This episode of the Tips for Teachers podcast is proudly supported by LUMEN
You can download an mp3 of the podcast here.
Julia Smith’s tips:
- Practice, practice, practice…not until you can get it right but until you cannot get it wrong (04:24)
- Revision should start from day one of a course, not at the end (12:57)
- It ain’t what you do, it’s the way that you do it…and that’s what gets results (23:13)
- Fluency in the four operations is a cornerstone of developing mathematical understanding (33:27)
- How to deal with students who say they hate maths or are no good at maths (44:28)
Links and resources
- On Twitter, Julia is: @tessmaths
- You can find out more about Julia’s 5Rs project here: 5rs.co.uk
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Watch the videos from Julia Smith:
Podcast Transcript:
Craig Barton 0:00
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. This episode I had the pleasure of speaking to the Queen of GCSE recent maths, Julius Smith, and it’s a crack. Now just before we get going a quick word about our lovely sponsors because this episode of the tips for teachers podcast is once again proudly supported by lumen. What is lumen? Well, lumen is the acronym for the Loughborough University Mathematics Education Network. And it’s a network very close to my heart. So I’m very proud to be a visiting fellow in the Department of Mathematics Education lumen have kindly sponsored three episodes of the typical teachers podcast. So each episode I’m going to tell you about one of their amazing free online CPD videos that they have available. This week. It’s the turn of how mixed the time that grouping affects the way students experience mathematics by the fantastic Tom Franken. Now this is the blurb for the video, you’re ready for this mix the time that mathematics teaching is not a common practice in England despite evidence that ability grouping is not an effective strategy for improving educational outcomes. It’s a much debated topic among teachers. In this talk, Tom Frankham addresses the background to the debates and discusses a study comparing mathematics in two schools, school lab mix stability, and school last sets. Now I’m a huge fan of Tom I’ve been lucky enough to have him on the Mr. Barton laughs podcast and many times over the years super smart super balance and that is going to be a cracking watch. And I’ll tell you what, there are loads more videos from early years to post 60 Just Google looming math CPD luminous l u m n or follow the link in the show notes. Now two quick things to remind you about before we dive into today’s episode. Number one, you can view all the videos of Julie’s tips plus the tips of my other guests plus 20 exclusive video tips from me on the tips for teachers website. That’s tips for teachers that code at UK. These videos are great to share in departmental meetings or training sessions. And number two, you can sign up for the tips for teachers newsletter, to receive a tip in your inbox every Monday morning to try out with your classes in the coming week. And please tell your colleagues about this if you think you’ll find it useful, not just your maths ones. Oh, and finally, one bonus thing. If you find this podcast useful, I’d be so grateful if you can take a very quick moment just now ideally, to review it on your podcast player. It really does make such a difference. Thanks so much. Okay, back to today’s show. Let’s get learning with today’s guests. The wonderful Julia Smith. Spoiler alert here are Julia’s five tips. Tip one, practice, practice, practice, not until you can get it right but until you cannot get it wrong. Tip two revision should start from day one of the course not at the end. Tip three, it ain’t what you do. It’s the way that you do it. And that’s what gets results. Tip Four fluency in the four operations is a cornerstone of developing mathematical understanding. And Tip five how to deal with students who say they hate maths and are no good at maths. Now whilst this may seem a very maths focused discussion, certainly those first three tips I would argue have applications for different subjects. But there is a lot of maths going on here but there’s nothing wrong with that. If you look at the episode description on your podcast player or visit the episode page on tips for teachers, Dakota, UK, you’ll see our timestamp teacher the tips so you can jump straight to anyone you want to listen to first or really enjoy the show.
Well, it gives me great pleasure to welcome Julia Smith to the tips for teachers podcast. Hello Julia, how are you?
Julia Smith 3:37
I’m fine. Thank you, Craig. Delighted to be here.
Craig Barton 3:40
Yeah, I’m really looking forward to this one Juliet. So for the benefit of listeners, can you just tell us a little bit about yourself ideally in a sentence?
Julia Smith 3:48
Okay, so I’m Julia Smith. I’m a rabid tweeter at tests maths. I’m project lead for the five hours revision based research funded by the E FF and supported by the Association of Colleges. It’s a big efficacy trial. I’m a shine award winner as well which is lovely maths teacher trainer, really an author for Oxford University Press, Cambridge University Press BBC bite size amongst other people, and I sit on the AQa expert panel as well.
Craig Barton 4:18
Julian no messing around now that summer credentials. Well, I do want to start straight in what’s tip number one for us today.
Julia Smith 4:29
It takes an influence from Dylan William obviously the great man I was listening to him the other day on your on this series. In fact, it’s wonderful absolute here hero legend. Practice, practice, practice, specifically with massed practice, practice, practice, not until you can get it right but until you cannot get it wrong.
Craig Barton 4:48
That’s nice. Well tell us a little bit more about this. I will fight as a quote and I love as a principal and what wherever you kind of see in this scene this inaction and why is important.
Julia Smith 4:57
So a lot of my work is based In further education is based on reset. Students who just are having to reset it because it’s mandatory. I don’t think there’s anything wrong in that, per se, however, they need so much more support. This isn’t to say it’s not relevant for year 11. And every year in fact, it’s also a note for teachers really to enable us to give our students plenty of opportunities for 24/7 practice, you know, they have a different timetable to us as adults, there are all sorts of hours. So the ability to go somewhere when they’ve got lots and lots and lots of practice opportunities, no logins, perhaps just going there for the sake of doing some maths work is a really, really fundamental part of what we’re talking about here. Dylan also talks about making the students the architect of their own learning talks about giving them self assessment opportunities you yourself talk about in your I’ve got this pile of books here I always collect always have them around me to reference other people as well. You yourself talk about, you know, the low state quizzes, the fact that they’re going into they can have their notes with them. Just practice, practice, practice, the only way to get good at maths is by doing lots of maths, lots of analogies as well we’d playing football, playing FIFA football on the on your Playstation or whatever, playing musical instruments. You know, you can find lots of connections there with learners in that way. How do they get good at those skills? Well, it’s the same thing they just need. You can’t read about it, you can’t look at it, you’ve just got to do it. And you’ve got to do it so much. So much practice that you can just keep doing it until we cannot get it wrong.
