19 March 2024
This episode provides an insight into how mathematics is more than just a set of skills and how educators can develop a joy and wonder for mathematics. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a former president of the Mathematical Association of America. He recently presented in Adelaide at the Numeracy Summit on the topic of mathematics for human flourishing.
Show Notes
Transcript
Dale Atkinson: [00:00:00] Hello and welcome to Teach, a podcast about teaching and learning in South Australia. My name is Dale Atkinson from South Australia's Department for Education. And today we join you from the Convention Centre in Adelaide where we've just finished the Numeracy Summit. And I'm joined by Francis Su, who is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College, and also a former president of the Mathematics Association of America.
He's been a keynote speaker with us. Thank you very much for joining us.
Francis Su: Thanks for having me. It's been a pleasure.
Dale Atkinson: So firstly, what drew you to mathematics and maths in the first place?
Francis Su: I was fortunate to have parents who instilled in me the value of a, of a good education. And I think I got interested in math when I first began to see, get a glimpse of the beauty of maths.
So I give an example, one of my parent's friends came over to the house once. And I remember I was a little kid, you know. I was learning how to add stuff at the time and he said, "Oh, can you add all the numbers from 1 to a 100?" And, of course, you know, I, [00:01:00] I didn't know how to do it, so I just started doing 1 + 2 + 3. It seemed very, really hard. And he said, "no, no, no, no, let me show you an easier way".
For the listening audience, I'm just going to do this with the numbers 1 through 10. And he showed me a beautiful way of adding the numbers 1 through 100, but we'll do 1 through 10. So he said, "imagine all the numbers lined up in a row, 1, 2, 3, 4, all the way up to 10. Yes? If you grab the first thing and the last thing in that list, 1 and 10, what do they add up to? Eleven, great. Now if I move in from both ends, so now I'm grabbing the second thing and the second to the last thing, that's 2 and 9, what do they add up to?
Dale Atkinson: Eleven.
Francis Su: Good, and then 3 and 8 add up to?
Dale Atkinson: Eleven.
Francis Su: And if you keep moving in from the ends in pairs, you basically get 5 pairs of things that add up to 11.
Dale Atkinson: Now you're going to test my mathematics here, right? You might, yeah?
Francis Su: What's 5 x 11? I mean, at that point you could probably figure that out any way you wish, but you'd see it's 55 and you're like, [00:02:00] 'Oh, I remember, I remember seeing this and thinking, "Whoa, that was a pretty cool trick"'.
Like suddenly this thing that seemed really hard became really easy if you looked at it the right way. And that's one of the ways that beauty pops up in mathematics. You use symmetry, or in this case, something that is anti-symmetric, but you, you, you take advantage of structure and you say, 'ah, suddenly a hard thing becomes easy'.
Dale Atkinson: And it is that beauty and clarity, I think, that people who enjoy mathematics, really enjoy about mathematics. But it's sometimes, I think, communicating that beauty to people who may be anxious about mathematics or maybe find it more challenging.
How do we do that thing with people who maybe don't feel like they're able to access the skills?
Francis Su: Yeah, well, mathematics is, it's an odd subject because it's a subject that is very important, very useful, as we know. And it's, you know, the backbone of science and engineering and a lot of the, the data revolution that's happening even as we speak. But a lot of that is computational [00:03:00] and the beautiful side of, of math isn't really seen until you explore it, until you start playing with the ideas.
And so I think we need to give kids more opportunities to just play with the ideas. The one thing I often talk about is if you think about what people normally think of math, they think of arithmetic, right? And you know arithmetic is, it's true, it's part of what you need. You need a solid foundation to do maths, you need to have arithmetic. But if that's all it is, it's kind of boring, right? Like it's kind of like, 'gosh, we could get a calculator to do that, right?'
And so, why do I need to learn this stuff? That's the question kids often ask. And so, how do you get kids excited about math? Well, it's the same way you get them excited about other things that motivate, that stimulate them. You, you go in through the human desires they have, right? The desire to know, to understand.
