Chris Colley: 0:14

All right, people. Welcome back to another episode of Shift ED Podcast. Well, you will not believe where I'm going to uh right now, or bringing you guys with me. Uh, we are actually headed to uh down under, or we're headed over to Australia. Um, I have the wonderful Dr Laura Tuohilampi. Um and Laura's coming in. Um, she works at the University of uh New South Wales, uh a book writer, a researcher, an intellect, a mathematician. Um and I found Laura on LinkedIn and I reached out, she gracefully um accepted my invitation to come here because I do think math is in need of some conversation and in need of some exposure. Um and you know, typically I think, oh, I'm gonna, you know, I have to find some old white guy that that can tell us about math. And not at all. And I would to my amazement and my pleasure, um, I've been doing a big deep dive into Laura's work and we've got something special for you today. So, Laura, thank you so, so much for for hopping on here in your early morning and my evening uh to share some of your thoughts on uh the teaching of math to our kids or our students. Thank you so much. Oh, it's a real pleasure. Now, Laura, I just want to start off this. You say maths with plural, right? We always see here in Canada it's math teaching, you know, math class, etc. Where does the S come from? I mean, I I I hope I'm not sounding too ignorant, but what what what's the origin of why would there be an S at the end?

Dr Laura Tuohilampi: 1:57

Oh, I love that question. Uh I come originally from Finland and I was ignorant as well. I first moved to Australia and I was using math actually, as I was, you know, more exposed to that version. And then I actually got one teacher correcting me and telling that in Australia we use maths, and it's like an American version to not use the S in you know at the end of it. So that's the um that's the explanation.

Chris Colley: 2:25

There we go. Very great. Um and I guess my first question is, and I kind of want to dive back into your time as as a youngster yourself. What were your what were those moments in your early education where math was, and I and I've read that you were always very into math and it was something that you you were you were attracted to and you were good at. What were some of those early moments where you realized math was going to be a path that perhaps I could take as as a career or leading me into the future?

Dr Laura Tuohilampi: 3:00

Oh, that's a very good question because there were definitely multiple moments like that. The first one maybe being when I was on the uh second grade and I was able to see the answer to this complicated, you know, mathematical question. But the teacher wasn't happy for me to know the answer because he had she had like a specific teaching strategy in mind, and there was a little bit of like a yeah um misunderstanding, I guess, because I was so keen to show that I actually know the answer, but she wanted us to go slowly. And while I understand that approach, it made me think about like all those you know different approaches dictating mathematics, and um I was also punished for telling the answer too soon. So I yeah, I ended up standing in front of a class for 40 minutes as an eight years old you know girl. So it I had 40 minutes to think about, you know, uh pedagogical strategies and mathematics. I was always always very into science and mathematics. I read, you know, uh scientific books and quantum mechanics and you know things like that at the very early age. But at the same time, I wasn't like I did get like A's, but I get like A minus, not like an you know, a full A. So I always thought that maybe I should be like a genius to do mathematics. Like maybe I can't actually make this in my career because I don't do like I always make a little you know error or mistake or something. And that's another, you know, uh like an important thing that made me better understand that we really need more versatile role models and more maybe like you know, comprehensive approach to mathematics, because oftentimes when you actually learn deeply and you're very into you know something, you do make mistakes. That's how you learn. And sometimes if you just kind of like get everything from the onset, you you don't develop this, you know, um competence of you know overcoming challenges and you know all kinds of things. So um yeah.

Chris Colley: 5:08

Um totally I I love you saying that too, because it seems like math, there's a right and there's a wrong, right? Like get it, you get your A, or you fail and you get your F. What is, if you could explain it to us, at the root of teaching math to kids. Now, I understand that numeracy is important um as a skill, as a competency to have. But math always seems to be this overarching subject in elementary school as much as in high school, that it's the subject, you know, it's like the important subject. Um, and it, you know, the teachers that tend to teach it seem to, you know, be a little bit more focused on the content and like um not really wanting to explore competency-based or skill development. It's like, no, the stuff, the stuff. Can you unpack that a bit for us, Laura?

