This episode of the Tips for Teachers podcast is proudly supported by Arc Maths
You can download an mp3 of the podcast here.
Jemma Sherwood’s tips:
- Plan sequences not lessons [3 minutes 58 seconds]
- Doing maths is not the same as teaching maths [16 minutes 07 seconds]
- What you say matters [25 minutes 48 seconds]
- What you don’t say matters [34 minutes 37 seconds]
- Teach what you mean to teach [41 minutes 10 seconds]
Links and resources
- Jemma Sherwood on Twitter
- Jemma’s book: How To Enhance Your Mathematics Subject Knowledge
- Mason, J. Effective questioning and responding. 2021. In Ineson & Povey (Eds.) Debates in Mathematics Education, 2nd Edition. Routledge.
Subscribe to the podcast
Watch the videos of Jemma’s tips
Podcast transcript
Craig Barton 0:02
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 or maybe even 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. Now remember to check out our website tips for teachers.co.uk, where you’ll find all the podcasts as well as links resources and audio transcriptions from each episode. But better than that, you’ll also find a selection of video tips, some taken directly from the podcast, and others recorded by me. Now these videos can be used to spark discussion between colleagues in Parliament or meeting at twilight inset, and so on. Now, just before we dive into today’s episode, a quick word from our lovely sponsors. This episode of the tips for teachers podcast is proudly supported by our maths art master is an innovative app created by teachers to help students remember all those crucial skills needed to succeed at maths. Art. Maths is built around research into the power of retrieval practice and spaced memory, sorry spaced practice on memory. Here’s how it works. Students crack open the arc maths app and are given a 12 question quiz with follow up practice questions on anything they got wrong, but 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. The more time they spend on the app, the better art or get to know your students and what they with no teaching required. You can spend more of your time inspiring your students with new ideas. So check out arc maths and remember that arc with a C knots okay. Okay, so back to the show. Let’s get learning with today’s guests. The wonderful Gemma Sherwood spoiler alert here are Gemma’s five tips. Tip number one, plan sequences not lessons. Tip two doing maths is not the same as teaching maths. Tip three what you say matters. And then a big twist tip for what you don’t say matters. And finally, tip number five, teach what you mean to teach. If you look at the episode description on your podcast player or visit the episode page on tips for teachers.co. UK, you’ll see a timestamp to each of the tips so you can jump straight to the one you want to listen to first or re listen at any stage. Enjoy the show
so it gives me great pleasure to welcome Gemma show to the tips for teachers podcast. Hello, Gemma. How are you?
Jemma Sherwood 2:54
Hi, Craig. I’m good. Thank you. How are you?
Craig Barton 2:55
Very, very good. Thank you, right Gemma for listeners who don’t know, can you tell us a little bit about yourself ideally in a sentence.
Jemma Sherwood 3:01
I am the senior lead practitioner for mass at the almost an academy is trust, which means that I am responsible for CPD and resources and looking after teachers across 40 odd schools.
Craig Barton 3:15
Wow. Nice. Sounds like a dream job. Fantastic structure. Excellent. All right. Let’s dive straight in. What is your first tip for us today?
Jemma Sherwood 3:22
My first tip is to plan sequences, not lessons.
Craig Barton 3:27
I like it right? Tell me more about this.
Jemma Sherwood 3:29
Okay, so I probably started doing some kind of version of this maybe about seven or eight years ago now. And absolutely revelant revolutionise the way I thought about teaching, because it changed the focus. And for me before my focus around what I did was governed by the timeframe that I had, and in some schools, it would be 50 minutes, and in some schools, it would be an hour. And my thought would be I have a fixed amount of time. What are we going to do in that time? What do I want to cover in that time, and the time was kind of the main driver of everything else. It was kind of the the overarching constraints. So when I changed to doing this process, it kind of flipped on its head because what I do now is I think, I need to teach certain things, certain ideas, certain concepts, I want my pupils to have certain types of practice, I want them to become fluid in things, I want them to be exposed to thinking in different ways about lots of things to do with maths. And now I structure what I do I thinking about that first. And I essentially for a kind of a unit of learning. I have one massive long flip chart or PowerPoint. And I just go through it. But I mean that sounds like I’m kind of slavishly following it. That’s not the case. What it means is I know key things that I want to do at certain times. And if those things happen to go across the kind of now what I see as an artificial boundary of one lesson to the next then fine. So I have no problem in something kind of being finished in the middle of a lesson and I would pick it up the next lesson because it’s more are important to me that pupils are exposed to certain activities, certain tasks or ways of thinking certain lines of questioning. And the timeframes that we have for our lessons are, they just have to kind of be subservient to that really
Craig Barton 5:13
got it? Right. The questions begin here. Yeah, because I’m allowed to ask you about this. So practically speaking, you’re talking a big old PowerPoint here. So just give give us a sense for like a two week unit of work or something. How many slides? Might we be talking
Jemma Sherwood 5:25
here? Probably about 70 to 80?
Craig Barton 5:29
And what kinds of things are on there? Like, examples? Is everything on that?
Jemma Sherwood 5:35
Well, okay, so yeah, this is this part, let me go back a little bit. This is partly because what I’m doing at the moment is I’m making resources that lots of teachers can use of varying levels of experience. So some teachers who are non specialists, teaching metal users, some of them are very, very experienced. So I’m trying to put all sorts in there. So that teachers can, can or cannot, can choose to use or not use things depending on how confident they feel with the material. So when I’m saying 70, or 80, slides, this includes loads of diagnostic questions at certain points in hinge questions and all that kind of thing. It includes ways of explaining things, it could include example, problem pairs, it also includes the activities that I want the pupils to do in case the teachers don’t have the capacity to do lots of printing. So it’s, it’s basically everything across, you know, two weeks across 70 or 80. Slides,
Craig Barton 6:29
nice on what tends to be the first slide that you write there, what’s what’s the first thing that you put out?