Craig Barton 6:50
I like it well let’s just dig deeper into into this a little bit. So obviously as you said yourself, you do a lot of work with GCSE research students and it’s a tough gig sometimes that isn’t it isn’t a Julius particularly when you when we’re teaching recent maths because these are kids who’ve big experience of failure over many years, they’ve already probably decided they can’t do it. A lot of them don’t want to be there and and so on. And when we discussed this when you’re on my Mr. Biomass podcast, one thing It always strikes me is that the practice whilst they obviously it’s super important, it perhaps almost has to feel a little bit different than used to be a bit of variety in the practice. And I’m thinking to two things here. I’m thinking first, they’ve probably practised a lot of these things in that way over the last seven, eight years, and still inevitably struggled with it. And also, if they find that challenging, and we keep getting the same type of practice, maybe that that is problematic as well is just variety plays a key role in this, Julia?
Julia Smith 7:42
Absolutely, certainly does. And it links to lots of my other top tips as well. You know, is it the five hours curriculum that I have is is a revision based curriculum, and a lot of people say but they’re not revising, they haven’t learned it before. What that’s that’s really a misunderstanding of what revision is. And I’m going to come on to that one of my most favourite books at the moment, revision revolution, Helen Howell and Ross Morrison, McGill. dougla MAF talks about in that in that revision revolution, he talks about practice may not make perfect, but it may make permanent it’s that that enough exposure to something but you’re right for a reset learner. And I also think for you 11 as well. It’s about revisioning the maths, that’s what revision means if you if you split the word re vision, you’re revisioning the maths, you’re seeing it differently, from a different perspective with a different resource with a different media. Just exposure to it any which way you can, as I say, I’m coming on these do link these five top tips. So I’m coming on to bits and pieces. But the five R’s curriculum really is that revision based year approach, practising daily maths anything that we can get students to do 20 minutes mat every day would be amazing. But we have to give them the the the tools that enable them to do that. I mean, things like Johnny halls Massport you know, there’s plenty of opportunities there for practice, practice practice. We’ve got on maths, you know, there’s some fantastic tools and bits and pieces out there. And it’s a message to us as teachers as well to allow them opportunities. And as he as you yourself have written in your book, which is here. And you can see all the post it notes I’ve got on them, you know, they’re full of post it notes, all these books, you know, you talk about going on, they’re not collecting in the marks Dylan William talks about that. It’s really important because what, what increases the mass anxiety is knowing they’re going to be graded, they’re going to be marked. They’re going to be looked at how long are you going on to the mass platform and how much have you done on it? Take away all of that, which is what the five R’s curriculum is doing. Just go and do it because you see the benefit of it if we think about National Numeracy we’ve just had now National Numeracy day on Wednesday getting learners to see the the the value in the qualification first of all this qualification will open doors that they don’t even realise a sharp yet valuing the qualification, believing that they can do it with you. And you talk about positive influence positive culture in the classroom as well and how we can get to that. But also they’ve got to put some effort in they’ve got a part to play Dylan William making them the architect of their own learning. So there’s a lot in that it’s not just practising until they can get it right and then we move on. It’s it’s that practising like learning to drive, you’ve just got to keep doing it haven’t used so that you it becomes unconscious. The unconscious actions that we have, it just comes become second nature and
Craig Barton 10:49
certainly does a quick fire question for you, Julia, and then a slightly longer one, just for the benefit of listeners who don’t know what what are the five R’s stand for?
Julia Smith 10:56
So the five R’s stands for recall of information, routine maths, revising a topic, repeating the topic, but with Exam questions, and then readiness for the exam. So those are the five R’s, they linked to the assessment objectives of the current GCSE iteration. So yeah, five hours Korean five hours.co.uk. Quick blog,
Craig Barton 11:18
nothing. My final question on this. You mentioned two things that I think are really, really interesting. First, is this, this ability to access practice outside of the classroom. And I know you make a big thing of this that try and reduce the number of logins reduce the number of kind of sites that students have to go to because it get it becomes a little bit overwhelming. And we had a previous guest on John Mumford, who’s a language teacher and he talked about how he organises all the resources the students need just in one place, so they know where to go. This feels like an important thing Giulia, like I mean, easy access to this practice, and also helping support students get organised, what would that be? Right?
Julia Smith 11:54
Exactly right. And that’s exactly what I’ve done with the five R’s curriculum. Now. The lockdown meant I had to rethink that. So I’ve produced a website and access for teachers so they can go on and they can give their students five pieces of maths or five hours, every day. For every week, day of the academic year, there’s about 36 weeks of work there. The shine award has enabled us to give out 150 Teacher licences to that for free, in the north of England. So that’s one thing that people might want to get in touch with, with me about and get involved. But also the F research trial is looking at the five Rs curriculum holistically with a daily match maths approach, we can’t see how often students are going on to it for how long what they’re looking at, we just want them to do that. Because then actually, when we do come to the formal assessments in class, it should be self evident that they are actually putting some effort in.
Craig Barton 12:56
Fantastic. Okay, Julie, what’s your second tip for us today, please.