Dr Laura Tuohilampi: 6:03

Yeah, I find it a very short-sighted strategy because um uh, well, first of all, we do have this normalization of you know, students becoming anxious about mathematics, you know, opting out for mathematics, even hating, you know, mathematics, or simply being ignorant, like I just simply don't want to engage with mathematics longer. And we spend, I'd say in all countries, we spend more than 1,000 hours, you know, lessons, uh, comprehensive you know, years only, like from one to uh, I'd say net nine years. So it's a lot of you know, working hours for students and teachers, teachers' salaries, you know, textbooks, all those things, and with the outcomes of you know, just passing some exams and then leaving mathematics for forever. At the same time, I'd say all people around the world use mathematics all the time. And now I'm not just talking about you know numbers or you know you know number strategies or you know, calculation strategies or something like that, but things like logical reasoning, what can be you know um interpreted from this data, like how am I being impacted by advertisements, political messaging, those kinds of things. And and even things like you know, geometrical, um, uh like spatial thinking, such as like how am I decorating my house, like what am I, you know, how I'm gonna, my removal, how am I able to get my couch out of the uh uh the door, and those kinds of things. And like when I observe people, I see them using mathematics in this broad sense all the time, and yet feeling horrible about their actual mathematics, like numerosity skills. And and um interestingly, I just collected data of uh students um asking whether they feel themselves as a maths person or not, and every single one of them said no, like I'm not a math person, who would ever be, you know, call themselves a math person. And and we did go through some you know situations where they used mathematics like brilliantly, like you sophisticated, you know, approaches, strategies, um, logical thinking, reasoning, and so on. And they all said that they feel very confident and competent in those situations, and they call them like my world, my maths world. And in that the world I actually like when I'm you know planning my travels, or maybe I'm like doing my workout, you know, planning or designing, or you know, any any kind of like you know, real life in a mathematics usage, and feeling like, of course, like I do, like of course I can trust my mathematics skills, like I'm great. But then like we went back to uh kind of like the memories of you know learning those skills in the maths class and thinking about like kind of doing it in a more mathematical or official or such way, and like immediately the uh confidence crashes, and it's like, but in that situation, I wouldn't feel confident, I wouldn't feel confident. So there's this weird mismatch, and yeah, that comes from just like you know, focusing on like can you do this one whatever pass closed, you know, question perfectly, and not just you know, thinking that in real life when we do things, we actually can like almost do them. We we're not doing things perfectly all the time. We use estimation, we we kind of like account for you know, there's be there's gonna be a little range of error and we understand how to you know deal with that. And yeah, I think that's largely missing in maths classrooms.

Chris Colley: 9:38

And yeah, and I I from what I've seen too, and I've been in education my whole life, as as you have. I mean, we see that kids in elementary school, so our our our younger learners going into high school already convinced they're horrible at math, right? Yeah, and I will say that I see more on of girls feeling that too. Like, I just no, no, I don't do math, don't do it, can't do it. And right away they have this fixed mindset that no good, no good at it. How do you start to unravel that? Because what I've seen also is that in elementary schools, we often don't have math experts, right? And they're kind of like figuring it out themselves as they're going through, which is no, which is fine, but that they're gonna make errors and there's gonna be mistakes made, and it might not be the most um confident teacher teaching math because they just don't feel they have that so it we kind of start planting the seed earlier so that when they hit high school, when there's high-stakes tests and graduations and all of that coming, they've already made their minds up. What can we do to unravel or prevent or minimize that impact on our kids as they're growing through formalized education in elementary school?

