the whole fractions unit, the kids would have never gone anywhere near their calculators because I think, well, the whole point of fractions is you’ve got to be able to do it using read and written methods and so on. But now, even in something like addition of fractions, they would always use the calculator to check. And this goes back to what Well, there’s two things here. One, it gets them fluent on their calculator. But two, it goes back to what we were saying earlier on about having the answers available, right? Because, again, that they then have a bespoke answer at the point they’re ready, they can check on their calculator. So yeah, I can’t see an occasion where I wouldn’t want a child having a calculator in their lesson as long as I can trust them, you know, and they the message is right, that obviously, you’re not going to always be able to use this in the exam. But let’s get really fluent with this calculator. And it’s your own private chat. It’s your own private settlement. Yes, that I can only see benefits.
Jo Morgan 29:39
I agree, essentially, because I had some year 10s. Recently, we were doing some work on certs. And there was a it was a question where there were quite a lot of manipulation of certs. I did see some of them using the calculator to simplify the certs. And I said to them like I can it’s good that you know how to do that on your calculator. But obviously, this whole question would be on a non calculator exam so you just need to you need to practice the simplifying asserts And don’t use your calculator to that. But for you, because otherwise, you know, that’s not gonna, you’re not gonna know how to do it yourself. So there are times where you have to just sort of tell them to Yeah, you’ve kind of you need to have that maturity, don’t you where it’s like, yeah, I know you’ve got one on your desk, but you need to be mature enough to know that this won’t benefit you if you use it for this particular thing. But please do use it to check your answers. And it’s interesting about the fractions because I have a, there’s a test that I when I given the end of unit fractions test, we did it this year, and it was mixed in of the fraction test had another topic on it where you had to use a calculator. And so it was a pain because we had to write a fractions test where it was okay to have a calculator. So that was quite challenging. So we did things like it was a fraction division question, but it said, You must show your method in full do not use a calculator here, and that’s fine. So then we can check their workings. But there was one question on there, and I gave a one mark for it. And it was multiplying two mixed numbers. And I said, you may use a calculator for this one. And it was something like one and a third multiplied by five and two fifths or something. And as I expect, because it’s always happens, that half the class got that wrong. And even though it says use a calculator, it’s one more question. And what they’ve done wrong was they had they don’t even know I had actually told this class hadn’t I hadn’t spent I hadn’t modelled it enough, clearly, they don’t know that shift, and the fraction button gives them a mixed number. So you know, if you want to input five and two fifths and use it in a calculation, you do Shift fraction button, and it comes up with the three little boxes. If they don’t know that, then what they do is they input like five, and then they’d press the fraction button, and then they do their two fifths or whatever. And that is actually given them a five multiply by two fifths, so you get totally the wrong answer out of it. And that’s the sort of thing where it’s such a basic thing, but so many students are not told about it. So many students are not told that if you want to input a mixed number, you need to do Shift and the fraction button. And that’s
Craig Barton 31:49
probably it’s probably, it’s probably because they haven’t again, fractions is treated as, as a written Yeah, topic, not a calculator topic.
Jo Morgan 31:56
Yeah. And it’s interesting. I remember, once I took I took over class you’ve been taught Pythagoras? No, it was, as I’ve been taught area of a circle. And what I saw them doing was they weren’t using the square button. They were just doing, say, radius times radius. And it’s not that they didn’t know that it was radius squared. So they didn’t know that they could use the square button, or anything. That’s like, Come on, show them how to use a square button, like, you know, what I mean, this is, again, really good use of visualizers, to show to model those techniques. So it’s like I’m modelling an area of a circle question. And I will literally tell you what buttons, you should press in your calculator. And actually, this is another example that you said, of where you can get into the calculators to check answers. So Oh, or to practice other bits of maths. So for example, if I was teaching over circle, then I might say, right, I want your, I want your answers in terms of pi. And then I also want your answer in decimal form rounded to two decimal places. And so there, they have to know how to do 16 times pi on their calculator, which again, needs modelling because pi is ridiculously hidden in a shift button for no reason. And so you have to model that you have to model the pressing the SD button to turn into a decimal. And then you then need to round it, which is testing another math skill. And in fact, you could even do that in a lesson or rounding in your seven before they’ve ever done circles. Because you could say, right, we’re gonna do some random practice today. But we’re gonna do it by doing 16 times by pressing the button and round that number. So you can actually use that for rounding. calculators are amazing, because you get them to do a whole load of calculator stuff around the answer. And the key topic in the lesson is practice rounding. But at the same time, they’re just practising using a calculator and they’re getting really used to using them, they’ve got the habit of using them.