Julia Smith 13:01
So the Ceph second tip we’ve already made mentioned, a little bit of it is talking about maths revision being revisioning of the mass. We know with maths revision, you know, we tend to leave that to the end of the year, towards the end of the year. Students spend a lot of time producing a revision timetable, figuring out when they can do it, getting all their books together, getting their revision guides together, but actually, in in the book, The revision revolution, which is my latest one, which is wonderful. It says that revisions should start from day one, of course not at the end, we need to keep going over what it means to revise, how to revise, when to revise, where to revise, who to revise with what to revise. And so you know, there’s a there’s a fantastic there’s two other elements to this there’s a fantastic PD guide Professional Development Guide that was produced years and years ago from the NCTM and it’s readily available still and it does help us to go through those aspects of math revision. What can you do where can you do it? Who can you do it with? How can you do it? Why should you do it? And what can you do so you know, there’s there’s a really good professional development angle there. As I said previously, seeing it differently revisioning the maths we’ve got some fantastic revolt resources out there not now you know, coming on stream the whole time we’re spoiled for choice with maths bought into woven maths starting point maths, fantastic ways in which we can be very efficient with not just one aspect of maths but tying them in together so it’s clever choice of resource. clever choice of media so it could be video could be some self assessment could be a diagram and animation to have a look at looking at things from a different angle. But starting that process from day one, that daily maths of wanting to do some maths for yourself because you actually recognise that that’s gonna have a significant impact on your your outcome. It’s a very different beast, isn’t it maths revision to anything else, you can’t just put a poster up on the wall and go, Oh, yeah, I know that no, now we’ve just got to do the maths, you’ve got to do the maths. There’s also a project management tool, which is brilliant, called the Pomodoro Technique, which is about using a little red tomato, kitchen timer, other vegetables are available. And actually using that as a project management tool to manage your time without distraction. So you put the timer on for 10 minutes, put your phone away, put everything else away, clear your desk and and work through that 10 minutes solidly 10 minutes complete focus until the timer goes off, and then you go and do something else, then you might come back and do another 10 minutes. But the Pomodoro is a kind of it might be a gimmick, but I think is a serious project management tool, because that’s what it is. It can really help us as well. And, and in my experience, those kind of gimmicky things in the classroom actually have really good effect. Oh, this sounds quite good. You know, it’s a project management tool. It can be a bit of fun as well. And it is all about focus. So giving the students the tools for the job to revise is part of this key, we can’t just presume that they can do it. You know, we’ve just got to recognise that we’ve had to tap spend some time getting them to value the qualification believe they can do it and put some effort in. But also then think well, how can we make that easiest for them? Do they know actually what to do? Where to go? What to look at? What can they do for themselves?
Craig Barton 16:37
Who? Okay, let’s dive into how I like this. First off, what’s the NCTM resource do now don’t think I’m aware of this one?
Julia Smith 16:44
It’s the revision based approach. So it’s a professional development module on Revision. I think it’s just called revision. It’s from years and years ago, but there’s about five different pages of activities, but the biggest one in there is a carousel activity. So your learners come into the room, the students come into the room and own five tables, there are how to revise what to revise where to revise, who to revise with, you know, they can go round and put their own ideas together, we can start the conversation around with maths revision. But starting that from day one, rather than starting at Easter or Christmas is so valuable. And as I say it, you know, there’s the book itself, the revision revolution, how to build a culture of effective study. With maths I think this is just fundamental starting it from day one, rather than leaving it to the end.
Craig Barton 17:32
That’s great. Um, just a couple of other follow up questions. The first is I’m always intrigued by by the messaging here, Julie, that you give. So obviously, I love this idea of starting revision on day on day one. What are you saying to kids there to get them on board? Because again, if we’re talking GCSE receptors, they’re probably not going to be like buzzing with enthusiasm to to get cracking, how would you get them on board with this?
Julia Smith 17:55
I think it’s just it’s looking at things. I mean, the National Numeracy themselves on their website, they’ve got loads of YouTube channel, videos from ambassadors and celebrities sending positive messages about maths. And it is about making that positive, creating that positive culture in the maths classroom. And again, you yourself in this book, talk about, you know, being the positive role model, if you’re not positive about maths and the impact it can have on your life on your work on your, you know, the statistics from National Numeracy over your lifetime at work, you’ll learn so much more than someone that hasn’t got the minimum qualification required. It is about being that positive Ambassador reminding them that you know that the stories of someone like Lauren Reed, Lauren Reed was a student at City College, Plymouth. She passed her maths, the ninth attempt. So talking about Lauren Reed, and the fact that she’d sat with every awarding body every tear. She’d gone through all of her cause she’d gone through school hadn’t passed, hadn’t passed at the particular grade. We mustn’t talk about the grade one, grade two, grade three as failures. They have got A grade, they haven’t failed. They haven’t made the minimum expected standard. Lauren read did that eight times that the ninth time she passed. So we need to talk about that we need to share that with learners. She needed it to get into university. And we know that you know, later on, people change careers, they might decide later on, they want to be a nurse or even a maths teacher. You know, it’s about selling those positive messages reinforcing why it’s probably one of the most valuable qualification for them to get and just, you know, reiterating the fact that you’re there to facilitate it. I can’t do the work for you. You got to do the work, but I’m going to do my damnedest to help you along the way.
Craig Barton 19:49
Is there any difference in message do you think between what a year 11 Teacher will be saying versus a year 12 reset? Teacher The only thing I’m thinking is that obviously the only difference is that perhaps almost by definition that those research students have experienced this, this negative experience at this high stakes exam is a really, is there any benefit in acknowledging Max, you can imagine a u 11. Teacher saying the exact same things that you’ve said about how important maths is positive role models and so on? Do we need to acknowledge that you know, this kind of in inverted commas, failures that has happened? Or is it the same kind of message and all the way through if that makes sense?