Jemma Sherwood 6:35
Um, oh, that’s a very good question. I think that depends depends on the content. So I wrote one recently for the very start with you seven, which is unit on place value. And we started with a bit of the history of number and the history of the number system and how we write and that kind of thing. That whereas recent one I’ve done on the introduction to algebra, that what did that begin with? I’ve only just finished writing it that began with a kind of a, you know, I’ve completely forgotten now, I’m not even gonna try and pretend. But it might be I don’t remember what it started with. It started with a discussion question, which was prompting the pupils to think about it basically, I had a set of examples of the form like two times three, plus eight times three, and two times six, plus eight times six, where it was all two, lots of number plus eight, lots of a number. And I wanted them to discuss these and say what they all had in common, looking at the fact that they all represented 10, lots of a number. And then we kind of go into drawing that as an area model. And then thinking about to n plus a 10, is 10, n and all those kinds of things. So it started with a discussion question,
Craig Barton 7:36
I guess the first thing that you so that’s obviously how your sequence of lessons would start. So is that the first thing you write as well, when you’re putting together this PowerPoint? Do you start your writing where your lessons would start? Or do you have like an end question in mind that you want the kids to get to, and perhaps that’s the first thing you bang down in your PowerPoint, if that makes sense. These
Jemma Sherwood 7:55
days, I start by thinking about the kind of the broad route I want to take through what we’re trying to learn first. So let me stick with this algebra one. For instance, I wanted to start with this idea of the structure, Tony Gardner calls it the structure of arithmetic or structural arithmetic. So I wanted to start with that. And then I wanted to look at how we use that to write it’s kind of to motivate writing expressions as a generalisation of numerical patterns. And then I wanted to move on to a bit more work in expressions in more depth. And we were using algebra tiles and what we’re making. So linking into explaining this variable x tile, which is a new thing to them. And then I wanted to move on to substitution as like a specific instance over imagine the x tile kind of areas, we can kind of fix it a particular number, and work out what the value of expression would be there. And what happens if we don’t fix it at a different number, what’s the value of expression then. So that was substitution, then I wanted to move on to solving an equation, which is where imagine this tile is moving, and then all sudden, we fix it there. And we know that the value of expression is nine, that gives us our equation. Now we can work backwards and find what the value of the tile is. So it’s all about it’s just an introduction to algebra, very kind of informal. But I start with that overview of where I want it to go. And then I go down a bit into a bit more detail into each section and think about what what do I think would be the best way to explain this? How can I link it to what the pupils already know? So that it doesn’t seem to just kind of poof appear out of thin air? And then what kinds of tasks and activities will we do to focus attention in the right places, got it, kind of started overview and then drills on down into each of the sections. And then as I go through, sometimes I go, Oh, actually, I’m going to switch that around now. But that kind of happens as you go along.
Craig Barton 9:41
That’s great. Now this, this has been a big change for me, because maybe similar to your job for many, many years, I plan on a very kind of lesson by lesson basis. But I think to kind of play devil’s advocate a little bit, there are a few potential pros of doing it lesson by lesson so I’m interested in your take on this. So I guess you could make the argument that maybe you’re a little you could fall into the trap of being a little less responsive if you’ve got everything planned out. So let’s say, Well what happens in this case you do your lesson on algebra. And it doesn’t go quite how you anticipated it, the kids are getting the hinge questions wrong, and so on and so forth. Is that is it that a case that after that lesson, you’re adapting that PowerPoint, how does that work in terms of being responsive from lesson to lesson?
Jemma Sherwood 10:20
So there’s a couple of things there, if I stick to the ones that I’m making, at the moment, as an example, I am deliberately putting in places, links to sets of questions. So for instance, you can generate endless questions on simplifying expressions from Johnny halls maths bought, so there’s a link somewhere to the ease, and I know that if I need my pupils to be able to practice this a bit more, I can do that. And there’s links to the OT to these kinds of things throughout. So the point when I when I said before that I go through the PowerPoint, that was a really bad choice of phrase that because that’s exactly not what’s happening, because what I’m doing is asking questions as I go along, and then responding to them. And of course, I have the benefit of lots of experience. So I know that if my pupils are stuck, I can generally figure out what to do on the fly. The reason I’ve made these so long is because I know that some of some teachers will not have that level of experience yet. So I want them to have plenty of stuff and plenty of activities there for them to do. If they’re not able to make it up as they go along. That makes perfect sense. So yeah. So I would say that, I think by having it so well planned, and so well structured, I’m better able to respond, because I’ve got time to think about those things instead.
Craig Barton 11:34
got it got it. My other question is often lessons have kind of key features in there. So a do now would be a classic, a lot of teachers would always start the lesson either with retrieval questions with the last lesson last week, or whatever it may be, and so on. How does that fit into your model? If you essentially don’t really know or care all that much where one lesson starts, and one lesson ends? How does that work?
Jemma Sherwood 11:57
Well, that’s one of those things you then have to do as you’re going along. So wherever you’ve got to at the end of a particular period, if your school says you must start every lesson with this kind of retrieval do now starter, you make sure that you put the relevant kinds of questions into that it might be that you want to practice something that they just need a bit more practice on, because you’ve identified it from a hinge questions that you’ve used previously. Or it might be something that you know, is going to help with what’s coming up that you just want to refresh their minds on. But that’s where you have to, I think you shouldn’t be planning a long time in advance. Because that’s the, that’s all to do with responding. If you want it to be effective, it needs to be reactive to what’s actually happening in the classroom.