Craig Barton 33:40
Lovely stuff, right, final two points on this. So the first thing to say is either a bit of a theory on this, you know how, obviously the GCSE used to be one cow on one non cow paper? Yeah, it’s one cow can then to calculate papers. So a must be a nightmare, as you were saying, for for the GCSE examiners to come up with all these questions were? Well yeah, it’s hard, isn’t it to to write a calculate a question where kids are allowed to use a calculator, but also, they can’t just kind of bang it straight into the calculator? If, if that makes sense. So I think that’s a real challenge. And I think you can do a fair bit of paper two and three in the maths GCSE, if you are a bit of a whiz on your calculator. Can you do some amazing stuff on the calculators these days, right. So obviously, you can do all your tables of values stuff, for plotting straight line graphs, you can do all your quadratic formula stuff, there’s, like, when you get to a level, you can do even more stuff. So it’s adding it’s a real wow moment. When you show the kids you teach them how to do it, you know, using written methods, and then you say right now I’m going to show you how you can do this on your calculator. Now, as you say, You’re not always going to have your calculator with you for doing this. But upskilling the kids to do some of the amazing functions that you can use on the calculator, I think is a really, really nice thing to do. And when you get slick on using your calculator, it’s Incredible write some of this stuff. Yeah,
Jo Morgan 35:01
it’s and the thing is, yeah, I’m not like, I’m not massive. I’m a bit old fashioned in a way. And, you know, I like students to use calculators from early on. But I don’t like it that I don’t like it that more expensive calculators give advantages that really really annoys me. So all of our students have the 10 pound you know, the classic Casio that kind of everyone has now. But it frustrates me that they can have a graphical calculator, and it can give them huge advantages. And that really, really annoys me like, I just I just feel like it should be a level playing field. But you’re right.
Craig Barton 35:30
This whole class this old classic, either the class whiz,
Jo Morgan 35:33
isn’t that’s I call that the a level class. Where’s Yeah,
Craig Barton 35:36
yeah, I mean, even that, the stuff you can do on that is mind
Jo Morgan 35:39
blowing. Yeah, absolutely. But yeah, like you say, a lot of students aren’t taught these little things. And I think that the good example is the fact that prime factorization, because I had a student, I had a group of students couple of years ago, and they were I’d have chops at year 11, absolutely flying through practices before their GCSE. And they had a question. And it said something like, it was asking them if a number was prime. And all they had to know whether a number is prime. And it was a huge number, it was something like 700, and something on there was a really big number. And they got stuck on this bit of a question. It was a big problem solving question, but they got stuck, because they didn’t know if that was prime. Now they know how to check if a number is prime. But you know, that’s going to take forever. So so that’s when I said, Well, you do know the prime factorization, but we didn’t know. And I said, Well, you can actually, you know, and then thing is I said it shows the prime factorization, but then they need the understanding to know whether that shows its prime. So you know, if they’re, if they’re putting in a number, and it’s saying, if you put in 16, and it comes up with two to the power of four, that’s clearly not a prime number, because we’ve got these factors of two. Whereas if we put in a number and to try and use that button, and it’s just coming back with the same number, that’s because it has no other factors to list. So it’s just it’s a really, it’s a really powerful part of teaching prime factorization, to get using that button and to and to look at what that tells you about numbers. But I just again, loads of students will have never seen that. And I don’t think it offers a huge advantage in having it in GCSE or a level, but it does help build understanding. And it’s just a really nice teaching tool for reasoning to do with primes.
Craig Barton 37:19
Absolutely. And my final point about calculators, yeah, this goes back to something you were saying earlier, as well, you’ve got to be able to visually show the kids the buttons that you as a teacher are pressing on the calculator. So whether you do this using an emulator, or whether you bang it onto the visualizer, it’s not enough. If I’m stood at the front, tapping, and like the kids have got different answers. And then then I’ve got to then try and figure out why they’ve got the different answers. Whereas a big old one on the board or stuck under the visualizer? It’s the key, isn’t it? Oh, absolutely.
Jo Morgan 37:48
Yeah, it’s really interesting when they come up with a different answer on the calculator. And sometimes like, it’s like, Oh, you just had to do it might be a trick question. And they had to do a close bracket or something, are they? And quite often, it’s where they haven’t squared and negative properly. And yet there’s common there’s compensate. So you can once you get experienced, you can kind of say, if they said you miss, I got a different answer. If you know what the common mistakes are, then you can say, just look at what’s on your screen now. Because that’s a good thing. These two calculators The way I still think it’s amazing that you can go back and see what they typed in. Like, you know, go use your cursor to go back look at what you typed in. Did you put brackets around that negative two squared or whatever? Yeah, so it’s that it’s that kind of thing where you get it gets the point where you can, as a teacher, you can predict where they’re going to mess up on their calculator and you can preempt that. But yeah, I absolutely agree they need to see it modelled properly. And you know, I the emulators are expensive, or you know, you can get them free if you buy if you’re going to buy calculators to sell or to give to your your group. You do get the emulators for free from Casio or used to anyway. But yeah, if you don’t have that, then absolutely a calculator onto a visualizer works wonders. But yeah, they actually, I literally say to them, check this in now, check the number on your screen. Tell me if that’s not what you’ve got. And I’ll come to you. Yeah, so when you know, we’re very, I’m very specific and like take the time to make sure that I haven’t just told them to put it in a calculator. But I’ve checked they’ve got the right thing on their screen when they’ve done that.
