More tips from Jemma Sherwood
Video transcript
right gemma what’s your second tip you’ve got for us right okay so this one is doing maths is not the same as teaching maths i like it i get another good click bait headline that gemma that’s good for the viewing figures that right tell me a bit more about that um i was started by trying to think whether or not this is actually a kind of non-math specific type thing um 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 nice um or let’s say in science doing a scientific experiment is not the same as teaching children to do a scientific experiment i 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 mathematic in a matty context because i think i’m particularly guilty of this because when i started teaching i had my favorite ways of doing things my favorite methods my favorite 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 making 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 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 um 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 memorize and if they’re the kind of pupils who struggle to make sense of it straight away 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 ah there’s so much to memorize in maths and those kinds of things and that means i’ve not done my job as well as i could have done it this is interesting so so how do you how do we kind of break that cycle jim because i’ve definitely fallen into into this trap myself what are some of the practical things that you yourself do to avoid falling into this trap there’s the question and that’s like the million dollar question isn’t it um so this is the one where i’ll probably watch this back in a few years time ago you were talking absolute nonsense but i think at the moment i think it’s about um creating coherence and coherence is the thing i’m really focused on at the moment um so for me i i in the materials i’m designing we have a core or a key number of representations for instance that we are weaving throughout the curriculum and so the the i’ve mentioned them already so i’ll stick with this with the example of algebra tiles so uh the area model in algebra tiles is built in from multiplying and looking at distributivity and those kinds of things with 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 factorizing brackets and it goes all the way up through to things like completing the square and into a level you could do it for polynomial division with that 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 then 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 peoples yeah that makes perfect sense does it mean gemini 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 it’s like solving equations is a 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 that the whole world falls apart you have to teach something else so it feels to me like there’s it’s 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 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 that make any kind of sense at all absolutely and i completely agree and i would much rather spend three weeks on um 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 um and the gains then become quicker as you go on through 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 that they want to use but we’re actually saying no no actually we’re going to use this one because we believe this is the best is is there a conflict there is is that a problem or not so um 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 people’s for a huge number of pupils because if you know if we’re saying that um there’s a massive number of peoples in this country who don’t get above a grade four at gcse or you know don’t even get above 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 that variety is important then i think you’ve got to justify that this variety is good for the peoples 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 peoples in our in our school um 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 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 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 um compendium of mathematical methods but can i have a read through that i think whoa there’s about 10 different methods for finding the highest common factor and lowest common multiple that i’ve never even considered a best case scenario that’s really good because she can say all 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 what are the connections and so on and i think for some students that’s really really powerful because they start to see different connections and so on but as you’ve spoke 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 i didn’t really understand i need to select to solve this problem whereas reducing the number of approaches by having these consistent coherent models i 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 seeing me 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 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 yes because actually there’s not 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 though 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 yeah 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 makes perfect sense fantastic