Craig Barton 12:35
I see. So there’s opportunities, although you’ve got your kind of general overview or play LiDAR, right now, there’s that expectation that you’re going to be slotted in things as and when appropriate?
Jemma Sherwood 12:44
Absolutely. Yeah. So it’s definitely not here is you know, the next two weeks worth of work, this is absolutely everything you will need, because that’s kind of the opposite of what I want to achieve in the classroom. But what it is, is, here’s the, here’s kind of the majority of what you’re going to need. Use this as your starting point and make it work really well for the peoples we’ve got in front of you
Craig Barton 13:03
got it right, let me put you in the shoes of a novice teacher who doesn’t have Gemma Sherwood planning out this incredible outline of a lesson and so on and so forth. But they want to do this, they want to break the cycle that perhaps mean you’ve been in, where they’re plugged in lesson by lesson, and so on and so forth. So let’s say it’s a Sunday evening, or whatever they sit down, they know they’ve got a two week unit of fractions to teach or whatever. And this could be non math, it could be any subject. Any advice on how they start? It’s quite overwhelming, isn’t it thinking, Oh, my gosh, I’ve five lessons, six lessons or whatever material? Where would a novice teacher start with this job? What do you think?
Jemma Sherwood 13:38
So there’s two scenarios I can think of, first of all, if you’ve got somebody in your department who you think you could talk to who is more experienced, and who you know, would be willing to kind of get involved in such a project, definitely do it, go and pick their brains and get their help on it. If you don’t have anybody like that, I think I would probably start by working with my first lesson. And then adapting to it and putting these resources together as I go along into one long thing. And at the very end of it, stop and look back and reflect and go, How well did that work? How well did the first bit work related to the second? Was there something I could have done between those lessons that would have helped though that little group of pupils over there that didn’t get this thing, but it’s about a reflection, because with the reflection, then comes the fact that you can adapt it and make it better ready for next time. But because you’ve then got the initial sequence, and you reflect it on it so that next time you teach it, you can just iterate it and improve it a
Craig Barton 14:35
bit more. Got it. Final question on this Jabra less has anything you want to add. It’s a little bit of a bonus question going off and a bit of a tangent here. Whilst we’re talking about do now as well, where do you stand on that? Are you if you were midway through some fluency practice or something like that, and the bell went, would you start the next lesson just cracking over that fluency practice? Or do you have a definite kind of starting point to your lesson, whether it’s a do now or something else?
Jemma Sherwood 14:57
I think that’s hugely dependent on the context and the School. So it may be that you’re in a school where you need maybe the pupils have come from PE and they’ve come a long way and they need something just to settle them. And you know that this kind of routine works really well, because they know what’s expected of them, then great, then then do it. If you know that they’re just going to come and they’re going to crack on with whatever you ask them to do. I don’t see the need to necessarily do something like that at the start of every lesson. But I’m going to kind of totally pull back by and be non committal there and say it really does depend on context, but I don’t think that they should be done, like as a kind of a blanket rule at the start of every lesson.
Craig Barton 15:35
Got it. Fantastic stuff. Right, Java, what’s your second tip you’ve got for us?
Jemma Sherwood 15:40
Right? Okay, so this one is doing maths is not the same as teaching us
Craig Barton 15:45
how like another good clickbait headline that German that’s good for the viewing figures. That right, tell me a bit more about that.
Jemma Sherwood 15:52
Um, I was started by trying to think whether or not this is actually a kind of non maths specific type thing. Now, other people watching this of other subjects might just laugh me off the screen now. But I was thinking things like writing an essay is not the same as teaching children to write an essay. Or let’s say, in science, doing a scientific experiment is not the same as teaching children to do a scientific experiment like it. Yeah. And I think by thinking it in those ways, that helped me to think a bit more clearly about what I mean in a mass economy in a massive context. Because I think I’m particularly guilty of this as when I started teaching, I had my favourite ways of doing things, my favourite methods, my favourite algorithms. And I naively thought that if I just showed pupils, what these algorithms were, and showed them what the steps were, that they would also then learn how to do these things. And obviously, you know, years of experience have shown me that that’s not necessarily the case. And there are pupils, who will make sense of it as we go along. And that’s great. But I think they are make sense making sense of it, despite my teaching, not because of my teaching. So what I’m particularly more interested in now is the pupils who don’t make sense of things straight away, because that’s where the challenge lies. And that’s where it’s a bit, it’s beholden to me to make sure that I’m actually teaching something really well. So just because I show pupils, the steps of solving an equation doesn’t mean I’ve taught them to solve equations, it doesn’t mean they understand what an equation is, it doesn’t mean they understand what what they’re actually doing when they solve an equation. And as well, if I have different methods for different things, then it kind of presents maths to my pupils. However, unintentionally, it presents it to them as this kind of hodgepodge of stuff that they’ve got to memorise. And if they’re the kind of pupils who struggle to make sense of it straightaway and struggle to make the connections. That’s where you get comments like, Oh, I just got to learn this bit now. And it doesn’t make sense to me. And there’s so much to memorise, and maps and those kinds of things. And that means I’ve not done my job, as well as I could have done it.
Craig Barton 17:55
This is interesting. So how do you how do we kind of break that cycle? Joe? Because I’ve definitely fallen into into this trap myself, well, what are some of the practical things that that you yourself do to avoid falling into this trap?