Craig Barton 39:15
Final word on calculators. Yeah, we’re old menu. Everybody, everybody knows that. I’m still blown away. A big game changer in the world of calculators will be was when fractions look like fractions. So when I was at school and stuff, it was a little ELS. Right? It was like, two thirds was L three. And then whenever the calculators could do fractions, I was like,
Jo Morgan 39:36
I still got students that we’ve got, you know, this was ridiculous. Our uniform supplier put calculators on the website so that when parents were buying uniform come in year six, they were like, oh, there’s a calculator on this website. We’ll buy that and it was like some helix rubbish like absolute nonsense. And so we have some students who would obviously we’ve now told the uniform supplier to get rid of that because that’s not the character to want to use. And then they join in year seven or We say right you have to have this Casio. But yeah, any of my students that have got that rubbish calculator, they when we get to fractions like there, they will say to me, what’s this on my screen? And I’ll say, I’m so sorry. You’ve got that. But yeah, I agree I am still, I’m still impressed with the I love the way that it can go. That SD bus. I don’t know what people call it. I call it the SD. Yeah, I wish I had a proper name. But why does it say? But I like the way that if your answer is a mixed number, you can convert between mixed number improper fraction and decimal version form just by pressing it. And I just love that because I say the calculators from our day. And I also the audiences were different, didn’t it? So like I used to have to check I had to put in the angle and then
Craig Barton 40:47
they were bad. Hey, yeah, yep, sometimes I just press that st button just for a bit of a laugh. Just kind of flicking between them makes me happy. And I should say, I don’t think he’ll ever going to be sponsoring this webcast. Never mind. Right, Joe? What’s your fourth tip, please
Jo Morgan 41:03
write Tip number four. use visual aids including props, images and online tools to bring explanations alive.
Craig Barton 41:11
Oh, okay. Right. Tell me more about this. So again,
Jo Morgan 41:15
I’m going to talk from a sort of masters perspective. But I think this probably applies in lots of other subjects as well, particularly, science, and well, lots of subjects, geography, all sorts of things. I remember going to see a science lesson a few years ago, and the teacher was talking about a balloon and he was talking about filling a balloon with air, and there was no balloon in the room. I just thought he was talking about filling a balloon with air. And he did not fill a balloon with air. And it’s a very, very, very simple thing to do. What I’ve done recently is I’ve taught a lot of volume and surface air, I just happened to teach it like similar topics to three year grips. And when I was teaching surface area, I found a shoe box at home. And I covered my shoe box. In paper, this took about five minutes. I’m not someone who’s going to sit at home and spend ages making props for my lessons. But I’ve covered my shoe box in paper, and I labelled the sides the faces sorry, ABCDE F. And then when I came is that right F. And then when I came in to school, I had my prop for surface area. When whenever I see a cylinder, Pringles tubes are great, I bring it into my classroom, and I have a drawer full of cylinders. And then when I’m talking about surface area of a cylinder, I’m sure lots of I’m sure hope all messages do this, I get a piece of paper and I wrap it around that cylinder. And then I unwrap it and say, hey, look, what’s this? Oh, it’s a rectangle? And what’s the length of that rectangle? You know, so I’m sure most teachers do that sort of thing. But basically, props are really, really powerful. And, and I use props alongside alongside animations, and alongside visuals. So I think these things will work together. But I do think, you know, I’m always on the lookout for things I can use as props. And sometimes they don’t work. Like I remember when I was a trainee or an amputee, I decided I wanted to make props for 3d Pythagoras. And I used I bought pipe cleaners online, old school crafting tools. And I made a cuboid out of pipe cleaners and then made that kind of space diagnosis. And I was, and it was just rubbish. I mean, it was flimsy rubbish that didn’t work at all, and no one had a clue what I’m talking about. And now I talk about the room we’re in and I talk to the students about the classroom. And I talk about the space diagonal, and I go, I literally like they think I’m crazy because I run across the room and I go and stand in that one corner. And I talk about the other corner and the top end, like sort of seven Tie Points of it not tall enough. And I talk about the space segment. So now I’m kind of using the Karlshamn as a prop. So you know, we, I once I mean I haven’t done one. So when I was doing vectors review 13. And you have to do, I can’t even remember because I’m talking so long. But I remember I once attached a bit of wool, from one corner of the room to the other to demonstrate whatever it was I was teaching, I can’t remember. But um, so I don’t I don’t do this very much. But in terms of like, things that take a bit of effort to do because I haven’t got time to do it. But there are some topics where without a prop, you’re really you’re really not helping your students with the with understanding a concept. Now, like I said, it doesn’t have to be a prop though it can be a metre ruler is a good example of a visual, like how can you teach units without for the entire lesson waving a metre ruler around because I don’t put that metre water down when I’m teaching units. I’ve In fact, I pick up the metre ruler in many, many lessons. And then I like sort of like pointing around with it. But really, I’m trying to say to the this is what a metre looks like. And I say so much. Surely they could never possibly forget what a mutable looks like because I think I’m a crazy person that’s just always say, this is a metre, don’t forget. And then things like