Julia Smith 20:24
It’s it’s the same kind of messaging all the way through, isn’t it? Why would you not want to be positive about the maths in your classroom or whatever age masses, maths, it’s not about beating the system beating the awarding body. It’s about building good mathematicians and getting them over that kind of mass anxieties, lots of maths, anxiety, the cultural references that we have to maths, we’d need to have those conversations. Yeah, it’s, you know, we have we do have some anecdotal evidence of year elevens, doing the five hours kind of revision year approach as well. And there’s all this motivational stuff in there. Little bit of maths every day, just do the maths, keep calm and do the maths. There’s little videos, I don’t know if you’ve seen that really old video of the boy that passes his GCSE result and he takes it home and is in his dad just cries, his dad just cries and cries out loud, it’s just the the most uplifting video ever. But having all of those messages for your 11 Year 10 Even going all the way through college as well will will really really impact the outcomes.
Craig Barton 21:30
Fantastic. Final point on this just on the Pomodoro Technique. I’ve doubled. I love any kind of flippin productivity hack or anything I try Morla Have you seen this Julian there’s a big trend at the moment for for people filming themselves studying on YouTube for like three hour videos. And the idea is you study along with them. It’s absolutely unbelievable. So these guys will sit down and they say, right, I’m going to work for two hours. And I’m going to do Pomodoro, whatever. And they find themselves doing it. And the idea is everybody else does it at the same time. And you’re getting hundreds of 1000s of people doing this. And that’s quite a nice idea, isn’t it? You kind of because revision can be quite an isolating experience. But if you’re there with someone who else is doing it, even if you’re not there physically with them, I think that’s quite nice. I I’ve never seen that until fairly recently. And I thought you know what you can imagine for some students who are particularly, you know, the sat in the room, they’re on their own, but actually, they’ve got a real positive influence there with them. Somebody’s working at the same time, I thought was quite nice.
Julia Smith 22:27
I haven’t seen that before. I think that’s just absolutely brilliant. And I think there’s a message there that if we can’t beat them, we have to join them. And one of the things I’ve got involved in more recently is a tick tock channel for alternative methods. I haven’t launched it yet. It’s quite a few glitches, because I can’t use the music I want to use. And I’m trying to get around that. But you know, it is about talking in their language, isn’t it as well and using the things that they they use? So highlighting in this carousel may be the NCTM carousel? You know, how can you revise when you could put the YouTube channel on with someone and join in a kind of, you know, a MOOC massive open online thing where everyone else is joining in? I think that’s wonderful. Why not?
Craig Barton 23:11
Fantastic. Okay, what’s tip number three, please.
Julia Smith 23:16
Write number three is, in the words of Bananarama. I’m really showing my age now. It ain’t what you do, it’s the way that you do it. And that’s what gets results. And again, Joe Morgan, huge influence of my practice, compendium of mathematical methods, you can see the post it notes in that one, the Yeah, the little notes, etc. Joe tells us that there are few if any longitudinal studies providing evidence that one approach is superior to another is left to you to determine which are the best methods. And she goes into detail about how you can then relay this within a mass team to find the ones that you’re commonly going to use with each other. I get slated sometimes for some of my mathematical approaches when I put my mathematical marigolds on. And I don’t care to be honest, because you know, if you’ve got a student that can’t do it one way, and they’ve got to year 10, year 11, they’ve seen adding fractions or subtracting fractions since primary school, and yet here they are, they still can’t get over that hump. It’s time for you to said, I think you learn it like that. Have you seen this method? It might be a trick, it might be a framework that they can use, but it has a value it seriously has a value is chicken and egg because actually encouraging someone to be able to do something that they couldn’t do before. does lead to some curiosity. Right? I can do it like that. You know, I’ve had a seriously I’ve had learners that get really annoyed when you show them alternative methods. I’ve never been shown that way how you know how can I’ve got to this, no one’s bothered to show me that way. I can do it like that. What’s going on? How does that work? The Curiosity can come afterwards. John It tells us you know, it’s our job as teachers to teach people if they can’t do it one way, we’ve got to find another way or another way or another way. But the important thing about the alternative method kind of debate is it isn’t for us to like or dislike a method. As math teachers, we should have a mathematical toolbox and you know, a virtual mathematical toolbox full of every which way you can methods again, another reference here to Clint Eastwood 80s References sorry. You know, Pam Harris on Twitter. Every week she has alternative methods how’d you do this? You post something up and and all around the world, educators take part and it’s absolutely brilliant. Because it develops your curiosity, it enables you to reconsider mass revisit revision, the mass, you do it your way, but actually, oh, I’ve never seen it like that, that looks quite good. It’s about finding efficiencies. I’m really, really good at long division column, you know, algorithm, absolutely brilliant. But I’m much better and quicker using the ratio table. Now, why wouldn’t I want to use that I was much quicker using Napier’s bones. Why wouldn’t I want to use that method. Rather than being pushed into a method, which we know for a lot of our learners is a key difficulty, we do have an ideal opportunity with the current iteration of the GCSE to explore a multitude of mathematical methods, as Joe refers to them. We know from the awarding body guidance that any valid mathematical method gets the marks. So we need to get out the whiteboards we need to share 18 times five, how would you do it? Can you do it another way? Can you do it another way we need to use that as part of our initial assessment, I feel use the visualizer explore the wonderful world of tick tock I’ve already mentioned the the alternative methods tick tock channel which is coming. And we just need to engage in that veritable feast of maths any which way that you can, it’s really you know, it really is we’ve got an ideal opportunity in secondary, they haven’t got that freedom in primary. And I think that’s a real shame, because some of those methods are, it’s, it’s matching the child to the method, when unless you’ve got that mathematical toolbox at your disposal, at your disposal, where you have an open mind to the approaches. I don’t care if I get the marigolds out, if I you know, do writing all over the glass or on the table tops, or, you know, it doesn’t matter. Any valid mathematical method gains them up,
Craig Barton 27:37
like you’re right. I mean, I have to ask, what are these marigolds? Julie, what are we talking about here?
