160 – Developing Modelling Courses for the Maths Innovations MSc

George: [00:00:00] Hello and welcome to the IDEMS Podcast. I’m George Simmons, and today I’m joined by David Stern, our founder and director. Hi David. 

David: Hi, George. Great to be discussing today. This is the first time you are leading a podcast. It’s great. 

George: Yeah. Yeah. And for a bit of context for our listeners, this has come from our development of the Master of Mathematics Innovation course we’re doing with the Open University of Kenya. My role is to work on the modelling courses, modelling components of that course, of which I believe there are six, six broad courses within that.

And the introductory one, which is where I started and what, I well, has inspired our discussion today is currently titled Introduction to Systems Modelling. And this is meant to be a very introductory course exposing learners to the [00:01:00] different styles or frameworks of modelling, why some are useful over others, and importantly that question in different contexts and different applications. The course then goes on to explore complexity and how at least philosophically you can start to think about how you can account for complexity in your modelling.

David: I should clarify, you’ve said this is very introductory, that’s from a sort of postgraduate perspective. This is something which is intended to be an eye-opener course for postgraduate students that have gone through mathematical science undergraduate that have already quite a lot of competencies but are maybe not expert modellers. So it is really introductory from the perspective of someone who wants to become a modeller.

George: Yes, exactly. And for many, this will be the first proper exposure to modelling that they’ve done. They may have come across a differential equations course where you’ve played with [00:02:00] something, but it’s not in the framework of modelling. It’s not designed to answer questions in a way that we want to try and expose.

David: Exactly. That’s correct. And I think I’ve spent a long time in Kenyan universities, and it is true that they have often quite a background which relates to ODEs, PDEs, all the concepts behind the modelling, but not actually the process of modelling. And that’s why this sort of introductory course, which in terms of the mathematics we aim to make accessible, but it really should open people’s eyes to the fact that, wow, these different things we’ve learned about, they’re all needed and they fit together in these interesting ways, and we have these decisions to make. We have to think about which of these we want to use and why.

And so it should be a real, it will be really new. I cannot think of a single course which [00:03:00] would prepare people for this really. So it is deliberately the preparatory course to enter into the modelling mindset.

George: Exactly, and part of that, and part of that requirement is, I suppose, the structure of the follow on modules for this, because we’re thinking about as a model and collaborative model, we’ve had a conversation before about, on this podcast, as a module devoted to agent-based modelling, there’s a model devoted to ecosystem modelling.

And all of these, all of these styles and frameworks they ‘re most helpful when you can evaluate them from the perspective of different frameworks, different contexts, different applications. And I think if we didn’t have those follow on courses in this way we perhaps wouldn’t be inspired to structure the initial course.

David: Yeah, this idea that these follow on courses are really intended to allow someone who wants to delve deep into this, to get the skills as a mathematical modeller that could be applied in many different areas. And I think it’s [00:04:00] important, this distinction that actually a lot of modellers I know, a lot of the best modellers I know didn’t start in maths.

It’s really interesting that although behind all modelling is the mathematics, most of them started in the application area and then saw the importance of the mathematics of the modelling. Very few mathematicians I, you know, work with in this way, get that really applied focus into the modelling because there’s a lot of work to be done in the theoretical maths.

This interface between actually building models, which can be useful for specific areas is a space where I believe it would be valuable if mathematicians played a bigger role. And that’s part of what we’re hoping to achieve by having these postgraduate students come out with these skills, both from the mathematics side, but also the [00:05:00] practical skills to engage with teams and modellers who come from the domain expertise.

George: Yeah. I think what you picked up on there as good modellers tend not to be mathematicians, I think leads into the main question I have come up with for the reason for this podcast. And it goes like this, so as a mathematician and, maybe not all mathematicians are like this, but I am used to a certain way of being taught a course or going through and learning a course.