Jemma Sherwood 18:06
There’s the question. And that’s like the million dollar question, isn’t it? So this is the one where I’ll probably watch this back in a few years time and go, you’re talking absolute nonsense. But I think at the moment, I think it’s about creating coherence. And coherence is the thing that I’m really focused on at the moment. So for me, I in the materials I’m designing, we have a core a key number of representations, for instance, that we are weaving throughout the curriculum. And so the I mentioned them already, so I’ll stick with this with the example of algebra tiles. So the area model in algebra tiles is built in from multiplying and looking at distributivity. And those kinds of things we’re multiplying, then through to using them for simplifying expressions. Before that, sorry, comes positive and negative integers and then weaving it on into area models with the tiles for expanding and factorising brackets. And that goes all the way up through to things like completing the square and into a level you could do polynomial division with that with with a grid method, for instance. So for me, I’m not saying that that is the best way to teach these things. But what I’m saying is if I have it as a constant or a coherent way that goes through everything, that every time I’ve got to teach a new concept, I’m just adding kind of an extra layer of complexity to something that my pupils are already familiar with. And that, I think, is more likely to make it have meaning for more pupils.
Craig Barton 19:33
Yeah, that makes perfect sense. Does does it mean Gemma, that sometimes things may seem a lot a little slower or less efficient to teach because you’re you’re trying to not just teach the concept, but also get the kids familiar with as you say, algebra tells like that solving equations is the classic right? Because we all know real quick ways you can get kids to solve some amazing looking equations. But the problem is those methods don’t scale because as soon as you then get into quadratics, then the whole world falls out. part you have to teach something else. So it feels to me like this is definitely the right thing to do. But teachers and the kids need to be aware that there might be. I’ve spoken about this in a previous teach tips for teachers video, this this kind of value of latent potential, where initially there’s a bit of a dip in short term kind of performance and progress, because you’re trying to get to grips with something that’s perhaps not as efficient a tool for doing that specific job. But we know that this tool has got these kind of long term benefits. Does does that make any kind of sense at all?
Jemma Sherwood 20:28
Absolutely. And I completely agree. And I would much rather spend three weeks on operations with directed numbers early on, in the knowledge that then everything we’ve embedded about that I can then apply to simplifying algebraic expressions. And it’s just a tiny step up, rather than being this whole new, completely unusual thing. And all the pupils have then got to see is that oh, now we can do the same thing, but with some unknown numbers, but actually everything else we’re doing is exactly the same. And the gains then become quicker as you go on through.
Craig Barton 21:03
That’s lovely. Final question on this one, Gemma, again, trying to play devil’s advocate a little bit, is the is there a danger that if we have these consistent representations and models, which I you know, hands up, I’m a big, big fan of that we we fall victim to having less variety and methods and kids may have these lots of different approaches and they want to use but we’re actually saying no, no, no, actually, we’re going to use this one because we believe this is the best this is a conflict there. Is that Is that a problem or not?
Jemma Sherwood 21:32
So first of all, I think the kind of traditional situation that we found ourselves in where we have lots of different methods for different things. I don’t think it’s too harsh to say it hasn’t worked for a huge number of pupils. For a huge number of pupils, because if you know, if we’re saying that there’s a massive number of pupils in this country who don’t get above a grade for GCSE, or do you know, don’t even get above a grade seven at GCSE. That’s a huge number of kids who don’t really understand a lot of maths after a long, long time studying it. So what we’ve done so far as a collective has been ineffective for too many pupils. So if you’re saying a variety is important, then I think you’ve got to justify that this variety is good for the pupils who find things difficult. Now, I have no issue with saying right, we’re going to do these consistent methods, because we are going to make sure that we have a coherence of a curriculum for our pupils in our in our school. But if you have pupils who really can’t get their heads around this, I have no problem with teachers having other things, you know, in their arsenal in order to help them explain things. But what I don’t want is the default position to be everybody just throws whichever method they want at the pupils, because that’s ultimately I believe, going to make it too hard for too many pupils as they go through. And we all know that our pupils reach a ceiling. And I feel like at the moment, and this is based on quite a few years of experience doing this. Now I feel like at the moment that fewer of our pupils will, or more of our pupils will kind of push the ceiling higher by taking a more consistent approach.
Craig Barton 23:13
Yeah, it’s really interesting. I’ve wrestled with this for a long time. So I assume you as well be a big fan of Joe Morgan’s compendium of mathematical methods, I can ever read through that and think, Whoa, there’s about 10 different methods for finding highest common factor and most common multiple that I’ve never even considered. And best case scenario. That’s really good. Because she can say, right, we’re going to solve this problem this way. But you know, what, there are five other different ways that we can use and let’s spot what’s the same, what’s different, one of the connections and so on. And I think for some students, that’s really, really powerful because they start see different connections and so on. But as you’ve spoken there, for other kids, it’s really overwhelming, right as well. And that then maths becomes, right, what is the problem? So what which one of those weird methods that I didn’t really understand what I need to select to solve this problem, whereas reducing the number of approaches, by having these consistent coherent models, I think for the majority of students is going to be the best thing. And then as you say, there’s always that opportunity, if they’re seeming to grasp things that then we can throw in these alternative methods, not just as a random thing, but to say, what’s the same, what’s different? What’s the connections, and so on? Does that make sense? I absolutely
Jemma Sherwood 24:16
love Joe’s book. And I think it’s brilliant for teachers, because it helps them to see how all these methods are essentially doing the same thing. Because actually, there’s not 20 Odd methods of adding numbers, there is one method. And there’s 20 different ways of presenting that method. And so that’s really helpful for teachers. But I think for us, looking at it with our knowledge and our understanding of adding is brilliant. If you’re going to know if you’re going to show lots of different methods to pupils who are still trying to cement their understanding of adding. I think that’s that’s cognitive overload there. So I don’t think it’s helpful. But like you said, there will be pupils who who can explore that, and I think everything we do In a classroom, we need to do very consciously and very carefully. So if I, if I have a group of pupils who I would like to show a different method to, because I would like to use that to illuminate something to do with this concept that we’ve been learning about, and I know that that would help them to make more sense of something. Brilliant. But I have to make sure that it’s kind of past that litmus test, if you like, before I do it.