Julia Smith 27:41
Oh, I’ve got some over there in the kitchen. So it’s the the hand multiplication method. I mean, there’s some wonderful videos on on Tiktok. for it, it’s about the 6789 and 10 times table, putting them together, it’s not the nines where we dropped the fingers. But it’s an absolutely brilliant method hand multiplication method. There is some great, you know, there are some people far better than me on the YouTube that can can demonstrate that one. But it’s a really good way for times tables, just quickly being able to calculate seven times eight or seven times nine, eight times nine. After a while of using the hand multiplication method. I’ve used it for years and years and years when I was teaching in college with all my students, after a while you see them dropping the hands because it’s gone from short term, it’s just that repetition, it doesn’t matter how how we do it Mark record talks about there’s no single one activity that will lead to that full fluency in times tables, it’s about exposure.
Craig Barton 28:44
When your shows like seven, seven, multiply by eight,
Julia Smith 28:47
just for the right, so I’d done my nose. So 6789 10. So on both sides, it means that I can multiply an eight which is 678 times a seven. So six and seven, I can multiply those two together those to form a bridge. The fingers on the bridge, I’ve got two fingers on the bridge, and the fingers above the bridge are all 10s they will represent 10 So I’m doing seven times 810 2030 4050. And then below the bridge, I’ve got two on one side, times two on the other two times three is six. So seven eighths or 56. Students with with memory issues, we need lots of these different methods. We have the knuckles method, don’t we for January, how many days are in each month, January, February, March and April. So we have the nines. You know you see learners doing that. So we have to be mindful of students with additional learning needs as well. That’s where the alternative methods I think is really key as well. But we need to be mindful you know that it is our job if they can’t do it one way, there’s no point and keep forcing them. to that to that method, adding and subtracting fractions for some learners can be learned in two minutes using the fraction frame, you know, and it’s time to say, I don’t think you learn it like that. Have you seen this method?
Craig Barton 30:17
I like this. And particularly like the fact that as you say, two things can happen as real to this one, like with the fingers, eventually, they don’t need the fingers. But two, I really like this idea that it can lead to curiosity, they’ve been successful with this method. So now they’re curious why it works. You would not get that curiosity. If we keep hammering this same method that they don’t get. I think that’s really important. And just a follow up to that yet. We’re big Twitter users, both of us, when somebody I don’t ever post any alternate method these days, you’re a lot braver than me because you get people in who haven’t seen the context. And like, well, that’s you can’t use that you can’t use that you should be doing this, this and this. And of course, with their, you know, in the ideal world, we’d start from year seven, we’d introduce you know, methods really slowly and so but by the time they get to GCSE research, they need something that works. So yeah, it’s, yeah, context is so important with this. Which brings me to my final point about this. And this is this is a bad question for you, Julie. But I’ll just chuck it in the mix anyway. Is there such a thing as a bad method? Is there a method that you wouldn’t show students and I’m not talking about rolling methods here, but is there a method that kind of works, but for whatever reason, you think I’m not gonna go there without one.
Julia Smith 31:27
It’s a difficult one in, in my experience, your 10 Year 11, I was head of maths in a secondary school, I’ve been head of maths in Peru pupil referral unit. And I’ve done a lot of work in post 16. I was head of maths for over a decade in the the local FE college. It’s about the learner, and the outcome. You know, if I need to get a learner to be able to comprehend the difference between Mean, Median and Mode, for example, Hey, Diddle Diddle, the medians, the middle, you add and divide for the mean, you know it, the poem will get them the mark, that they need to be successful with finding the mean of a set of numbers or the median of a set of numbers. What it won’t do, is it won’t develop that, that understanding and that comprehension of if the mean is five or four numbers is five, what might the numbers be? That’s a separate piece of work but if it’s about grabbing those one mark questions, because they are over a grade three, but need the grade four for whatever reason for progression on to another course or simply leaving school at year 11. And going into college to get on to the level two course because quite a few won’t get on the course at the particular level because they’re held back by the maths and English ability here. And then I think there is I’ve got the analogy there with I can never remember how to spell necessary and are always have to say, Never eat cake, eat salad sandwiches and remain young. Rhythm rhythm helps your two hips move, what is the difference? What’s the difference in being able to spell correctly which makes me look quite professional, then you know, in using mnemonics, acronyms, whatever it is, if it works to gain that stickability from the short term into the longer memory, then it’s the right method to use. Okay, I’m gonna get slated.
Craig Barton 33:27
What is your fourth tip first, please.