lining people like if you’re going to if you’re gonna talk about the concept of a median, I don’t, I don’t necessarily get students out of their seats. I don’t like doing that anymore. But it might have been the time where I lined them up. But now I might say right, I want you to visualise a line of students and we’re gonna lie Send them up in order of what they got on their last maths exam. And I said, I would never do this to you because this is cruel. But let’s imagine that I am a horrible teacher. And I’ve got the person with the lowest marks standing over here. And this person got 43% on their maths exam. And next to them, I’ve got personally got 45%, that did a bit better. I’ve got more lined up and then right over by this wall over here, this person got 100%, that’s kind of a person to really please stand against this wall. And everyone’s thinking, Oh, my gosh, she’s never going to do this issue. And then I said, I’ve got them all picturing this line of students. And then I said, right, so what’s the median score, this find the students standing in line, and it’s pitch to that student, and they’re standing in the middle, and they’re looking, they got the same amount of people over here, they’ve got the same amount people over here, and that students score is the medium. So this is an example of using it’s not even a visual because I haven’t got the students up there, but it’s a visualisation. So, so that’s one part of it. But I also mentioned online tools. And it’s really what was really interesting, Craig is that when I did my PGCE, I reckon like, the only thing they taught me on my PGCE was that I should learn to be a god expert. Like this was the one thing they said a million times, they were like, oh, and at the time, it was geometers, sketchpad and God. And obviously, now we’ve got stuff like Desmos. And we have, well, I suppose it’s autograph and what else there’s loads of stuff, there’s loads of cool tools you can use to, to do like dynamics, software that you can use to show geometry. And I have never, I mean, I know you’re a bit of an expert on these things sort of autograph or things like that. But I’ve never learned how to build things on that. And I don’t think it matters, because you can just Google it, and someone else has done it for you. So that I will Google surface area of a cylinder GeoGebra. And I find that some lovely person has made a Jabra, that where I can move a little slider along and it unwraps that on the board for me. So I would use that as well as physical prop. And I think that a lot of teachers don’t know that you can google GeoGebra. And other people have made all these amazing things. Even last week, I was teaching concrete triangles that didn’t occur to me that if you Google GeoGebra, congruent triangles, there’s some really cool stuff you can use. And basically, you can use dynamic software to explain math concepts, without having to know how to use dynamic software, because lovely people have all put it online for us. So yes, I’m talking about dynamic software, I’m talking about actual props, and I’m talking about visuals, basically anything to help our students get over, remember, and understand the concepts we’re trying to explain.
Craig Barton 47:24
I love it. Right few things about this. So I couldn’t agree couldn’t agree more with you. And God has come on leaps and bounds, right? The things that people can do on that just absolutely blows my mind. I’m exactly the same. I’m a Google GeoGebra surface, well, whatever, whatever it is, I do the same. So a couple of things there. One thing that’s great about all visuals, but particularly I think this works well with the online stuff more is you can change something and observe the effect it has you’re not fixed with this, like hand drawn diagram, this static thing on the board. But one thing I think there’s a danger of I don’t know if you agree here. So obviously, a lot of the Geogebra stuff has these sliders and stuff and things changing everywhere. I think there’s a real danger as teachers, we can just kind of just whiz things from left to right and things magic things happen on the board. And it’s just, it’s almost like watching a movie for the kids. Whereas if you say right, what I’m going to do now is I’m going to increase the length of this dimension, what impact do you predict that’s going to have Think, think about it yourself, maybe put it on a mini whiteboard or something. And now I’m going to do it, that way that they’re a bit more engaged in it, it has meaning to them, they then have an opportunity to explain it discuss. Whereas whenever there’s loads of sliders and same, the same on Desmos, when you when you do like y equals mx plus c, and then you just kind of increase the value of m things are just whizzing around without that time for the kids to just have a think what do I think’s going to happen? Now, this has actually happened? Do I understand why so? Yeah, I’ve been guilty of that in the past. And if you want to say about that, before I tell you,
Jo Morgan 48:51
Well, you’ve made me think of a good example on maths pad and these is that they’re probably God, we’ve got some of these as well. MasterCard has a great animation of exterior angles and a polygon and how if you shrink that polygon down, they all sum to 360. And I think, yeah, I’ve I’ve definitely there’s been times where I’ve just like, let’s look at the five sides, it’s got six sizes, because it keeps adding up 360. And it’s a bit too quick. So thinking about it now, based on what you’ve said, I probably would be better to say, right, so we’re going to start with this fight pentagon. And let’s, let’s watch what happens when I shrink it down and look all those angles summit 360. What should I do next? Miss, can you try six sides? What do you think might happen? So yeah, you’re right. I think I’ve been guilty of going too quickly on those things and getting them to either make a prediction or keep a record of what they’ve seen. So you know, like, five sides? Three 360. And then like, you know them actually keeping a record as you do the demonstration. It’s a good idea. Yeah.