Craig Barton 25:23
Makes perfect sense. Fantastic. Right? Jabber. Tip number three, please.
Jemma Sherwood 25:29
Right? This is what you say matters.
Craig Barton 25:33
God, hello, I get cryptic. Go on, tell me what
Jemma Sherwood 25:36
this is probably the worst of me to say, because I’m very, very Wofully. Here we go. So you need to pick your words carefully. It’s very easy to get nervous in the classroom, whether you are novice or experienced. And when you get nervous, you waffle, you repeat the things. You say things in a way that’s not particularly clear. I’m deliberately trying to be very conscious of it. And that’s not helpful because we have pupils, as we’ve said already, who are trying to learn something normally completely new. And they need the explanations to be as clear and as uncluttered as possible, if they’re going to make sense of it quicker. So I think I now believe that people, maths teachers should be or any teachers should be practising their explanations going away and thinking carefully about how they’re going to explain something, what vocabulary they’re going to use what, but not just that what questions they’re going to ask and when and why. It really, it links back to what I said before about being a reflective practitioner. This was something that was taught to me on my PGCE a years ago by Dave here and Pat perks, and they were constantly telling us you’ve got to be reflective, you’ve got to look back at what you’ve done. And when I was early on in my teaching, I suppose I didn’t really know what I was reflecting on because my own kind of schema of teaching maths was so limited. And but you have to start the process so that it becomes embedded and so that it becomes internalised. So I think that it’s hugely important that we plan not only what we want the kids to do in our lessons, but what we are going to say and how we’re going to say it.
Craig Barton 27:20
Lovely that I saw a couple of things on this. It was I don’t know if again, this may not have been true for you, gentlemen, but for many years, it was the last one, I never even thought about what I was going to say. So I’ll just put that on the table. And now I just kind of wing that as I went along. But even like the examples, I was going to ask my kids to what I was going to use for modelling they were the last thing I would plan my plan was all activity driven, task driven, and so on and so forth. So that’s the first thing I completely 100% agree with you about the the words we say I waffle. I mean you think you are for Gemini never shut up. It’s like why say things one way we say it 58 times and I just keep repeating repeat opinion, and it’s too much for the kids. How do you get better at this though? You mentioned there practising? Are we literally talking here? Like in your bedroom or whatever? Like practising how what you how you’re going to talk kids through an example or how you’re going to introduce always is that the best way you find it to do this, at least initially.
Jemma Sherwood 28:16
I think initially Yeah, writing down the key things that you want to say so that you’re you’re conscious of them so that you’re aware of them. But then also, it’s it’s cringe worthy. But if you stand in front of a mirror, and practice the way you’re going to explain something, you’re able to watch yourself and you’re able to pick up on your irritating mannerisms. I I had while I’m early in my second year of teaching, the school I was in had one of those classrooms where they would video you. So they gave me this DVD and they said go away watch this. And I said okay, after every third word, I think Okay, so now we’re gonna do this. Okay. And by the end of watching this video, I just wanted to shoot. Yeah, it was so good, because I didn’t know that I did it. So I think it’s really I think it’s it’s cringe worthy and potentially very frustrating. But if you want to get better at communicating, it’s actually a very important thing to do.
Craig Barton 29:17
So it’s interesting that we’ve, we’ve had on the put on my best about maths podcast a couple of times teachers who use booklets in their lessons and Danny Quinn’s been undefeated and so on. And a lot of people criticise booklets for many reasons. But one thing that and it kind of fits into this mould of kind of in inverted commas the scripted lesson, but if you have a really well thought through explanation that’s in bullet point form, and as you say, removes all the clutter. And a teacher reads out that explanation there’s a lot to be said for that isn’t that particular if you’re a novice teacher, you find it hard to to get that explanation concise and clear and the right amount of information without overwhelming having a kind of script that you perhaps don’t stand in front of the kids or read out but that you’ve rehearsed yourself that an experienced teacher has helped you with? I think there’s a lot to be said for that. What do you think?
Jemma Sherwood 30:03
Absolutely. And at the very least some key words and key phrases that, you know, I absolutely must say this. And I absolutely must emphasise this. Because like we said before, when you stood in front of your classroom, it’s easy to get distracted by things. It’s easy to get nervous, it’s easy to forget stuff, because it’s just the way our brains work, isn’t it? So if you have these things that you know, are the absolute musts that you want to get across, and you’ve practised them, you’re less likely to forget these things. What it’s what it means, of course, is the more you do it, the less you have to rely on that. Yeah. So I I’m relatively confident now that I could walk into a classroom just like that. And I could give a pretty strong explanation on pretty much anything across 11 to 18 months. But that’s because I’ve done it for however many years. But it’s taken that kind of conscious repetition and reflection and practice, to get to that point.
Craig Barton 30:59
I’m going to talk so that I don’t know if this is a good idea, or the worst idea. So I’m just going to run it by you and see what I see what you think of this jabber right. So whatever remote teacher was happening, I did a series of podcasts with people who were teaching from home, and just the tips and so on. And Adam Boxer was on there. And he was saying how he was creating a lot of videos for Froch national and National Academy at the time. And he said, his explanations in those videos were far better than any explanations he would do in the classroom for the very reason you’re speaking about there. Because he could just focus all the only thing he was thinking about was his explanation, because he was recording it into a microphone and a screen. So it got me thinking, and as I say, this is this is where the worst idea I’ve ever heard comes into play. What’s the argument against let’s say that you you’re you’re gonna teach solving equations, and you at home, have written out this, essentially a script, and you’ve recorded yourself explaining it, microphone screen, maybe you’ve used the tablet, or whatever it’s got, you’ve got it, you’ve got it perfect. You’ve got this example, this explanation perfect. What’s the argument against you pre recording that you play in the classroom for your kids, and you’re, they’re kind of on hand, if the kids are stuck, they can pull the handle, you can just kind of have a whisper to them, you’re, you get to put your full attention on to your kids, whilst you’re kind of virtual self is given this crystal clear explanation? Where’s the floor in life if there is a floor?