Dr Laura Tuohilampi: 10:57

Thanks for this question. It's a global issue and we face it everywhere. And the usual solution to this has typically been you know, let's either bring math experts to you know primary um stages, or let's just you know, upskill you know, primary teachers' mathematical skills. But I'm actually gonna disagree with that. While you know, you know, knowledge of mathematics is always important and like there's no nothing wrong with it, obviously, like increasing teachers' mathematical confidences, but like there's another reason that is more, you know, or you know, issue or problem that is more pending, which is those teachers' relationship with mathematics. Like you said, like many of the teachers struggle themselves. They might have had you know difficult negative experiences, they struggle with their confidence. So it's less about like you know, a teacher not really not being able to know what a faction means. That's not the issue. It's more about like, what if I make a mistake? What if I don't understand you know deeply in all these things? So once you have that confidence of, you know, but we can always explore things together, like like this is my understanding. Let's, you know, you know, kind of discuss these ideas and make new discoveries together and having that confidence. But once you feel like I'm not a math person, I don't actually know how these rules work. It's very difficult. And that's why we do, it's actually something I've been working on a lot uh in my own work and also in UNISW, uh, that we do have for our teacher students courses where we don't start with teaching strategies or you know, increasing competences, but you know, kind of like what is your perception of mathematics and identifying, like said earlier, like mathematics that you use in your everyday life, like the maths that you already do, and feel confident with. And then you can bring those experiences to the maths, you know, class and make it more like just a normal thing to do, something that we just do, like, and then maybe add a little more accuracy and a little more of those like mathematical, you know, rules and and you know, principles on top of what we already do and feel just you know normal and confident about it.

Chris Colley: 13:15

I love that. I love that. And what about our youngest learners, Laura? Like, when do you start bringing in concepts or you know, counting or numbers? And like I work a lot in preschool kindergarten areas, and it's always like when is it uh when is it time to bring those ideas or play around with those concepts? Is it is there is there um you know any research or information that sh tells us along the child's development when talking about math can come into play?

Dr Laura Tuohilampi: 13:54

Yeah, I there's definitely lots of studies showing exactly like how to sequence things and like what building blocks must be you know established before you go any further, or you know, when you uh and especially when you utilize things like cognitive load theory, like you you you shouldn't put like too many things uh into the situation at once, but that also again kind of like addresses these more kind of like accurate, like how to make things you know perfectly, how to understand the rules and principles perfectly. So I would say this is more about that would be more about procedural knowledge, but at the same time, like when you let's say let's let's say let's talk about multiplication, for instance, and how that um can like manifests when we work on areas. So we we essentially know that there might be you know five rows of you know four pebbles, say, or something like that. So so we can kind of like you know bring this multiplication into when we start you know understanding what area means, and obviously you need to understand what multiplication means before that, and you probably need to know what four times five is in its situation, but at the same time, you can like work with two-year-old kids with Lego blocks, for instance, and just give them like 20 Lego blocks, and like how can you, you know, or say, you know, three years old or four years old, maybe not two years old, but um, like can you build you know rectangles out of these, you know, 20 blocks? And like how would they look like? Like, are they all like do you are using the same amount, but you know, number of blocks for each of these rectangles? Maybe one is you know building two times 10 and another one is building uh four times five and so on. So kind of like it in in that way, we can kind of like bring those ideas constantly into you know explorations and investigations. And then like when the time comes, we can then introduce like the actual formula for you know calculating area, and and then we need the multiplication skills, but we can still kind of like instill that foundation from from very early on.

Chris Colley: 16:11

Yeah, well, I love that. And I love what you're saying too, that teachers just have to um you don't have to be an expert. You can explore, you can be curious and show curiosity to your students, and in turn they might start reflecting those kinds of um, you know, uh skills as well of curiosity and oh mistakes are fine, and we'll try again and uh let's problem solve this and figure it out. And I like that that that can be an approach rather than you know focusing on too much on the text and on the on the workbook and like not understanding it, but just having to go through the routine, which kind of kills that uh idea that math is everywhere, um which you had mentioned before. And when you um created like you have two um well, I saw that uh math for humans, the one that you have on Australia website. Um it's such a great resource. What what do you hope that that information can help teachers with?