Craig Barton 49:42
Yeah, it’s good. And particularly as you say, they’re getting the kids to say, since these What do you want me to do next? What you want me to try next? That’s always a lovely thing. Okay. So Joe wants me to try this. What do we think’s going to happen here? Write it down at the end? Yeah, really nice. And the final thing I want to say? Dodgy props. He was interesting. You mentioned the PI cleanest I’m crappy, anything creative anything like that. But it was remember when Danny Quinn came on my Mr. Biomass podcasts years and years ago, I think it might have been when I asked her what her favourite failure was. And she described and I don’t know if you’ve done this lesson, I’ve tried this and it’s a disaster. It’s when you’re teaching surface area of a sphere. And Danny describe bringing in and bringing appealing it because of course, I mean, what’s the surface area? I always forget what?
Jo Morgan 50:33
Oh, pi r squared, four pi r squared. Yeah.
Craig Barton 50:35
So the the brilliant ideas, of course, you peel this orange, and it’s gonna fit brilliantly into four circles all of it, and it never ever does. So you end up kind of dis you kind of getting the kids mind that this thing doesn’t work before they even see what the thing is. So yeah, I’m all for the props. But it’s got to be one that you’re pretty sure he’s going to convey the idea. Yeah,
Jo Morgan 50:55
especially because setter is smooth. I’ve never done that one. But I used to have a giant tennis ball, which I lost at one school, I’ve no, I don’t have it. But I bought this, you know, we shouldn’t be spending money on these things for a start. So I should not have bought giant tennis ball just to show some service. But if you look at the markings on a tennis ball, you know how it’s got that kind of it’s like, it’s like two circles that are joined together wrapped around each other, like a tennis ball is the one that shows that you could don’t see it on other types of ball. And then it basically if you unwrap those parts, you get these four circles. And so I always thought that was quite a nice way of showing it. Although again, it’s still not ideal, because it’s like a circle with a bit in the middle of another circle. And they kind of blurred together in the middle, but actually is equivalent to four four circles. But again, it’s not the perfect thing. But yeah, so I think you’re right, there are some things particularly to do with well, a sphere is a really good example of if you’re going to prove or if you’re going to show them the derivation of the surface area or volume of a sphere. I believe you need to use calculus to do that. I might be wrong. I believe that particularly. Yeah, I think I think you need to do that with much more advanced maths, and it is quite frustrating. There are some things that we can’t actually explain the why because the students haven’t done advanced enough maths. So that’s probably one of these ones, where you just have the formula, and that’s fine. And you don’t need to
Craig Barton 52:10
show them. Like an online version that you know works like you know, you can imagine that the font Cgo Jabra one demonstrates
Jo Morgan 52:18
Oh, yeah. And a good example of that is with the ones that you know, I now show for a service account, being a third of a senator, I’ve just got a couple of demonstrations. I’ve got a picture that shows it. And I’ve got a demonstration that shows it. And I am certainly not I mean, I never did this. But I always intended to somehow get hold of a cone and a cylinder that had exactly the same height and radius and fill one with either water or sand and pour it in now I’ve never done that. But I remember I used to want to do it. I just couldn’t get hold of the right equipment. And but yeah, I think that’s fine done with a with an animation. I don’t think we need to take the water in the classroom necessarily. Some people might do it really well. But I don’t think we need to kill ourselves trying to do these things.
Craig Barton 53:00
Right, Joe? Morgan? What is your fifth and final tip?
Jo Morgan 53:04
Right, tip number five, don’t forget the respond part of responsive teaching,
Craig Barton 53:10
or catchy? That’s the kind of clickbait headline I’m looking for that that’s gonna drag on tell me about this.
Jo Morgan 53:16
Right? Well, what used to be called assessment for learning, and now more commonly called responsive teaching, it comes up a lot in Lesson observations. So quite often when you’re observed, or if I go and observe someone, one of the things that often people are writing on these decimalisation forms is could be more iafl? How are you assessing what the students know? So, but when we’re talking about that, we’re often talking about how the assessment takes place. So we might be talking about are using mini whiteboards or using questioning effectively, or using I don’t know exit tickets or diagnostic questions, you know, if they’ve got iPads, you get them to do some diagnostic questions at the end, before they leave, or you circulating and looking over their shoulders. So there’s all these different techniques for assessing. But I tend to find that when people are given feedback on their on their lessons, the focus is on Did you do the assessment rather than how did you respond to the assessment that you did? And that’s the hard bit and that’s the bit that actually I think a lot of people aren’t I aren’t, I don’t know how to do so. When you see them get something wrong? How do you then on the fly, adapt your lesson, or adapt your next lesson to respond to it?