And that tends to be something like: here is a concept here is it defined, and then here’s a simple example of it working, and then if you’re lucky, here’s an application. And you don’t always get that. And for me personally, that structure works quite well. That’s how my brain likes to absorb stuff, okay, I’ve got this concept, can I [00:06:00] furnish it somehow with a simple picture in my mind that I see this thing working. And then, from there, then I can actually start to engage with what’s in pure math context, maybe what theorem follows from this, or what application follows from this.

And my initial attempt at building this course was pretty much to follow that mental structure. So concretely introducing modelling by difference equations as a concept. And then here is a simple example of a difference equation model for some population growth, for example, here is how you’d implement it, run it, and then we move up to differential equations, to statistical or empirical models, to agent-based models and build up the theory that way.

And then at the end of the course, we could then start to think about combining these or comparing these. That was my [00:07:00] vision, and I did that because for me personally, that would be a great way for me to learn it. And we had a conversation about that, and you pointed out that from a perspective of this course being useful or eye-opening about different frameworks of modelling, the really much better thing to do would be to start those comparisons between these frameworks from the get-go.

And for me, that kind of then created this difficulty in how to then go about creating a course in that way. And the difficulty is, for me personally, I wouldn’t find that structure as helpful to learn the concepts. But I can see that structure is really helpful to learn maybe not the concepts, some of the bigger messages that we want to get out the course. And I think, yeah, my question is philosophical at this stage, and we can try and [00:08:00] break this down, but how do you go about building a course that you personally wouldn’t find very helpful, is how I phrase the question.

David: There might be other better ways to phrase it, but I understand exactly what you’re saying. And what I want to reframe this as, because this is a problem that I’ve encountered in maths education for a long time, maths education is notorious for not serving the majority of the population. But a small minority of the population, it serves them extremely well.

And then of course, the people who it served really well, they become the mathematicians. And the mathematicians then become the educators. And so the education systems for mathematics are often set up, and they’re defined based on what works for a minority, not what is necessarily best for [00:09:00] a wider audience.

And this is one of the big challenges in mathematics education, and it is a broader challenge that, if learning in a particular way has worked for you, it’s difficult to imagine that you could have learnt the things you learnt if you were taught in a different way. What would you, who would you be if you hadn’t learned the things you learned the way you did?

So often we as educators, we teach the way we were taught, because we wouldn’t be us if we were taught differently, we’d be somebody else. And it’s difficult to imagine anyone being better than me. And especially as an expert in your domain, how could I have become the expert I am today unless I had gone through the experiences I went through?

It’s a really big philosophical question. And so I’ve [00:10:00] opened it up a little bit more, it’s not just about how do you do it differently if this isn’t how you would want to experience it? It is also how should we as educators recognize that it is not always best to teach the way we were taught or even to prioritize the way we learn?

That’s been a really difficult lesson for me over the years. The way I learned was an anomaly, and I recognize this. I learned pretty well the things that I learned, but I didn’t learn in the same way as others, even at the level of my university education. There were many ways in which my learning style was different to others’. And actually, I was very lucky to even at that level be interacting with math educators who helped me gain an awareness of that.

Just very simply, very concretely, many [00:11:00] mathematicians and math students have a very visual memory and a way of conceptualizing and viewing things, and I don’t, I have no visual memory. So I remember concepts, I don’t remember, I don’t have visualizations. So a lot of my colleagues at university, they would write beautiful notes because once they’d written the notes, they’d remember what they’d written, and it was a visual memory they could recall what they’d written.

That didn’t work for me at all. Just ’cause I’d written it, it made no difference I needed to concentrate on it. So I basically stopped taking notes halfway through my first year ’cause it was pointless for me to take notes. I did much better to really concentrate and listen to what was being said and see do I understand the concepts. If I don’t understand the concepts, I needed to work on the concepts, and if I ever needed notes all my colleagues had notes, but they often didn’t understand the notes ’cause they’d spent their time writing the notes and they remembered the notes, but they hadn’t actually asked the questions, did they understand [00:12:00] them?

