More tips from Jemma Sherwood
Video transcript
okay gemma what’s tip number four please okay it’s kind of a converse what you don’t say matters oh i like what you’ve done there okay told me more about this right so um two parts to this one the first one is don’t assume that something is obvious it’s very easy for us as ex 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 we get a few lessons down the line and you see and a pupil makes a mistake or does something and you go 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 um so if i don’t say something it’s sorry well any example spring to mind that you can think of i knew you were going to say that [Laughter] so okay so i a couple of years ago i was teaching a lesson on um differentiation with year there 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 um and i said to them it was something along the lines of right off we go then we’ve done loads of differentiation let’s have a look at this one now and they all started to do really weird things like differentiating the polynomial on the top and then differentiates polygons the polynomial on the bottom and keeping it in a fraction um and i said and i remember stopping at one point going out to one people and stopping it and stopping you 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 realized that i hadn’t actually explained to them that we need to split this up into separate terms and then differentially differentiate each term separately so that was completely on me because i just assumed that they would know they had to do this yes i would like to say this a long time ago by the way um 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 that’s really good and i i know i’m interrupting you because i don’t give a second part to this but just just on this um do you think that comes down to oh well a lot of that can be solved just by the choice of examples that you use because i i thought foul of this all the time to use your differentiation was a great one there if you’re really careful about your selection of examples and particularly kind of boundary examples things that right on the edge of either fits into the concept or doesn’t that it solves quite a few of these kind of curse and knowledge problems because you’re you’re forcing the kids to attend to a wider variety of examples so they start to make those connections a bit a bit clearer do you reckon examples of the key to this um yes and no i think you were gonna um because we can never um give examples for every single possible misconception 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 for example for example and look how this one’s a bit different now 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 bit we’re doing they are able to deduce these things for themselves in a lot of cases and that’s okay as well 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 context is 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 got it what was your other thing you were going to say about this tip gentlemen before i cut you off 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 a link about questioning and how you show care to people through questioning and show that you value their thinking and all those things although they’re not explicitly about the kind of maybe like a utilitarian aim of teaching mathematics what they’re about is showing pupils that um their thinking is valued and their contribution is valued and and and that you have high expectations of them and and and it helps to communicate what you expect a mathematics classroom to look like that’s lovely that it just made me made me think of top and top of my head and again thoughts off the tomb ahead are always high risk they’ve not been processed at all so this will be sub-optimal 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 you saying that’s made me 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 ask 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 mine whereas if the kids are answering if every child’s answering every question and showing you on the mini whiteboard even if you don’t pick up on their answer you’re at least communicating that you value their response if that makes sense and i don’t often hear that absolutely in the context of mini whiteboards it’s i think it’s a 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 yes so you want to make sure that your actions communicate that every pupil is important that every people’s 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 yes that’s lovely love that one you