Episode 67 Creating Lifelong Mathematicians with Katherin Cartwright

In this episode, Dan interviews Katherin Cartwright from Primary Learning to talk about strategies she uses in Mathematics that help students become lifelong learners.

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Episode 67 Creating Lifelong Mathematicians with Katherin Cartwright is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Katherin is from Primary Learning. She has worked for the Department for 20 years and at state office as an advisor for mathematics. She currently runs Primary learning with her friend and works casually at Sydney University.

Video show

Show Notes

Episode Highlights

Key Point #1: What teaching strategies do you see helping students develop learning skills in math?

  • We are lucky in NSW with our focus on the proficiencies “working mathematically” – communicating, problem-solving and reasoning. 
  • This should be at the heart of our mathematics
  • Student talk and voice is very important for this.
  • Help students make connections between different parts of mathematics.
  • Students need experience with representations.
  • Students should be challenged. tasks with a low floor and a high ceiling for differentiation.

Key Point #2: Can you give an example where you have used 2 of these?

  • Number talks and talk moves.
    • Focus on mental mathematics and talking about strategies.
    • Giving students plenty of time to think
    • Let students share with a partner and share the ideas
  • Use inquiry to have students thinking about challenges
    • Students need to have productive struggle with the math challenge
    • Teachers need to talk less

Key Point #3: How do these strategies help students become lifelong learners?

  • We want to build our students up to be thinkers not calculators
  • They develop their collaboration skills and reasoning skills
  • I need to work with other and problem solve
  • Content is only the vehicle process is the focus.
  • Giving students a context and purpose for the mathematics
  • Maths is meant to be the pain relief from the hard work because it has the formula

Key Point #4: What 1 thing should our listeners do this week in their lesson to help their students become lifelong learners?

  • Stop talking as much and listen to the students. 
  • Stop telling them. Stop over helping and let the students struggle and think
  • use the advent calendar here



Hi everyone and welcome to the Effective Teaching podcast I’m your host Dan and today I’m talking with Katherin from Primary Learning who is a very experienced and very young maths teacher thank you so much for joining me Katherin. 

Thanks for having me Dan.

So can you just tell me a little bit about yourself and what your role is and who Primary Learning are? 

Yeah sure so I’m a primary teacher that I’m trained in NSW and I worked for the department for about 20 years as both a teacher and I worked at state office as a consultant as an advisor for mathematics yeah I got a love of mathematics during my career it wasn’t something I came with but recently when I left the department I started my own company with a friend of mine annette gray who does the literacy side of things and I write the math blogs and we just sort of work together and I also um work casually at sydney uni training pre-service teachers in mathematics.

Awesome well I’ll have to get Annette on next then maybe and we can do a literacy thing in addition to the math that’d be great so can you tell me then you know math is your specialty what teaching strategies do you see helping our students to become well just learning better maths really let’s let’s start with that?

Yeah and look it’s a great question and it’s one I answer a lot of the time when I go out and support schools as well I think um we’re very lucky in NSW in Australia in general we have a real focus on the proficiencies from the australian curriculum and in NSW that sort of worked out as working mathematically and that’s communicating problem solving and reasoning and that really should be at the heart of the types of strategies we then implement as teachers to help students become better mathematical thinkers uh we want them to be thinking and sharing what they’re thinking and so to be able to do that we need to allow them to talk so student talk and student voice in the classroom is really important part of one of the strategies that I would be encouraging teachers to use in their classroom we also want to help them make connections between different parts of mathematics so that I don’t think it’s all really separate and so my job is to make those connections for them so if I’m teaching multiplication the next topic or within that topic I should teach maybe area because I use multiplication to work out area or volume or something like that so we need strategies where we’re making the connections and that also means that students need experience with representation so as a teacher I need to use visuals and hands-on materials to show students how the math works and then there’s another aspect where we want students to all feel comfortable starting a task but also being challenged and so that’s part of differentiation and we talk in primary in particular at the moment about tasks that have a low floor and a high ceiling so the idea is instead of having you know seven different tasks in my classroom I don’t have time to prepare I can try and choose one task that is low enough or easy enough for all of my students to start but is open enough and high enough challenge for my students who are really capable to have a real go out and dig their teeth into. 


Okay now within that you actually talked a bit about you know making sure we don’t see maths as separate topics within maths what do you think of the idea of maths not being separate on its own too like I think there’s a big push in you know secondary schools for stem or steam or whatever you want to call it these days it gets changed all the time and often in primary school project-based learning is getting used and maths is very much incorporated into those kinds of things do you think that is good or do you think there needs to be a balance between both like what are your what’s your perspective on that?