Jemma Sherwood 32:22
Okay, it’s not interactive enough. And there is a huge difference between teaching something on a video or explaining something on a video, which is more akin to a lecture than and there’s a huge difference between that and teaching something in a classroom and teaching something in the classroom relies on being able to have those very human interactions, being able to respond to cues, nonverbal cues as well. So for me, that would be suboptimal, because I’m not able to interact with what happens as I go along. But if I’ve already thought really carefully about how I want to explain something, then I’ve got my own kind of brain space freed up to actually do those to actually respond and to and to question in the right places, and to go, you’re paying attention Come on, and all of those things, because I am more confident in the in the kind of the core substance of what I’m doing and saying,
Craig Barton 33:24
got it suboptimal is a nice way to support that idea. That was nice. I like that. That’s perfect.
Jemma Sherwood 33:30
And there was something else on that as well. And that was that. When I said what you say matters, I think it’s also important to, to be aware of the things that you want pupils to internalise as well. So there will be certain phrases and concepts that when I’m teaching, I want my pupils to associate with certain ideas. So when I don’t know, let’s say, when we’re solving equations, I want them to know that the second they see an equation and the word soul that they’re going to be thinking about balancing. So I will be saying and what we’re going to do now and I’ll be all the peoples to go balance and getting them to repeat these things over and over again, because they’re more likely to internalise something if they’re rehearsing it as well. Yes. So for me when I say what you say matters, it’s not only about the way I explain something, but it’s about the repetition that I build in for pupils and the opportunities I give for them to be able to actually vocalise things as well. Nice,
Craig Barton 34:23
lovely stuff. Okay, Gemma, what’s Tip number four, please.
Jemma Sherwood 34:28
Okay, it’s kind of a converse, what you don’t say matters.
Craig Barton 34:31
All right. Well, you’ve done that. Okay. Tell me more about this. Right. So
Jemma Sherwood 34:35
two parts of this one. The first one is don’t assume that something is obvious. It’s very easy for us as x as experts in mathematics, to assume that what we think is obvious is obvious to our pupils. When we do that, we tend to not make things explicit, we tend to not say things and then what happens is that it will get a few lessons down the line and you In a pupil makes a mistake or does something and you go, Well, that’s obvious. You should know that. But they don’t. Because I never actually made it clear. Yes, because I just assumed that they would know this thing.
Craig Barton 35:13
So if I don’t say something, it’s sorry. Well, it examples bring to mind that you can think
Jemma Sherwood 35:19
I know you’re gonna say. So, okay, so I have a couple of years ago, I was teaching a lesson on differentiation with your 12. And we had expression is where we’ll there were, they were algebraic fraction type expressions where we had something like x squared plus 3x on the numerator and x on the denominator, something like that. And I said to them, it was something along the lines of right off we go, then we’ve done those differentiation, let’s have a go at this one now. And they all started to do really weird things like differentiating the polynomial the top and then differentiate is pulling the polynomial the bottom and keeping it in a fraction. And I said, I remember stopping at one point going out to one people and stopping it stopping here and going, why are you doing that? And she said, well, because you’ve told us to differentiate like this. And I said, No, but this is this is a different type of function. And I suddenly realised that I hadn’t actually explained to them that we need to split this up into separate terms, and then differentiate, differentiate each term separately. So that was completely on me, because I just assumed that they would know they had to do this. Yes, this is I would like to say this was long time ago, by the way, but this is a perfect example of one of those things where you do you look back and you go, obviously, that’s my fault, because I didn’t explain that to you. That’s a really good example, if you don’t say something, it matters.
Craig Barton 36:42
That’s really good. And I know I’m interrupting you, because I know you’ve a second part to this. But just just on this, do you think that comes down to a well, a lot of that can be solved just by the choice of examples that you use, because I fall foul of this all the time to use your differentiation was a great one there. If you’re really careful about your selection examples, and particularly kind of boundary examples, things that right on the edge of either fits into the concept or does it that it solves quite a few of these kind of curse of knowledge problems, because you’re you’re forcing the kids to attend to a wide variety of examples. So they start to make those connections a bit clearer. And you drag an examples of the key to this?
Jemma Sherwood 37:21
Yes, I know, you’re gonna say, you know, because we can never give examples for every single possible misconception our peoples going to come across. So I think what we need to do is, is direct our examples towards the most common things and what we might perhaps term the most important ideas to communicate. And then as we go through, there are going to be times where something else crops up, and you’re going to have to address it there. And then, but you’re never going to be able to predict all of those things. So what I wouldn’t want to do is say yes, because what I would, because an unintended consequence of that might be that kind of lessons, people’s lessons, turn into just example, after example, after example, and look how this one’s a bit different look on that one’s a bit different. But actually, when our pupils start to get more fluent in the way the mathematics is working, whatever, whatever we’re doing, they are able to deduce these things for themselves in a lot of cases. And that’s okay, as well. And and I would go further and say that’s okay, that’s really important that they start to kind of apply what they’ve learned in unusual contexts, hugely important. But when there are more obvious things, really important things that you want to make sure that the pupils absolutely are aware of, yes, definitely highlight it in an example.
Craig Barton 38:38
Got it? Well, what was your other thing you’re gonna say about this tip German before I cut you off?