So, for instance, you might give them a puzzle that has a, an interesting aspect to it that makes you want to go, 'Oh, I wonder how you, how [00:04:00] did you do that?' If you can motivate a kid's curiosity in that way, then they'll be more motivated to learn, to learn maths.
Dale Atkinson: So that seems like one of the things that educators can do or try to access.
What are some things that, perhaps, we need to stop doing in the classroom and elsewhere?
Francis Su: So one of the things that I've been changing the way I teach is thinking about my assessments. So I like to distinguish between skills and virtues. So skills are things that people traditionally think of as math. Like learning your number facts, knowing how to factor a polynomial or use a quadratic formula.
Virtues are aspects of character that shape our attitudes, our habits. And with a virtue, a virtue might be something like creativity; persistence in problem solving; courage to tackle problems you've never seen before. A skill, unfortunately, is something that, it's all the stuff that people think of as traditionally math, and they say, "why do I need to know this stuff?" Right, like, most of us never need to know how to factor a quadratic in our lives, why are we learning it? [00:05:00]
Well, actually the reason we learn maths is not just for the skills. Some people will use them if they go on to a career in science and math, but most people won't. The reason we learn maths is for the virtues, like the habits of mind that it builds, the dispositions that it builds.
And so one thing I realised even after many years of teaching was if I say I value persistence but I only give traditional assessments, like exams where you're graded on whether the answer is right or wrong, then I'm not really sending the same message in my assessments that I'm sending in the classroom.
Dale Atkinson: That is a huge step-change for a lot of education and for education systems. To kind of move away from this idea that there's a bit of data that comes out at the end of any learning process which tells you how well you've done that learning.
What do we need to be thinking about in that assessment space, in that evaluation space, to make that the reality for us, our [00:06:00] kids?
Francis Su: Yeah, we need to value the process in, in find ways to value the process. So I'll give an example of something that I do now is I often ask my, my students to reflect on a problem. Let's say this past semester when, you know, at the end of the semester I might say, "think of a problem that you wrestled with that you struggled to solve and didn't solve and reflect on, explain to me why the struggle itself was valuable".
That's, I think, an example of a, of a reflection that it's, you know, in some sense it's formative assessment. You know, I don't worry too much about, you know, I give close to full credit for almost any thoughtful answer. My students do a lot of really healthy introspection through that. And often they write these wonderful responses that show me that they've grasped this idea that math is actually about building persistence and problem-solving.
That the struggle itself is valuable. That even if you don't solve a problem this time, that act [00:07:00] of exercising your persistence muscle will pay-off down the line with some other problem.
Dale Atkinson: Can I talk a bit about standardised testing? Because every student in year 3, 5, 7 and 9 is going to sit down and be tested in various different domains, one of them being mathematics, mathematics capabilities.
That sends a certain signal. The results have been interpreted in a certain way and used in a certain way to rank schools, rank schools performance based on that dataset. And I understand this is an issue that is not universal to Australia. It's something that happens in the United States as well.
How do we shift the narrative with our parents, our families, to indicate that that outcome is not indicative of the quality of education or how well their kids are doing overall?
Francis Su: Yeah, it's a very, it's a very hard question because basically you can say whatever you want in the class, but what kids remember is the stressful test, right? Whatever that is.
Are you saying that you could change, that there's a possibility of changing the [00:08:00] assessments? Cause that's the first thing I would try to do.
Dale Atkinson: Okay.
Francis Su: Is to change the assessments so that it, it values process more than just outcomes.
Reflection is one way that I try to do that. There needs to be a lot of serious thought about, about how to change assessments. Now, one of the things that's hard is that the, the kind of assessments that need to be done for this to be done right often involve a lot of human labor to grade. So, the people are, you know, used to grading math exams as automated, right?
Like just something I could feed through a, through a computer. But ultimately, I think that's self-defeating in the sense that it's hard to measure things. If we're trying to measure the virtues, some of the human virtues, those things are actually often hard to measure in an automated exam.