And I just I don’t think it’s happening. I don’t think it’s people are adapting their lessons as they should do it for a couple of reasons. One, I think it’s you have to be able to think on your feet and think very quickly. If you’re gonna if you see a big misconception or lesson, or you see that you’ve explained something and no one’s got a clue what you’re talking about. You have to think very quickly to think, you know, is there a What’s the other way I can explain it? What different examples can I use? How should I you know, how should I respond to the fact that half the cost is more than half the cost? I have no idea. So that’s that’s sort of in the lesson. But the other thing is, there’s this kind of fashion at the moment for we’re all talking about how, why are we all built voting our own lessons, why aren’t we using centrally planned lessons and there’s like quite a thing at the moment. And I’ve heard, I went to a talk recently with the NCTM, where they were saying, You know what, how silly the all these teachers plan their own lessons on their own What a terrible use of time. And there are parts of the argument I’ve strongly agree with. But also, if we’re going to use a centrally planned bank of lessons, where a whole unit of teaching has been planned in advance lesson by lesson that doesn’t really give us the opportunity to respond to our students. And I tweeted about this recently about how I did a lesson on scatter graphs with your aid. And I’ve got a pretty, I’ve got a pretty smart girl class of your rights, they’re really good. Like they, I can rely on them to be good at wherever I give them here, though, a good class. And they had done scatter graphs and science. And I knew they just scatter graphs and science because I had asked them in advance. And also, I had checked with the science teachers. And yet when I saw what because I was short on time, because my stitches are always short on time that I had, I was rushing topics because I spent a long time going to depth for one topic. And it left me very little time for scatter graphs, I thought I could do in two lessons, I would do one correlation and do one line of best fit, because I’ve done it before. And of course, what happened was in that very first lesson, they got the correlation thing, no problem. And then I gave them a task, where I wasn’t really testing an auto correlation, because the task said plot a scatter graph, and then write down what the correlation is. So really, the task was testing wherever they can plus a scatter graph primarily. And they just couldn’t like this scales were out of control. Crazy, awful, awful stuff. Like they had no clue how to draw graphs and axis. And the thing is that I hadn’t taught them that hadn’t modelled it. So immediately, I thought, well, that was that was a, that’s my mistake, I should never I should have assessed upfront, or I should have, I should have checked before I got started whether they could do this particular skill, because basically, I’ve just made a mess of this. So what I did was, was I scrapped my next lesson plan, which I was going to do line of best fit. I hadn’t planned it yet, though, because I don’t plan lessons a long way in advance, because I know that that’s a silly thing to do. So that’s fine hadn’t planned it. So I then when that evening, and I planned the next day’s lesson, where I got, I taught them about scale. And we looked at some scales with mistakes. And we talked about why those scales were wrong. And we talked about how to draw axes. And we practice that. And then by the end of that lesson, they were doing axes and scatter graphs much better. So I fixed the problem. Because I was responsive to what I saw in the lesson. Now, if I was teaching a very regimented pre planned series of lessons, that I wouldn’t have been able to do that unless of course I had, I was kind of allowed, I guess in some schools, they might say, Yes, we have these lessons that you have to use, but you are allowed to adapt and veer off them if you want to. So I suppose that would have been right. But you know, I think I feel like I have to defend myself in the school. As a sometimes as a member of leadership team, I get the Bible, the other men’s leadership team, I get told off for why you play why you plan your lessons in the evening, and I or why you’ve had your lessons in the afternoon, you’ve got other things that are more important to do. Why aren’t you just using other people’s lessons? Why aren’t you sharing lessons in the department? Now we do share stuff, you know, I save my stuff in a shared area, other people are welcome to use it. But the reason I’m planning my lessons the night before, is because we have mass four days a week. So I’m not gonna cover subjects where I have a nice three day gap between lessons. And I have to respond to what I saw that day. Like I can’t, you can’t just ignore what you saw in today’s lesson, and just carry on regardless, you have to respond to it. So yeah. And there’s I mean, there are there are other examples where you don’t have to, it’s not about changing the next lesson. So for example, this week, I was doing lesson on transformations with your team. And they were doing some practice on invariance, the whole lesson was about invariance. And then there was one question they got to on negative, which they had to do negative enlargement and write about which points were invariant. And like I had one hand went up first person that got to that question, I can’t remember how to do a negative enlargement. They did it in year nine, and then another hand went up. And by the time the third time went up, I stopped them all. And I said, I’m just going to model a negative enlargement question, because I can see that everyone’s forgotten how to do this. Now, I don’t like to interrupt people when they’re working on the task. But you know, that required me to adapt my lesson during the lesson, because I was responding to what I saw. So basically, there’s a couple of things. One, I do see massively the advantages of off the shelf units of lessons that are planned in advance, I definitely see their advantages to teachers that need support, and to, to say to for efficiency, but we have to make sure that if we’re doing that, that we are still allowing our teachers to be responsive to what they see in front of them and adapt those lessons massively if they need to. Because being responsive is the right thing for our students. High quality lessons are important for our students, but being responsive as part of that high quality teaching, and you lose the being responsive if you’ve planned the whole thing in advance. And then the other part of that is learning techniques to be responsive in the lesson and knowing when it’s the right time to say that I’ve got this plan and I was hoping to Up to this point in this hour, but actually halfway through, I’ve realised that I’m gonna have to scrap the second half of the lesson and divert because of what I’m seeing in front of me. I think teachers have got really good at the assessment, part of responsive teaching. But we need to do more work on the responsive part of responsive teacher.