Jemma Sherwood 38:42
Oh, well, only just in the context of what you don’t say matters. That also goes towards creating the culture you want in your classroom. So everything you do, as the teacher will contribute, either intentionally or unintentionally to the culture in your classroom. So your body language, the care you show to your pupils, the attention you show them by asking them questions about what they do, John Mason wrote a lovely chapter in a book a while ago, and I’ll send you I’ll send you the link code, about questioning and how you show care to pupils through questioning and show that you value their thinking, and all those things. Although they’re not explicitly about the kind of the maybe like a utilitarian aim of teaching mathematics, what they’re about is showing pupils that their thinking is valued, and their contribution is valued and, and that you have high expectations of them. And it helps to communicate what you expect a mathematics classroom to look like.
Craig Barton 39:39
That’s lovely. That is you just made me made me think of top on top of my head. And again, thoughts off the top of my head are always high risk. They’ve not been processed at all. So this will be suboptimal as well. General, I’ll warn you in advance now. There’s been a lot of chat on the tips for teachers podcast so far, about use of mini whiteboards, and I’ve recorded a few videos on this and so on. I just use saying that maybe think that one of the big advantages of mini whiteboards that I don’t think I’ve ever heard before, is that it communicates to the kids that every answer matters. Whereas, you know, you could if I if I’m teaching and I just asked you that you a question, and Joe Morgan sat in the class, you might be thinking, well, he’s only bothered about Gemma’s answer. He’s not really concerned about him. Whereas if the kids are answering every child answered every question and show you on the mini whiteboard, even if you don’t pick up their answer, you at least communicated that you value their response, if that makes sense. And I don’t often hear that mentioned Absolutely. In the context of mini whiteboards.
Jemma Sherwood 40:31
It I think it’s this I think I mentioned it earlier about being trying to be very conscious about everything you do in the classroom. But understanding that every single action of yours will have an effect. So you want to make sure that your actions communicate that every pupil is important that every pupils thinking is important, and that you expect every pupil to think hard and that you expect that every pupil to work hard. And what you don’t say, is also communicating all of these things.
Craig Barton 41:01
Yes, that’s lovely. Love that one. All right, Jabba fifth and final tip, please
Jemma Sherwood 41:07
write, teach what you mean to teach.
Craig Barton 41:11
You’ve really fought through these these titles, I like this, right and told me about this one.
Jemma Sherwood 41:16
Okay, so I’m going to illustrate this one with an example. A few years ago, I was watching somebody teach a lesson on velocity time graphs. And they were teaching the idea that if you find the gradient of a line, it will give you the acceleration. And the the teacher explained this idea. And they worked through an example. And they got to the point where it was something like acceleration equals six divided by three. And Craig, what six divided by three and the pupil said to and he said, Great, you’ve got it. This, this then happened over and over and over again. And I spoke to the teacher at the end of the lesson. And I just said, I want to point something out to you. Every single question in the 10 minutes that I watched, was around mental arithmetic. And the only things that people had to answer was mental arithmetic. Do you know that they understand understood that the gradient of the line is the acceleration? Or do you know that they knew they know their division factors. And that was the first time I’d ever noticed it. And then I saw it more and more. And then I was aware that I did it as well. And I suddenly realised that we, I think it’s very easy to ask pupils the kind of the simple end bit of the question the mental arithmetic, because we know they know it. And maybe it’s because we want them to feel successful. And we want them we want to be able to go Yeah, well done. Yeah. But actually, if we think about what we know from cognitive science, we know that what pupils think about other things they’re going to remember. And if we can prompt more pupils to be thinking hard for more time, about the key thing we’re trying to teach them, they’re more likely to remember that thing. So if we have one or two pupils thinking about mental arithmetic and knots, that acceleration is the gradient of a lie. We are less likely to have our pupils remembering that concept
Craig Barton 43:09
is great this job but I’ve I’ve done this tonnes and tonnes of times for the exact reason you say is because the kids feel great, you can calm yourself into thinking what a great explanation I’ve done here if this complex thing, because the kid is like the punch line to it, six divided by three is two are brilliant. They’ve understood calculus or whatever is terrible. But I’ll tell you the interesting thing about this, a lot of focus on the kind of classroom techniques is based around formative assessment check for understanding use many whiteboards diagnostic questions, whatever it is. But the point you’re making there, I think anyway, what I’ve taken from it is you’ve got to be careful what understanding you’re checking for. So you can imagine you do the lesson on grading that you’ve described there on velocity time graphs. And the diagnostic question or the mini whiteboard check is okay, so write down what the final gradient is. What if it’s all just checking that they can do the six divided by three, you get a room full of mini whiteboards where everyone’s nail there, and you think, Oh, I’ve done that formative assessment. I’ve checked everyone’s understanding amazing stuff. But it’s what understanding Are you checking for? is the key to that feels quite, it’s quite a complex skill, isn’t it? for a teacher to get to get right. I think
Jemma Sherwood 44:13
it is one thing that I have to say to staff increasingly now, especially when I noticed that they are they are more inclined to do this is as a way of kind of trying to reduce it initially. And as I say, I don’t want you to ask a question, unless it’s about the very specific thing that you’re teaching. So if you’re teaching expanding brackets, for instance, I don’t want you to ask any questions unless it’s one actually about the expansion of that bracket, that bracket and everything else you just got to say it.
Craig Barton 44:39
Yeah, that’s lovely. Love that one.