Dale Atkinson: Yeah, absolutely.
I saw a clip of John Cleese, the comedian, talking the other day when he was giving a lecture from a number of years ago where he was talking about the link between creativity and the childlike ability to approach things with a [00:09:00] sense of play. Is that important in mathematics?
Francis Su: Yes.
Dale Atkinson: And how do we activate it at kids?
Francis Su: Yes. Well, I mean if, if you have the luxury of changing 'K through 6' education, then I think play needs to start early in, in people's experience with mathematics, mathematical play needs to happen. And you know, what does that look like? People often think of play as just gamifying something, turning everything into a game, right?
That's, I think a, maybe not a, a rich view of what it means to play. So to play with an idea is to allow kids to tinker, right? To give them an interesting question and then allow them to wrestle with different ways of solving the, that puzzle or problem and might even be collaborative in some ways. But play looks like trying things out. It's maybe not that different. It has, it shares some features with the way people play a game, right?
Every time you play a game it's a little different and a lot of play involves trying out different strategies on the, on the field whatever they are. And looking [00:10:00] at something from many different perspectives, right? Your, your perspective and your opponent's. That, that's what we do when we play a game, don't we?
And these things are very valuable in mathematics as well. Like looking at a problem from multiple perspectives is actually the key to experiencing joy.
Dale Atkinson: So I think the areas of impact we're going after in our Public Education Strategy are really looking at wellbeing, learner agency, equity and excellence, effective learners.
What are the connections that you see between mathematical flourishing in those areas of impact?
Francis Su: Well, I mean, I think of, of flourishing, certainly flourishing is a, a notion of wellbeing, right? And it's not the same as, as just being happy. Because you could be flourishing even in a very difficult circumstance. I like to think of it as, often involves realising one's potential. And so, even in a hard circumstance, you might rise to the occasion to address some challenge that you're facing.
And so, wellbeing is a huge part of what it means to flourish. The, the [00:11:00] idea of equity or the inequities that we're trying to address, you know often I think can be more effectively addressed when you begin to value each person, dignify each person as a competent mathematical learner, right?
We've written-off too many kids as not "cut out" for math. And that's often we have a gender bias in that and a racial bias sometimes enters into that. And so often people ask, well, people are saying, "we need make our systems equitable, and we do. But I think fundamentally, if you want to change the system, you have to, and you want kids to have, have excitement and agency over their learning, you have to appeal to their humanity.
And certainly there are structures externally to them that maybe prevent them from learning, but for each person to have a productive, exciting relationship with mathematics, we have to give them opportunities to experience that joy and stop thinking about maths as just creating better human calculators, right?
We don't need better human calculators. Our [00:12:00] world doesn't need that, right. We have calculators, right? And that's not to say kids shouldn't learn how to do their basic maths and become fluent and have, you know, automatically be able to do certain skills. But it is saying that like, hey, you know, what does the world need now, especially in the age of AI? What they need are people with human virtues, be people able to think, who are able to look at the output of some computer program or some AI ChatBot and say, "Hey, something's not quite right here", right.
Someone who's, we need people who are creative. We need people who are able to, to reason, to, to, to quantify, to define, to abstract. Right, those are all virtues. Those are aspects of character that we need. We want to shape in our students through a great maths education. It can't just be about skills.
Because skills, as I like to point out, skills are going away. The coming AI revolution, all the jobs if they depend on skills, those jobs are going away. [00:13:00]
Dale Atkinson: Professor Su, thank you very much for your time.
Francis Su: Thank you. Thanks for having me.
Dale Atkinson: And if you'd like to hear more from Professor Su or any of the speakers at the Numeracy Summit, those presentations are available on plink and you'll be able to find those in the show notes with this podcast.
And if you'd like to look for some extra resources, check out the Number Sense courses on plink, which have got a lot of professional learning that's available for you.
Thank you very much for your time. See you next time.
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