Dr Laura Tuohilampi: 17:15

Oh yeah, so the whole thing like ideology behind math for humans and like you know, establishing such a conduct concept. Um and I do want to mention that the page is a little bit out of the day, so I'm gonna work on that very soon. But there are some resources there, and I do uh post uh, you know, blocks well, posts and stuff there. But the whole idea is to, as you said in the introduction, introduction, that uh, you know, the whole mathematics education needs an overhole. Like we need to really like think about like how is mathematics education going to serve humankind in the future. So not just uh not just kind of like how do we keep doing, how do we keep like educating, you know, new cohorts with these mathematical competences that can nowadays be done with AI. It doesn't mean that we wouldn't need to, you know, have people understanding those principles, but we do have like a very different, you know, world, and it's only gonna change even more. So like um like the whole idea of reimagining what mathematics could look like and what are some skills that people really do need. For instance, like I said earlier, better understanding how algorithms work or advertisement work or political messaging works and how data can be used correctly, but deliberately, you know, choosing you know certain numbers or certain trends, or you know, not lying uh directly, but just you know, kind of like giving some little messages. So all those things are extremely important to you know have you know critical citizens that can also be confident in and in their skills and understanding what is going on and not be kind of like uh like victims or whatever like other people say and just like not really understanding how things actually work and you know, so and I think mathematics education, if anything, is the place to develop those skills. Like, how do you how do we think? How do we share information? Like, how do we understand you know these kind of like numerical databased messages? So, yeah, so through math for humans, I I'm kind of like free from what is in the syllabus today and what is in the textbook, you know, for the next lesson. And like, really, like what are we doing like in in you know 30 years or like 300 years? So, yeah, that that's the idea.

Chris Colley: 19:57

We're not doing the same thing as we're doing now.

Dr Laura Tuohilampi: 20:00

Yeah, yeah.

Chris Colley: 20:01

That we're we're and I love what you said that we're selling it better. Like, I think our messaging is just not so good. Um, and it's very constricted, you know, like it it's it seems like there's one way, and if you don't do it that way, it's the wrong way. Um do you ever have you ever heard of computational thinking? Um, the the idea from uh Seymour Papert out of MIT, where there are four main you know, pattern recognition, uh decomposition, abstraction, and algorithms, right? It was it had to do around coding. But I guess my question is is the idea of coding can can that be integrated into math? Possibly? I mean, can can math and coding coexist as one instead of it just being math? But there I mean, because once you open the doors to coding, there's so much more that you could do. There's so many more, you know, robots and microcontrollers and whatever that you can actually play with. Um where do you sit on on that idea that instead of like formulaic that we're looking at more of the bigger view of things?

Dr Laura Tuohilampi: 21:16

Yes, I'd say there's uh as soon as we can get rid of some ideas that even us educators cannot justify for students, because there are certain mathematical concepts that like like students might you know question like why do why are we learning this? And nobody can answer that question. So as soon as we you know reduce the kind of emphasis of those ideas that we really don't see much relevance longer, there is you know room for all kinds of new ideas, computational thinking being one of them, and like the whole again, like the whole idea of how is this kind of like techno-based universe working around us at the moment. So I think it's extremely important to bring that. I don't think we need a new subject, I think we just need to like broaden the idea of what mathematics you know inhales, what can be like you know examined under its scope. Um but then this just you know kind of like uh makes me think of something else that I just noticed when I was doing that data collection of you know students mad worlds where they you know felt confident and so on. Because one thing is to utilize mathematics for um, you know, in situations where we where things actually work pretty neatly. So we know that if I you know program something or you know ask you know an algorithm to do you know a certain thing, they will actually do it. So there is like you know, this causational, you know, if I do this, then this happens. Uh maybe there's a little bit of uncertainty or no likelihoods involved, uh, or you know, if I use this data, I get these you know implications or conclusions and so on. So kind of like this the whole kind of you know accuracy of mathematics. But those students actually quite a lot of them brought up the um concern of how mathematics uh you know historically has been used to also justify biases and like injustice and you know inequalities when we are you know just selecting or can like maybe putting too much emphasis on numbers or patterns or trends and not seeing that you know things can always be contextual or individual and you know that kind of like human aspect. So, you know, kind of a long, long answer to your question. I think there's definitely a need to include you know things like computational thinking in you know under the uh you know the official math syllabus, but also I think we need even more. Like what is the kind of like the little less mathematical human side of you know, again like encountering and dealing with you know situations that still are based on data and information?