Craig Barton 1:00:16
Lovely, that giraffe, just a few thinks about this. I think there were kind of three pillar times in a lesson where I would do kind of what I call kind of formal formative assessment. And I think the first one is probably the key that prereq Knowledge Check. If you get if I spoke about without unboxer about this, if you get that bit, right, you just save yourself a load of potential hassle going forward. And I think, if any, if teachers are going to be responsive anywhere, that’s possibly the easiest part to be responsive, because you ask this question, the prereq knowledge isn’t there. So you don’t really have a choice, you have to stop and teach that that prerequisite knowledge, I think it gets a bit more difficult when you start doing formative assessment midway through a lesson when perhaps the kids are practising a new concept that you’ve taught them. It’s quite tempting just to kind of let them kind of crack on with it and keep practising. But then if you if you stop them there and just do a bit of a sense check of where all the class are either with diagnostic questions on mini whiteboards, or whatever, it’s then sometimes quite difficult to respond there. Because sometimes it’s alright, the rest of you crack on with this. Whereas the ones who are struggling, just watch me at the board or kind of come round in a small group, but it’s something that it’s so important to do. And then that final part, as you say, whether it’s an exit ticket, or a final question at the end, that’s quite nice, because then as you say, you then have a bit of time before the next lesson to think. And it might not be scrapping the whole lesson, it might be saying that for the first 10 minutes, I’m just going to need to go back over this, and so on and so forth. Second thing was, I’ve definitely been there with this, certainly when I was much less experience, your lesson plan, it’s almost like it’s set in stone. So you’re going to I’m going to use this slide, then I’m going to use this slide and so on and so forth. I’d never put the two and two together, though, Joe, to start thinking about the pre prepared resources, which are really high quality, may actually cause teachers to be less responsive. It’s a really interesting thing, then it goes back to that story I was talking about previously with this guy was clicking through the PowerPoint, there was no way he was going to do anything apart from click Next slide, there was no way he was going to be able to respond, because then what was he going to do? He’s gonna have to close his PowerPoint down, get up on the other, it just wasn’t going to happen. So that’s really interesting that I’m a big proponent of these shared resources for workload, and also kind of lesson sequencing reasons. But yeah, I’d never put two and two together. That’s really nice that Joe Well, I like that. And the final thing, and I’m obviously ridiculously bias, but I think diagnostic questions are quite good for responsive teaching for two reasons. Well, three reasons. So one, they’re very quick to kind of ask and get the whole kids, you get a response off all the kids, whether it’s ABCDE, cards, or mini wipers, or whatever, to if the kids get it wrong, you have a sense of why they’re getting it wrong because of their choice of wrong answer. So each wrong answer will give you an insight into the specific nature of their misunderstanding. So you can then put then you’ve got if you’ve looked at the question and advance it, and you think, okay, loads of my kids are getting a going for a a is wrong. And I know why. Because I’ve looked at the question before, you then probably in a better position to have a good explanation or a demonstration or whatever. But finally, I think the most challenging thing about responding in responsive teaching, as you’ve said is, is what how you actually respond. If you’ve got half your kids, you’ve know what they’re doing. And half the kids who don’t, that’s potentially difficult. But with diagnostic questions, what I tend to do is the kids who don’t know what they’re doing, I’ve got an insight as to why so I can support them. But the kids who do know what they’re doing, I can simply say something like or one of my favourite things to say to the kids is for a diagnostic question, can you write me three more days? Three more questions, which would make each of the wrong answers, right. So I can give this like, Okay, we know D is the right answer to this question. Whilst I’m helping out the rest of the class. Can you write me a question as similar to the one that you that we’ve just seen here? So just change one thing, but make a the right answer, then change one thing, it might be the right answer. And that means that I don’t have to give out another worksheet, another activity or anything like that. They can be busy in a useful way, whilst I can help the other kids out? Because to take your right at the point you may right at the start. The reason I think teachers struggle with the responsibility responsive teaching is that that is the hard bit. That’s the hard bit and it’s it’s, it’s a lot easier when all the kids either know it, or all the kids don’t know it, when you have this split, it’s quite difficult to respond. So that’s some of the kind of things that I would do. Did you have any thoughts? If you get that position, Joe, where you have a bit of a split in the class of knowledge is tricky, isn’t it?