And so we worked very well together as a collaborative approach. It served me very well. But it gives you just an insight into this fact that even if you think about your own learning style compared to those around you, there was a diversity of skills, of ways people learn, of what actually resonates for one person and another.

So the fact that as a good educator, you need to be able to think about education beyond your learning preferences and what works well for you, that to me, as a math educator, this is critical. You need to be able to recognize that there are going to be different ways to learn this. And I know the audience that will be in this course, and the audience in this course is going to be heterogeneous, everybody’s going to be different.

And so what we need to focus on for this course, [00:13:00] for other courses later, maybe the sort of approach you described, which is much more tools focused or skills focused, or you are learning a particular approach and then you are learning how to apply it. So you are building tools and you are putting them into your toolbox.

I can see that being something which may be more suitable for some of the other courses later. The problem is, if for this sort of course you started with that approach and somebody was not able to grasp a tool quickly enough, so you moved on from one tool to the next, but somebody did not grasp it, they are lost, they now get nothing out of the course. And this is what I’ve observed many times.

Whereas the sort of approach we’re taking, I believe somebody who is interested in a tool, well there are resources that can be provided, they can go further, they can go over and above to learn the individual tools [00:14:00] if they want. And some of them may know them already, they might have gone through a degree program where actually, for whatever reasons, their PDEs course was extremely good. And so the tools that relate to PDEs, they actually really get it. They can do that sort of modelling, that differential equation modelling really well because they understand those components really well.

But, everybody should be able to gain this broad, high level understanding. And then the question of who then digs deeper and goes into this, remember, this course is not just for the people who will choose to specialize in modelling. This is also for the people who are going to choose to specialize in math education and really focus on becoming really good educators. And them having this overview and having been able to grasp this overview is so important.

So I’ve not yet [00:15:00] answered your question, but I hope I have framed why this approach is important in this context. 

George: Yeah, two little follow ups, and the first is, you spoke a lot about people have different learning styles, and I think that’s something that’s quite well appreciated, that some people are visual, some are auditory, some are kinaesthetic. And often that’s seen as applying to how people interpret the same learning materials as each other.

What we’re talking about here seems to be structural differences, which somehow from your experience will enable more people to engage with the course regardless of learning style. Is that kind of a good take?

David: Yes. And I’ve actually had some rather heated discussions with educators who say all this stuff about learning styles has been disproved. And that’s a whole different discussion and [00:16:00] I would love to continue that discussion with educators on both sides of the fence. And my conclusions and when I’ve seen the research papers, which essentially disproved it, what they disproved was that certain implementations of adaptation based on learning styles weren’t effective. That I absolutely understand and I think there’s very interesting research on that and I appreciate that. And you’ve articulated quite well my approach.

My approach isn’t to say I know how to deal with different learning styles, but my approach is to say that I believe from my experience in the classroom, so to speak, and I should be clear, when I was a lecturer in Kenya for six years, I got a lot of experience in the classroom. The teaching load was extremely heavy, and this meant that I got more experience than you would normally get in many years, I had maybe three times as much experience within the period of time as I [00:17:00] would’ve had in another context, which is a really interesting advantage.

Of course the disadvantage is you’re teaching three times as much, but you get more experience. But one of the really deep understandings I came out with was this appreciation that students that I considered good students and students that I’ve considered weaker students, it wasn’t the case that good students did better work.

The best two masters projects that I had were from two of my weakest students, and it’s a huge credit to them and the work they put in, that, despite their weaknesses, if you want, as students, they did the most amazing master’s projects. Both of them changed my thinking, one on education and the other on climate data and perceptions of climate data, because the work they did was just astounding and it was truly valuable work.[00:18:00] 

And the fact that both of them, when they finished their coursework in applied statistics, their digital literacy was such that they would get someone to type up their thesis for them because they weren’t comfortable doing that themselves ’cause they didn’t have the digital literacy. That explains why, by some definitions, they were weak students.