Chris Colley: 24:08

Yeah, excellent. And I guess my last question, too, just because it's such a hot topic, um, and we alluded to it artificial intelligence before. I mean, it seems like it's taking the world by storm, and education's kind of like, whoa. Like um where do you see your work evolving with artificial intelligence down the road?

Dr Laura Tuohilampi: 24:32

Oh, yeah, so I think this is my personal opinion. Like obviously we can use and we can utilize, and I think we're already doing it quite, you know, uh quite a lot uh to kind of equipping AI to keep off. So it can be a good, you know, just you know, informants, we can, you know, program AI to teach, you know, kids, mathematics, whatever, like you know, skills and competences. Uh but I think it's maybe even more effective if you use AI to uh increase our confidence and agency. So having it more as a like a support partner that we're working together with. And uh we currently just uh developing a project where we're examining just that, like how can we um make AI respond to teachers' needs better in a way that the teacher informs like what are some of my issues, what are some of my goals, and at the same time, because AI can also like um uh like strengthen or confirm certain like biases that the teacher might have. So they might think that you know a certain strategy is great without noticing that it might be you know uh not good for certain demographics or you know certain you know group of students or something. So there's this risk of AI just can like you know increasing those biases. So in this project, we're examining how can we how can AI be programmed so that it can better show for any teacher that goes to you know asking you know help or support, like if you do this, this will be you know some likely coin uh what is it, like uh um results. And if you do that instead, so this is something that you might you know expect. So then that gives you know the teacher the um uh the opportunity to make more informed decisions and not just kind of like you know, can you give me something and the LEI is doing the work?

Chris Colley: 26:38

Right, right. It it demands critical thinking of the user, it's not just yes, yes, give me a lesson on math on fractions, like it's not they've got to think about it. Why? What's your intent? What competency you're looking to develop, etc. I love that.

Dr Laura Tuohilampi: 26:52

I love that.

Chris Colley: 26:52

Yeah, I think that that might be also kind of an avenue um for educators to kind of actually start to explore more.

Dr Laura Tuohilampi: 26:59

Um yeah, and and and it would kind of like the similar situation um like like uh resembling example would be when uh in another project, we helping students use AI in an almost similar way. Uh that's what we call vertical contextualization. So instead of just you know having students to work on their typical tasks, uh not asking AI to help them or teach them, but asking to envision contexts where you know certain skills are used. And the word vertical contextualization comes from, you know, let's envision the future and ask AI to you know tell us why where we might be using these skills in the future. An example being I was working with year five students and they had decimal multiplication or multiplying decimal numbers, and they couldn't really say like what where would we ever use this and using vertical contextualization, which is like asking AI, how about 30 years from now? Do you think that human humans are still using you know multiplying decimal numbers? And AI can quite nicely give some context. So maybe you know in this situation or that situation, and the students then choose like, oh, I'm gonna have a smart home and I'm gonna, you know, need to adjust my you know temperature or something like that. They are actually have decimal numbers and I need to you know use modification. So kind of like helping using AI to uh broaden our imagination and like helping us to make those connections rather than just simply like can it hit me this?

Chris Colley: 28:34

Right. I love that. Well, Laura, this has been I'm just popping now with ideas and thoughts. Um I really thank you for for taking some time um and sharing your ideas. And I'm glad that we're exposing math a little bit more. It's a it's a it's a valued subject that needs attention, um, but maybe some little tweaks along the way to make it more relevant for kids so that they can see that math is important. Um, and they use it every day. I loved how you describe those kinds of scenarios. I I I wish you all the best. Check out Laura's website. Um, I'll put the information in the descriptor. And also check out her book, Seriously Fun Maths. Definitely gonna dive into that one, Laura. Um, I wish you all the best in your day. Um, thanks so much again. And uh I hope one day we can uh pick this conversation up. I feel we could talk for another half an hour.

Dr Laura Tuohilampi: 29:29

That will be lovely.

Chris Colley: 29:31

Thanks so much, Laura.

Dr Laura Tuohilampi: 29:32

Thank you, Chris.