Julia Smith 33:30
So again, back to Gemma Sherwood with her wonderful subject, knowledge enhancement book hear lots of post it notes in that one. fluency in the four operations is a cornerstone of developing mathematical understanding. That’s what Gemma tells us. And she’s so right. We wouldn’t build a house on dodgy foundations. So we can’t build a mathematician without that solid base. The Latin word flew into them fluency flew into means to flow. We want the mass to flow. So we can’t do that unless we tackle because of the hierarchical nature of mathematics. We’ve got to tackle those nine basics of maths. I think Mark McCourt refers to it as the numerosity. We’ve got a lot of debate at the moment about renaming, maths, numeracy, you know, all of those kinds of things. You can call it I tweeted this morning, very irreverently, you could call it doggy doo da or wherever I don’t care. It’s still maths. It you know, it’s not going to Opal Fruits are not Starburst in March. This is just a renaming thing. But the difficulties are not going to go away. What will tackle the mass anxiety and the fear of mass and the loathing of mass because I do see it a lot with with post 16 learners. Lauren read after nine attempts. You can imagine how she felt about maths, but she did it in the end. So it’s about shoring up those basics. That’s the first thing to do and I I would suspect that’s the case for a lot of law. They will make those numpty mathematical errors with the easiest questions. So there’s even evidence from Polya George Polya from the 50s. You know, the problem solving is hampered if the solving the problem is distracted by an easier question within the problems so it’s it’s relieves it. It it frees up some working memory for the hardest stuff as well if they’re fluent in their times tables, for example, Gemma talks exactly about that, you know, if they’re, if they’re stuck on nine times eight and have to start writing out the nine times tables, it you know, they’re gone off the boil with the meteor problem that they’re trying to do. One of the greatest resources that I love is the work of William m&e, his wonderful posters about you’ve never seen a curriculum quite like this. And it consists of two posters, and it’s just it’s like a, it’s like a space diagram really, with lots of nodes is 184 nodes, with the connections between each nodes, and that’s the GCSE maths curriculum. Then the second poster has all of the labels on so it shows what underpins each topic. And the more connections the topic has, the bigger the node. And what lies at the heart of mathematical curriculum, add addition, subtraction, multiplication, division, fractions, decimals, percentages, scale, and ratio. Pete mattock. Here’s his book, Pete Matic gets over PD library, that’s another top tip PD library. absolutely invaluable. Because you can just go to wherever the evidence is. Pete Matic tells us the difficulty that students have been in the space between zero and one, that’s you fractions, decimals and percentages. And Ed Saville must mentioned Ed, yes, but why, in his book talks about the unpredictability of negative numbers in addition, and subtraction and multiplication and division. So the more work we can do on those, actually, everything subsequent to that standard form, for example, becomes easier and faster. So it’s a way of speeding up that curriculum by shoring up those basics. As I’ve said, with times tables, you know that Mark McCourt says there’s no single activity or task that will lead to pupils fully learning their times to tables, its exposure, in multifarious ways. On his complete mathematics website, he’s got a lovely tool for times tables, which brings in the area model which brings in all sorts of different connotations with different ways of doing mathematical methods. So yeah, that’s kind of where I’m going with those nine basics are fundamental. To a bit you know, they’re building those cornerstones as Gemma refers
Craig Barton 37:50
to this is great. Well, I’ve got two questions, but they’re quite big question. So so the first one you’ve alluded to, it’s a little bit here, but but how to do it, Julie? What what are some of the go to either resources or approaches to kind of get these nine, nine skills or areas or concepts in place?
Julia Smith 38:06
So one of the things that I wrote for AQa a few years ago, was the basic skills tests, which were primarily for reset learners to quickly ascertain their set one, set two and set three, they’re readily available. And there also is an online version of it, I’ll tell you about. They’re readily available on AQa maths, they will tell us very, very quickly, there’s teacher guidance on there that I wrote, they’ll tell you very, very quickly, within 10 minutes if there’s a difficulty in a particular area, and those are the first ones to start with. So it’s about initial assessment, maths, bought Johnny at maths, but I took these to Johnny and said, Is there any chance we could have an online version of it and I know that in the GCSE resources that are a really popular resource for students to go to for these practice opportunities, but also for teachers to use with them. To ascertain where some difficulties might lie within those basics. There’s no point in going on to area and volume calculations if they’ve got difficulty and you know, multiplying and dividing. So it’s about quick analysis of those skills, and then regular practice through different media. So the world of transom games has some wonderful bits and pieces on there. You can’t do simple maths under pressure is a wonderful game, which will develop that mathematical fluency. So it’s about clever resourcing. It’s about resources as well that don’t need usernames and logins, because that’s the excuse they will use. We’ve got learners. We’ve got teachers all over the country and schools all over the country and colleges, putting on Revision sessions now. And they’re not coming. They’re not coming. We know. So we’ve got to work with them. We’ve got to give them online bits and pieces that they can use. It might be a game. It might be other times tables that lap on complete mass Johnny his old site study maths dot code at UK has got six little lovely games on there, using negative numbers, the times tables dash, you know, you can tell I use all these things the whole time. And it is about, you know, emphasising to learn to sharing this with the learners as well showing the why why have we gone back to addition of fractions? Why have we gone back to the basics, because actually, it will speed you up and make you much better at the hardest stuff, because you’ll have more working memory to deal with the problem solving, because you don’t have to worry about what nine times eight is. So I’m absolutely you know, rabid about this one as well. I think it’s really at the heart of the five R’s curriculum as well, which does do your 10th Year 11th, as well, I know that right? Well, here’s
Craig Barton 40:45
here’s the big question. Then Julius, I’ll build on to this. So one thing I always get whenever I’m working with with math teachers or departments is I always say, look, it’s really important to assess prerequisite knowledge before you do a new idea. And the comeback I was gay is I don’t have time, like, what do I do if I assess it and that knowledge isn’t secure, and then don’t have time to fix it. So I’ve got to teach the kind of rest of the lesson I’ve got a scheme of work to follow. Now I imagine that that problem is exacerbated for GCSE recent teachers because you’ve gotten this GCSE curriculum to cover. But let’s take those nine areas, or even just the four operations. If they’re not secure, you kind of almost can’t move on. But Then how’d you ever teach anything? So yeah, you know what I mean? Like is, can we move on, but in a certain way that we keep revisiting things? Oh, God, can we move on? It’s a tricky one isn’t it?
Julia Smith 41:34
is a tricky one. But I’m just reminded of that phrase that teaching without learning is just talking, isn’t it? What’s the point of going on to standard form, if they haven’t understood indices and place value? What’s the point, we have to take it right back. However, there is a part that learners can play as well. So if the practice opportunities that you’re putting in front of them, and encouraging them to use but not tracking it, and not collecting in results, because we know that as you yourself have said in your book, you know that we take away those things in the low stakes quizzing, kind of approaches, that quizzes are an informative part of a central part of every session as well. They’re not just there, if we’ve got time, access maths, he’s got some wonderful resources on his website, where you have a central problem is a pentagon problem a bit, there are five essential prerequisites around it. So you’ve got the opportunity to either dive straight into the question. If you’re, you’re confident you can have a go, or let’s build up the five prerequisites, let’s do those exercises, first, see where the block might be. And then you’ll be able to access the area. But, you know, I think there’s a lot of good messaging here that we can have with learners. And as Dylan William says, you know, make them the architect of their own learning, they have got a role to play with researchers, they just think, well, they, they should come to lessons, attendance is an issue, but if they are there, they just think it’s something that happens to them, and they develop this math skills by osmosis. The only way to get good at maths is by doing a shedload of maths, daily maths is really going to help you here’s about the easiest way that you can do to develop those those skills, but share that share the research with them, tell them the practice tells us that this out and the other, tell them the story of Lauren read. And you know, it’s hard work she had. So not only were we teaching the curriculum, she had the persistence, the resilience, the tenacity, that is is really difficult to engender in those learners is that if you get so frustrated after after seven years of adding two fractions together, or doing multiplication of decimals, or subtracting two negatives, you know, seven years of doing that often after time, you are going to get frustrated, aren’t you? So for us as teachers as well, it’s about revisioning it doing revision going back over the topic, but seeing it differently and maybe interleaving it as with inter woven maths, which is my my new favourite website along with starting point maths, you know, being very clever with the choice of resources as well, that will allow us to do two things at once. But yeah, it’s it’s an age or age old problem. It really is. But I think it’s about clever initial assessment, and then putting the onus on a lot of learners to do some work for themselves as well.