Yeah I think the points you’ve brought up are really important that um we don’t want to negate maths as a discipline on its own um there’s value in understanding basic or fundamental mathematics but absolutely as much as possible you want to have connections across subject areas as well and stem is something I’m really passionate about and i’ve done a number of projects with schools both when I was at the department and through sydney uni using stem because if you look for a primary person in the science and technology syllabus anytime it mentions data or measuring data that’s mathematics so why teach it twice in two separate occasions teach it all together so if they’re growing plants and measuring how tall they are over a number of weeks I have to collect the data I have to graph the data I have to write up you know information about the variables I use that’s all mathematics so I would totally agree that that needs to be part of how we plan and in primary we actually have a we have it easier than secondary because generally we teach the kids ourselves most of the day so I can draw those things in and I know where my students are at mathematically when I do it in a science and technology or stem you know project based problem base whatever kind of inquiry you want to use and if if they need that skill and they don’t have it I can just drop everything and do a math lesson right there and then so I would totally agree with that integration but there’s definitely times where I’d want to do some straight math lessons too yeah yeah I’m going to say I teach at a very unique secondary school and we very much it’s a core teacher model and that ability to just bring related content together and to plan that really well has such a better impact on students learning and even on just saving time if you’re not addressing things twice it means you’re going more depth you can have more fun and yet still have more time at the end to do other things with your students as well. 

So let’s have a look then in math specifically and we’re not talking about trying to develop students skills in learning overall with this can you give some specific examples where or that you’ve done or that you’ve encouraged and seen other teachers use that you think in math is really helping students to develop those lifelong learning and aspects those skills that they needed for that?

Yeah yeah I think um it’s hard to pick two but I did try and do that um so I think one that we’ve sort of started to take on and some of these come from um um different parts of america which is which is good like we’re trying to draw on other countries that are having successful strategies and one of those is number talks um and using things like talk moves so um there’s sherry parrish who writes a book about number talks and a lot of primary teachers now know a little bit about that but the essence of any of those is that at the beginning of the lesson I want to have a real focus on mental mathematics and actually the students talking about strategies and I can use talk moves to facilitate the discussion so things like um you know and dylan william talks about it I think I can see you’ve got embedding formative assessment in the background in your picture I do I certainly do and he talks about the idea of wait time and having teachers just give the kids a few extra seconds before they blurt out answers and that’s one of the talk moves that we use or things like you know you turn and talk to someone next to you and so that when I then ask for feedback from the students about their strategies if they’re not comfortable sharing their own they can share their partners so it’s trying to take some of that anxiety away from mathematics or you know another talk move is that you ask students to repeat something so it actually means they have to be switched on to what everyone else is saying because you know Dan you might have given a great suggestion of a strategy and I ask you know melanie next to you what what did Dan say can you can you repeat what Dan said and melanie’s like I wasn’t listening so it starts to sort of be almost a behavior modification as well but it it’s a culture that you build in your classroom so I think things like talk moves and number talks are about mental um strategies is good oh that’s the first one. 

Yeah actually I like a a pause pounce bounce type thing you pause let the students think and then you pounce on them because you don’t let them raise their hand is the whole idea of calling the student out by name. 

Hands up yeah and it’s really good and like in I don’t know if you can see my shirt but in younger grades we use like a thumb on the chest so they’re not waiting with their hand up but I know you’ve got an answer and I can acknowledge that without you yelling out so there’s little things that are helpful your second example let’s let’s try another okay my second one is about using it’s the types of tasks that I’m choosing as a teacher so um almost that inquiry sort of idea to get students reasoning about a topic the task needs to be challenging so I mentioned that low floor high ceiling um and part of that is using challenging tasks now peter sullivan and a range of other researchers that I won’t rattle off every name but um you know James Russo and Jeanette Bobbus who I work with at Sydney Uni to name a few they’re doing a lot of research into challenging tasks and they’re often open-ended where there’s either multiple strategies or multiple solutions so that the students can spend longer on the task and the idea is that they’re having struggle it’s called productive struggle it’s not drowning but it’s letting them have a bit of time to wrestle with the mathematics and letting them know that that’s okay um and there there’s some really great resources to help with that and you know I I use a lot of enriched tasks it’s from it’s from the um cambridge university in the uk um it’s just nrich.maths.org and they’re all free and they’re fantastic ways to start that in the classroom um and it gives me as the teacher time to monitor and ask questions and probe because my job is questioner um it’s not always explainer um teachers like to talk too much way too much we need to let the kids do it and it’s actually I know I haven’t got a lot of time but um James Russo from victoria and monash university he did a bit of a study where he he’s got his own class as well and he did this study where he gave the kids the hard task first and then did the teaching and then at other times he did the teaching first like front loading the kids and then did the tasks he wanted to know what kids liked did they like the teaching first then to do a task or do they like the challenge spit first and then the teaching and he found out it was almost 50 50. so no matter which way you go you need to be flexible and so he found that the kids who were more capable liked the challenge first where because they thought hard was good whereas the kids who maybe maybe struggled with a certain concept like the teaching first because they thought the help was good so it just showed that yes using the challenging tasks is good and I can use them at different times in my lessons because they have different um meanings for kids. 