Jemma Sherwood 44:42
There’s another part to it as well. And it’s kind of very closely related. And that is that if you let’s pick the example of expanding brackets again, if you are doing a kind of a period of instruction in the classroom, and you’ve got this this bracket that you want to expand and you can see the people struggling so you show them how to do the expansion, whichever methods you’ve chosen. And you then ask them questions about just the multiplying but at the end, and let’s imagine that you’re kind of interspersing, this example with all these questions or when and what’s five times 3x? And what’s two times what’s five times two here, you then have it kind of links to my tip from earlier, you then have the problem that you haven’t given a clear explanation at any one point because your your explanation of the process has been punctuated with questions about mental arithmetic. So the pupils who are able to make sense of the process have made sense of the process, but the ones who couldn’t haven’t benefited from a really clear explanation from the teacher, because it’s been they’ve been distracted by all these questions going on.
Craig Barton 45:41
That’s interested. So is the solution to that. And again, this, this could be nonsense, is it if you get your prerequisite knowledge check, right, because that’s when you can sort out all these bitty parts of it, right. So to take your expanding brackets, that’s where you can check that they can multiply A term together, that’s where you can check that their family negative number arithmetic, all the things that they need to, that’s fine to be bitty that bit. And then when they come to do this new concept of expanding brackets, that’s when you can be a bit more coherence in your explanation, because they’re the bitty bit should be familiar to them. You don’t have to assess their understanding of that. So they can focus on on the whole narrative, if that makes sense.
Jemma Sherwood 46:19
Absolutely. And then you once you’ve, you’ve explained it really clearly, you can use as much questioning and as much mini whiteboards as you want to see whether or not they can make sense of this, whether or not they can replicate the process, whether or not and then you go into kind of how they can reason about it in more depth, and all those things that come afterwards. But you’ve got to make sure that you are focusing your let me let me get back a second. Every question you ask will direct people’s attention at something. So you’ve got to make sure that you direct their attention at the thing you want them to learn, not the mental arithmetic.
Craig Barton 46:52
Lovely, lovely. Gemma, they were five fantastic tips. So now it’s over to what you’re going to plug what you’re going to tell people about First off with your book, not enough people know about this, tell us tell us about.
Jemma Sherwood 47:03
Okay, so back in 2018, I wrote a book called How to enhance your mathematics subject knowledge, number and algebra for secondary teachers, which is a beautifully short title. It’s, I did it because I’ve been working with lots of people, lots of people on a subject knowledge enhancement course at the time, for quite a few years. And I wanted a book that teachers could pick up at any point in their career, but particularly at the start, and just kind of pick it up and put it down. And it would help them to deepen their knowledge on school level maths. So it takes things through everything that we would kind of consider 11 to 16 number and algebra, and it goes into loads of depth about it gives them tips for the classroom. And it kind of is got quizzes in it to really kind of push the limits of their understanding of these ideas, talks about where it goes next, be it at a level or beyond brings in elements of history of maths that are relevant to it as well. So the whole point was not to necessarily not to specifically think about pedagogy, but to think about the mathematics at school level and how you can deepen your knowledge of it.
Craig Barton 48:11
Brilliant. It’s a fantastic book, anything else you want to direct listeners to or to be aware of. I see on Twitter, you talked a lot about this kind of curriculum designed the work that you do it in, I saw a tweet. So these can be freely available later later on in the year. Is that Is that true? Is that a world exclusive?
Jemma Sherwood 48:26
You know what, let’s make it a well. Yeah, so I’m, I’m a little bit obsessed with this idea of a coherent curriculum at the moment. So there are multiple ways of doing this. So I have picked my way of doing it. And I am making the resources that go from year seven all the way through to Year 11. And we’ve got some schools at the moment in our trust that are trialling the resources with iOS seven and they’ll eventually be the ones that kind of take you through all five years. And I’m hoping that hope, before the summer holiday, I want to say I’ll be able to kind of go here’s the whole of the year seven resources for people, and it’s going to be completely freely available. Eventually it will be five years and it will be all there for anybody to access. It will be booklets full of all the tasks activities and these associated unit long PowerPoints that I was talking about earlier.
Craig Barton 49:19
It’s a world exclusive. Gemma what ordering Have you gone for Is this your bespoke ordered or have you used NCTM nonstatutory?
Jemma Sherwood 49:25
It’s it’s kind of bespoke. So it’s based on ordering that I have used historically when I was head of maths but kind of the lessons that I learned from that. So changes have been made from that. So it’s kind of comes from a tried and tested base. But then I’ve tried to improve upon it there. We are making things so what we’re doing is we it’s a bit it’s a kind of combination of curation and making things from scratch. So whether our existing activities or tasks that I think are high quality and fit the brief so fits the path of the path that we’ve chosen to take through Then we’re using those with the web, obviously, with people’s permission. And then if not, we are creating the tasks and activities to fit it as well. And the sequencing is kind of broadly based on the ideas of embedding the most important things at the beginning and most important ideas around number and then going out into algebra. There’s, I mean, I could talk to you about this for hours. So I’m not going to do that now. But we’ve made it so that there is flexibility in it as well. So certain units are absolutely prerequisites to others. Because the one thing I will say is that I’m really excited about is the fact that when things are prerequisites to others, we deliberately weave the content in from previous units so that the practice to use a few years time the practice of one skill becomes subordinate to the practice of another skill. So yeah, there’s kind of flexibility in terms of how you can move certain units around certain ones have to go in particular orders. But yeah, eventually it’ll be five year fully resourced, coherent curriculum, a not the coherent curriculum but a coherent curriculum for their
Craig Barton 51:01
work and it’s worth if people don’t already follow you on Twitter because after you’re chucking out ideas at this stage, why she created and getting feedback from people and examples of stuff it’s that exciting anything else to plug Jabba?
Jemma Sherwood 51:15
Not Yeah, asked me that a few months, Craig.
Craig Barton 51:16
Okay. All right. Well jabber showed it’s always a pleasure speaking to you and definitely husband today. Thank you so much for joining us. Thanks, Greg. Bye.
Transcribed by https://otter.ai