Craig Barton 44:25
Fantastic. Okay, Julia, fifth and final tip, please.
Julia Smith 44:30
So the final one is selling a positive message. It’s about this creating the positive classroom maths culture. I hate maths. What’s your answer? What’s your answer? Craig?
Craig Barton 44:42
What if sir, I hate math. I love the twist. I’m pretending to be so real tricky with that. I mean, I always go for the overly overly over enthusiastic approach, like I used to make tonnes of mistakes with how you step particularly teaching GCSE reset. I used to approach topic saying, Look, I’ll be honest, this is a bit of a painful one this but you know, we’ll muddle through it. I’m not convinced that that that works. I think straightaway, the kids are like, Oh God, this is going to be painful. So now I try and pretend everything’s brilliant. Like I love a percentage. I love a fraction. So I, I try and get them on board with enthusiasm. But I know that’s not not for everybody. So I mean, I’m intrigued by your approach here.
Julia Smith 45:25
Yeah. I mean, this isn’t this isn’t just for researchers. Remember when we used to go to parties, and someone would sidle up to you and say, Hello, my name is Derek. What do do? I’m a gardener. What do you do? I’m a maths teacher. Oh, it’s like Marmite, isn’t it? Oh, I hated maths at school. Oh, how can you be a maths teacher? We have to tackle it everywhere we see it and if we see it in our year, 10 glasses. You know, I’ve had students in the past that were coming. I’m not going to do anywhere I hate maths misses right I’ll do it again at college. What do you mean your do it again at college? You know, wouldn’t you want to earn more money? You know, your children will be better educated. You know, all of those positive statements we get from national new people like National Numeracy to backup the messages were saying, I asked this question of every teacher training group that I deliver, I deliver all around the country on Zoom, and now more face to face. Everywhere I go, I always ask when a student says I hate maths, what’s your answers? I need get some crackers, yet some crack a cracking answer. I hate ironing, but it’s very necessary. I’ve got to do it. So we’re going to be fine. They are you’re right being the positivity that they need is exactly right. And I know you allude to that in your book as well. You know, you have you are the only positive mass role model they’re going to have it you know, which bits mass Do you hate? Exactly? Because it’s a huge topic, you know, are you you’re alright with money and you will write the time because you hear you’re okay, you know, you’ve got to college however you got here. So which part is exactly what I hate algebra. Okay, well, there’s only ever nine things that we’re doing in algebra. If you look back at the wonderful, great maths teaching ideas from William m&e, that his his approach to algebra is really, really good. Well, I love it. So we’ll be fine. You know, just taking that pressure away from them is sometimes just enough, I had one and I do give away. I don’t know if you can see here that their money can’t buy mathematical detail behind me. For the best for the best responses this woman in Middlesbrough at the FE conference out there. She said, right, I want that tea towel and want that tea. She’s to put in about multiple entries. And she said, Well, I’m going to bet you bet our W Manny, going to make your bet that you’re going to pass your GCSE reset with me. So if, let’s bet 10 pounds, so if you pass your GCSE, I am going to get 20 pounds. And if you pass it, I’m gonna give you your money back. So you’re gonna get 15 pounds from me and the learners go, you know, cheek cut, and she tried to outwit the learner. But she was desperate for a tea towel. But it’s a really serious point. We have to challenge it wherever we hear it. I’ve had learning support in classes have sidled up to students who have got their head on the desk or Come on, what’s the problem? Come on, I hated maths at school, we’ll do it together. It’s not the right approach. I don’t care how you feel about maths, you have to park it, you have to keep it under your, your radar. If you’re working with my learners in the class or in the college or in the school. We need to have those positive conversations around in maths, maths and English in any school or college is everybody’s problem. It isn’t just the maths teachers problem. It’s that cultural, making a positive culture in an organisation as well. And many places I go into, they give badges out to learners. I love maths and English. I love m&a. And, you know, it’s a really interesting one, it can lead to some great postcard project pedagogy as well as if you’re doing this kind of thing early on. Asking students you know, well, what went wrong in school? Why are you in the GCSE resik class, the postcard pedagogy really, really works and they know all the answers they know or my teacher hated me at school. I had seven supply teachers. I was really naughty. I was ill I was awful lot. You know, everything comes out and all of those postcards go up on the wall. And then you can start to see that there’s lots of learners like you whose teacher hated them. Whose teacher was rubbish. It’s always someone else’s problem, isn’t it? But some of them do start owning up to say, oh, no, I was terrible. And then you give them a second postcard to say well, you know what, what will it mean to you to get your GCSE reset this time round? They know the answers. They know they’ll probably earn more money, they’ll get a better job. They’ll be able to progress on to the level three course they’ll never have to do it again.