Okay so then how how does that actually help to create the skills that they need for learning?

That’s that’s the next thing so these are ones you think are doing that but then how does it do that yeah yeah well um and I love the fact that you have that focus on lifelong learning because that’s my role like I might only have my students for a year but that’s only one year out of their maybe 13 or more year journey as a learner at school and so I want to make I want to build them up to be thinkers not calculators I used that phrase recently because it’s not just about regurgitating facts I’m not going to walk down the street and someone’s going to go stick students you know it’s going to be in a different context so um the idea of doing this is to help them see that they can come to the understanding themselves that they might need to ask for assistance so maybe collaboration is important working with someone else that’s a lifelong learning skill um that I need to be a problem solver that if something doesn’t work the first time I should try a different strategy and that that’s a great idea I don’t just have to go I don’t know and give up so it’s trying to make them persevere on tasks it’s trying to help them see um that I need to work with other people and problem solve because that’s generally what they need to do in the workforce so any of these times where you’re I guess taking the training wheels off a bit and not just spoon feeding them content um content’s important but that’s the vehicle um the what that’s the content but the why and the how is the reasoning and it actually leads them to make generalizations that they can use again later yeah actually if you’ve read understanding by design by any chance he’s all about that process of making sure you’re actually transferring the understanding so they’re getting that essence and then they want to apply in multiple contexts in order to really understand that rather than just having that knowledge that regurgitation aspect to it and that’s right and if you do start with the end in mind you know where you’re going to so my assessments are planned at the beginning because then I can map out the steps that’s going to help the student get there and you know it’s not about them just knowing what they need for the assessment I do want them to transfer and that’s the hardest bit is getting kids to use something they already know so it’s getting them to stop trying to just answer the question and go what do I already know oh do I know something that’s going to help me here to answer this question and I think that’s the beauty of when you’re talking about stem or making connections outside of maths is you’re bringing in a context and you’re showing a purpose for maths now there’s plenty of maths in secondary school that might not have a lot of purpose for every single child or every single student when they leave school and that’s okay but the idea that maths is supposed to be the pain relief so Dan Meyer from um america talks about that showing kids that it doesn’t always have to have a real world context but that it’s supposed to make life easier you know if something’s going to take forever to add all these numbers together if I use a formula it’s much simpler and more elegant and it won’t take me as long so…

I like that he calls that’s the pain relief that’s good I like that I’m going to start talking about pain relief maths now at my school we had this math that means we’re doing some pain relief for your students we’ll use it in recovery methods for pdh. So can you tell me then so for our listeners today yeah they’ve got probably one week left of school most of them at this point but they’ll listen to it possibly at other times as well so can you give us just one thing that they should do this week that can really impact their lessons for their students with maths? 

Yeah I guess the first thing I would say is stop talking you know as the teacher just listen to the students give them the opportunity um and stop telling them we love helping kids that’s that’s I guess why a lot of people go into teaching and particularly primaries to help students but you can overhelp them so it’s really hard but sometimes just leave them with the problem let them go and have a go and then when someone has a problem I go to them because if you spend the first 20 minutes answering all the questions some kids already bored because they knew how to solve it the other kids haven’t really got it because you didn’t actually talk to them directly and it’s it just ruins the the aha moments that kids get to have but apart from telling teachers to stop talking um I think one of the things I could try if they do listen to it this week before school ends is that that enrich site that i’ve recommended they have an advent calendar at the moment for primary and for secondary of 24 of their favorite problems so you could just choose one a day and have a go and let the kids just explore the excitement that is mathematics when you start to look at the patterns and the fun things about it that aren’t just you know memorizing formulas or you know trying to to remember things that I needed to know so um it’s a really nice way to just start to dip their toe in the water.

Yeah well thank you so much for for joining me today Katherin and I’ll make sure that the links that you’ve mentioned there will actually be up on my show notes page. So if you want to go and have a look at that that’s it teachespd.net/67 because this is episode 67 pretty sure if not it’s episode 68 no its episode 67 uh 

I should have got interesting facts about number 67 for you but that would be great 

It’s been great look I think it’s fantastic to to have you come on and chat about maths because so often maths gets pegged as the one particularly that’s you know it’s all about the exam what’s in the exam uh learn the formulas plug it in do well on the exam so I’m really excited to see that there are teachers like you out there who are going and helping other teachers to to see how maths really relates better to life uh how it really helps them to prepare for prepare for life too because it’s not just about math that is used in life it’s also mass gives you so many quality skills for learning I think that you can then use as you go on to your life so yeah that’s that’s it for this week thank you so much for joining me and I will chat to everyone else next week

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