Jo Morgan 1:04:37
Yeah, you’re right. Because you’ve got this thing where that if the whole class is useless at something, then you either change that lesson or you change the next lesson, and you just have to teach that thing they all can’t do. But yeah, it’s if it’s one or two students, and that’s easier because you can just go to them directly, but you’re right if you’ve got half as cars getting it in half the class not that is that is really challenging. So like you say, you need to find something fun So I’m saying that it’s going to get the ones who get it doing some reasoning, while you’re still explaining or adapting your explanation for the ones who don’t get it. Because that’s the thing isn’t, it’s about adapting your explanation, like, if you shown them, like, if you’ve shown them a way of doing it, if you’ve modelled a number of examples, and they’re still not getting it, you need to model them differently, or you need to find a different explanation, or you need to find a different method. And so it takes a it takes quite a lot of experience and expertise to get it right. It’s definitely, definitely the hardest bit of teaching. And, and it’s interesting is that because you think about the other subjects and how, you know, you could have where they want students to write a paragraph. And, and, you know, like, they’re going around saying that some students are writing these amazing paragraphs, and some students are just writing nonsense. And I can imagine it’s, it’s just as hard there to sort of decide, you know, without if there’s too many students to help individually, then what are you going to do then, and you really need to minimise the amount of times you stop a class and interrupt them, particularly for those who are getting on with it. Like, it’s really hard if there’s some who are just happily working away. It’s to say, right, everyone, I can see some of you aren’t getting this. So well, pens down and allies back on me, because that’s really frustrating for those who are fine with it. So yeah, I don’t have all the answers on the best way of doing it. But I do know, that I’m really worried about, I really worry about these dis big trend at the moment for collaboration is a really good thing. And we should be collaborating, we should be being efficient. But there’s off the shelf lessons they have to be, they have to be used with caution. And they have to be really strongly emphasised that if you’re using a potentially I’ll say, one teaching departments gonna plan all the angles lessons, I can see the advantages. But it also means that if you’re delivering a series of lessons that someone else has taught, you need to have the confidence to not use that less than halfway through the lesson. If, if your class depending on what your class say, because otherwise all the assessment for learning is just a waste of time. If you’re just you know, if you’re getting into do stuff on the right boards, or you’re circulating, or you’re questioning, and and then you’re saying, Oh, they haven’t quite got this, but I need to click on to the next slide, then they might as well not have done it. So yeah, I do think it’s really, really tough. I say one more example, I use my, so my year nines. This year, they’ve done they’ve got a cast of your nines who struggle with maths. And they did a grid method last year for expanded double brackets. Early this year, I gave them a end of unit tests on some topic. And I included some retrieval questions in that. And I could see that three quarters of the class got the double bracket expansion wrong. They’ve been taught the grid method last year, they made all the common misconceptions you get with that method, particularly that filling in the last box with by adding the numbers like that’s really, really common. So then I responsive, the responsive teaching for me there from seeing that one test question that they all got wrong was a couple of months later, when I did have the opportunity to do some algebra, because algebra came up on the scheme of work. I tried showing them a different methods. So I said that you all know how you’re taught how to do the grip method, I know that some of you have not remembered how she quit method, I’m going to show you a different way of doing it. And I use the distributive method. So which was modelled very well by Chris Bolton at a recent maths conference, and I used his series of examples to model it. And it worked really well. And at the end of that series of lessons I did on that I said, right, so in year eight, you were taught a great method for expanding brackets, I’ve taught you a different method, which basically just requires expertise and single brackets to be successful, and which was really good for them because they had the expertise and single brackets. And I said, and I’ll let you decide going forward, which method you’re going to use for this topic. But yeah, I if I hadn’t, if I hadn’t spotted that a lot of the class had not coped well, with the methods they’ve been taught in your eight, then I wouldn’t have adapted my lessons for your nine. So I do think, this responsive teaching thing, it can be short term, like in the lesson, or it can be kind of one lesson to the other. Or it can even be like over a long period of time, looking at how they did in end of your assessment, or how they do in the end of unit test, and then thinking about how you’re going to do things differently next time. So there’s a whole load of responsive teaching that we all need to be thinking about. I think it’s a massively important part of what we do. And and yeah, I think sometimes, like I say in Lesson observations, the emphasis is on how are you assessing? Not how you’re responding. So yeah, we do need to think as a professional we need to get better at thinking about the best ways to respond.
Craig Barton 1:09:32
Fantastic. Joe Morgan, over to you now what are you going to plug Have you got anything you want listeners to check out here? What are we plugging?
Jo Morgan 1:09:40
Well, I wrote a book a couple years ago and it’s not selling as much as it used to so I couldn’t do it
Craig Barton 1:09:48
I got my royalties through the other day. Yeah.
Jo Morgan 1:09:51
Yesterday I got my
Craig Barton 1:09:54
new car being bought here. I can tell you
Jo Morgan 1:09:57
I’ve the only other thing that I’ve got coming up is I’m speaking at the I’m a conference in the Easter holidays and I’m doing the keynote on the first day. People can attend online for a couple of days and see my keynote. And it’s actually super cheap. But also there’s a third day which is in person and shouted upon Avon and that’s really exciting because you know, these in person conferences coming back is good times, isn’t it? Where we can actually sit in a room for the maths teachers is really nice. So yes, there’s there’s all sorts of stuff coming up. But yeah, I don’t have I don’t have any new websites to plug but I haven’t you do?
Craig Barton 1:10:30
A one day job. Well, Joe Morgan as ever, it’s been an absolute pleasure speaking to you. Thanks so much for joining us.
Jo Morgan 1:10:35
Thanks.