But if that’s motivation enough, that’ll work for me, but it’s a really important conversation to have. I hate maths, what’s your answer? If you can premeditate that and have something witty, or something very positive? We’ve never had me as your maths teacher and that’s my usual stock response. You’ve never had me as your maths teacher. So you’re going to be amazing. And it make you a genius level at this and the other you’re going to be absolutely fine. Yes, what you need the reassurance don’t Yes and important conversation to have
Craig Barton 50:30
great this Juliet. Now she’s just triggered something. So I realised this idea that when they say I hate maths, you tried to drill it down. Okay, well, what areas of maths da da because maths is huge. And it’s just just made me think I don’t know, if you’ve you’ve come across. So I’m calling Foster’s writing a series of fortnightly blog post as part of this role as president of the AMA. And there was one, a recent one on times tables, and it was fascinating. And part of it. I mean, it all went into the kind of what the key relationships kids need to know and so on. But one one really interesting approach that you just reminded me off there is when kids say they can’t do the times table, he puts up the full 12 by 12. Grid, and says, Okay, well, you know, your wands, everyone knows the one. So straightaway, they get crossed out, and you probably know your tattoos as well. So let’s rule out everyone knows the 10. So let’s cross them out. And it’s this idea that also this massive thing, these 144 facts that kids need to know, with a couple of strokes of the pen, they’re down to about 30 straightaway. And then if we can learn one of them, we probably know another one as a result of that. And so I just wonder you can almost imagine that approach with maths right? If you had some kind of strong visual like that something perhaps like well Emmys curriculum that you spoke about before. And you say, as you say, Well, you know, money, you’re good at math. Okay, let’s rule that one out. And actually money then leads to this, this and this. You can imagine something while being quite powerful, right?
Julia Smith 51:51
Oh, definitely. Definitely. Definitely. And, you know, most of them are so hate fractions. Well, they see them in isolation. They see these things in isolation when you’re right with money. Yeah, okay. Well, what’s what’s 50? P? You know? You’re okay with potentially 100%? Yep. 50%. Yeah, I’m okay with that. 25% off in the sale. Yeah, yeah. Okay. Well, you know, they see fraction to something completely separate. And again, this is part part of the five R’s curriculum resist mixed. or forgotten. The phrase is my age. Keep topic models keep topic models apart. So when we come back to revisioning area, don’t do it with perimeter. Because what did they muddle up in the actual paper area or perimeter, they get them in the wrong way around, don’t matter lcm and HCF. Because in the paper, they quite often put to down because they’re not they can’t remember they can do the maths, they can’t do the back with fractions, decimals, percentages, keep referencing the equivalences every time because they see them in isolated silos, they don’t see. One faith is 20%, they don’t see the connection. So there are key messages as well, when you’re going back over the mass, this doesn’t have to be predominantly reset as it can be, you know, you’re going back over stuff in year 11. Throughout the year, always keep those equivalences in mind, and even, you know finding 12 and a half percent of 80 most learners do 10% by 1%, double it half of it to get half percent add them together, that’s five steps, knowing that 12 and a half percent is equivalent to an eight because 25% is a quarter so it’s half of that knowing that because they’ve they’ve had this almost like a drill practice of it. 1/8 of it is 10 They’ve saved themselves four steps of error there so it does come back to these alternative methods as well doesn’t it seeing the masks in so many different ways of doing things? So yeah, key points there. And you’re right about you know, calling foster the wonderful bit on the times tables. Yeah, it’s a really interesting point isn’t it that if we did have a lovely visual and I think we’ll remember these posters are there they are fantastic. But you know, a self assessment checklist of GCSE maths confidence isn’t the same dynamic as with the times tables grid, I’m afraid but no fractions, decimals and percentages, treat them all the same. So always have a reminder. Always have a reminder of all what’s that as a percentage remind me What’s that as a decimal, just so that they get over that fear of fractions. But with the other mean median and mode they can do or you know, what do you hear or is that where you put them in order know that the you add them up and divide by Hamet? You know, they don’t have trouble with the procedure of it. They have trouble with the words they bubble them up. So keeping those topic model apart quite often is it is a real key.
Craig Barton 54:55
Brilliant. Well, there were five absolutely brilliant tips. Those Julie I love those So over to you now what what do you want at once you want to plug in what should listeners check out.
Julia Smith 55:05
So there’s two opportunities at the moment to join the five R’s research. We have the shine Award, which is fabulous. And it’s great to see that the shine foundation and also the education Endowment Foundation are are looking to the post 16 area to support research in that arena. So the shine foundation opportunity is asking organisations with post 16 Although we have just put it into a Peru in Cumbria. So we are looking at some year elevens as well to trial, the daily maths approach that we have. So this is just about the student resource using that to good effect from September fully supported by me through to the next June 2023 GCSE. So if people would like to contact me if they’re interested in getting involved in the shine Foundation, which is just the daily mass, the work that students can do at home for themselves, then I am doing a lot of showcasing that to different people, the E FF have a big research trial, which was abandoned during the COVID. Time in 2019. Because of the exams, which were cancelled, the F we’re now currently calling for up to 80 colleges and schools and sick forms to join us we’ve got quite a few already. But we could always do with a few more to join us for the full research trial looking at classroom practice in a five hours curriculum approach. Alongside the student work the daily maths kind of work fully supported, again, by me with full teacher training. That’s an EC efficacy trial. So if anyone again would like to get involved in that if you’re not happy, particularly happy with your GCSE recent outcomes or want some support and help through that process, then that might be an ideal opportunity for you to get involved. So please do it’s it’s great that both of those organisations are looking at post 16 And the difficulty that people have, so it’s all free or free training or free free support. But the idea is is very student focused and and and achieving better outcomes for them.
Craig Barton 57:16
Brilliant. Sounds fantastic. Well, Julia, it’s always a pleasure and a speech I always learn absolutely loads and this has been no exception. So thank you so much for joining us today.
Julia Smith 57:25
Thank you so much for the invite. It’s an honour
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