As an applied statistician, you need to work with data, you need a particular level of data, you know, literacy, you can’t get that if you can’t use a computer well. And so in many ways they weren’t correctly considered weaker students. But the work they did was astounding and it was exceptional. And that really changed my thinking about these learning stars and the fact that actually what a strong student is, what a weak student is, what this means, this diversity of skills that you get within postgraduate programs in places like Western Kenya where I was based.

The [00:19:00] range of skills that came in were huge, and it was a huge insight to recognize that even those who, by my academic definitions I considered weak, could do incredible work. It has transformed me as an educator. 

George: I think you’ve certainly answered my second follow on just for our listeners who noticed I said two, which was, do you believe that your ability to think how to structure content or courses differently has come from your experiential work and your interactions, and it is not something that, me, sat there to my own devices would ever really come up with, this kind of structure. 

David: No, absolutely not. Once you’ve taught, you know, you can roughly do the maths, it’s a minimum of three lecture courses a semester for six years where you have two semesters and sometimes three semesters in a year. You’ve taught quite a lot of courses, and very rarely the same course [00:20:00] twice. I delivered over, and developed and delivered over 20 different courses within a relatively short space of time to this wide range of different participants in different ways, including on mathematical modelling, biological processes, as well as the number of data courses, pure math courses as well.

And so a real wide range, as well as developing new degree programs and thinking about that from that. That experience is what has led to some of these insights. And so the fact that this is challenging the way you would have developed the course, I’m afraid that’s part of the experience that I’m bringing and the context that I understand. We are developing this course for the Kenyan context, which I understand very well. 

George: Yeah. But I think in there you have answered my base question, how can I develop courses in ways that, in this reframing that more people would find more useful or accessible, and the answer is really [00:21:00] for me, collaboration with people like yourselves, with other educators. That’s I think where we’ve got to. 

David: It’s collaboration as an initial point. And then the second point is experience. This is not part of your day job, so to speak. But I’m so delighted that you’ve taken on this challenge to be involved in this, so that you are going to have these experiences. This is where the collaboration with the Open University of Kenya is potentially a great win-win for us because they don’t have a whole wide range of staff yet, it’s a new university, it’s a year and a bit old. Maybe it’s two years old now, it depends when you’re listening to this, but at time of recording it is a young university.

And they don’t have all the skills they need, and it’s one of the exciting things that we as an organization with some of these skills can provide some of that. And part of my role and also Mike’s role, who you’ve interacted with, as a somebody else who has deep experience in the local context and is really leading quite a lot of [00:22:00] this program, he’s really the person driving this forward, which is so exciting. So he’s another person you can rely on and get that information on.

You’ve got Geoffrey who is another Impact Activation Fellow who’s just gone back to Kenya, and is now embedded in Maseno University, but working on this degree program with you. And so there’s a number of people who can collaborate with you on this. And that collaboration is the initial point, but it only takes you so far, nothing replaces experience.

So actually being involved in the delivery, I love this fact, and Chris Sangwin, who’s also been on previous episode, he said it always takes him three times before a course is actually developed, you need to deliver it three times. And that’s a wonderful way to think of this. The development of a course, you can only get so far in advance.

You actually need to have the experience of giving it, understanding the audience you’re teaching, [00:23:00] understanding how they react to the context, ’cause it’ll always be totally different to what you expect. And then you iterate on it. And yes, good preparation, good collaboration in advance with good critical reviews will help you in that initial stage. But nothing replaces experience. 

George: I think that’s a wonderful note to end on and definitely eye opening for me. So I guess I should say thank you, David, for your great insights on this conversation and we’ll be having another one on another one of my education questions very soon.

David: I look forward to that. This has been fun, I miss being a lecturer. I love teaching. Being a lecturer in Kenya with the workload that was there was intense and it was challenging, but it was, I, I loved it. Anyway, I miss it’s great to talk about this stuff. Thank you so much. 

George: Thank you, David. [00:24:00]