Transcript

Maths Matters with Marcel Jackson

31 October 2008

Dr Marcel JacksonDr Marcel Jackson
m.g.jackson@latrobe.edu.au

You can also listen to the interview [MP3 13.3 MB].
Matt:

This is the La Trobe University Podcast, I'm your host Matt Smith, good morning, good afternoon and good evening, it does all depend on where you're standing. Joining me today is Dr. Marcel Jackson from the Department of Mathematics at La Trobe University. Thanks for joining me, Marcel.

Marcel:

That's fine Matthew, it's a pleasure!

Matt:

So you're here to talk to me today about the wonders that is maths.

Marcel:

That's right, yes. I know that sounds like a bit of a contradiction…

Matt:

That's right, don't turn off, everyone.

Marcel:

I guess everyone knows of mathematics because it's a core topic at high school level, but unfortunately many people get put off by mathematics at high school level, and this is a great shame because mathematics is a beautiful and wonderfully creative discipline, it's just that it really requires a certain degree of engagement in order to actually see that. I guess that I always think of it as being a bit like reading a novel. You don't ever go up to a novel and just start flicking through pages, having them blur across in front of you, looking at the words and not actually reading it, that just doesn't work, you get very little out of a book by doing that. Unfortunately this is a little bit similar in the way that people tend to experience mathematics. I'm not saying that they're forced to flick through mathematics at some great pace, what I'm saying that there is a tendency for people to not engage properly in it.

Matt:

So you're saying that mathematics has a very slow start, it might pick up in the second setting.

Marcel:

That's right, and like with a book, if you actually start to read it properly, and in the mathematics' case if you get out and try and engage in it, and think about what's being said, then it becomes a really interesting thing. But really, mathematics is a very interesting discipline. At high school level one has to do a lot of fairly routine material that doesn't seem really creative at all, it's mostly following little formulas, and principles that are given to you, whereas in reality what mathematics ends up being is about, if you like, constructing your own principles, and that's why it ends up being a creative discipline. So the kind of places, maths is used all over the place, even in places that you wouldn't think maths was really being used at all. A classic one for example is when you use your keycard. You go to the bank, the ATM machine. Now I guess everyone is familiar with the fact that somehow there's information stored on that piece of plastic, and that somehow it's secret. It's certainly secret from a common person perspective, you can't just look at the card and find out what the bank account details are, it's somehow encoded in there, but it needs to be encoded in ways that are hard for people to take off unless they have the right kind of information. So the mathematics of securely encrypting information is an area of mathematics, and any time you use a card, or do an internet transaction, or anything that involves some kind of electronic transaction, there is mathematics happening every time that happens. It's quite unexpected just what that mathematics would be, it's not obvious what it should be, in fact the typical situation involves tricky facts about multiplying numbers and dividing numbers. So of course, those kind of things are a bit of an impetus for developments in mathematics, whenever you have big applications like that, but that's just one case of mathematics that's used all over the place.

Another one would be, say, Google searching, or searching using some kind of internet search engine. Well the Google company was founded by people who had a strong mathematical background, and in fact the way they rank pages is highly mathematical. You can find it if you do a Google search in fact, you can Google search for the mathematics of Google searching, and you'll find lots of information.

Matt:

I've heard that Google would explode if you tried to do that!

Marcel:

Yeah, it might! They'd probably like it actually; I think they're quite keen on people with mathematical skills. But that's another place, everyone knows about it, I think the word Google has even made it to the dictionary now, so this is a very familiar thing. But what happens every time you search, reasonably complicated bits of mathematics, certainly from a high school perspective. That's another example of things.

I could talk about the popularity of Sudoku. It would be classed as mathematics. Sudoku really has a name in mathematics, it's ‘completion of Latin squares'. It certainly a mathematical kind of thinking, and while it's a rather singular form of mathematical thinking it's rather interesting to see how popular it is. When so many people seem to express a dislike of mathematics and at the same time so many people seem to enjoy doing things…

Matt:

They're quite happy to sit there doing a number puzzle.

Marcel:

Yeah, no doubt that the kind of thinking involved in Sudoku is quite similar to aspects of mathematical thinking, to the degree that most mathematicians, or many mathematicians that I talk to say they don't like them because it's too much like their own work. That's something that I would identify as being kind of mathematical thinking, and yet it's probably not what many people identify with when they think of mathematics.

Matt:

Best memory of Sudoku is going to the football with my family and sitting there completely bored just doing Sudoku the entire time because that's more interesting than football!

Marcel:

Well there you go, maybe you're a closet mathematician.

Matt:

Probably not!

Marcel:

You never know! I would say, you see, that Sudoku is really a mathematical activity. I was talking recently to some people who were at La Trobe, in fact, who are becoming involved with some mathematics associated with the synchronising of traffic lights. So this is something that's familiar to people, certainly it's nice to have the traffic lights all synchronised for you but it's also believable that the timing of the lights is a complicated issue, because if you synchronise the lights for one road, what happens to the lights that go in the other direction? Because you could try and synchronise them on that individual road, but of course the layout of the roads is an enormous network of traffic lights.

Matt:

What, you mean trying to synchronise the crossroads as well?

Marcel:

It's probably clear I think that one can't hope to have everything synchronised for each individual car, because that assumes that everyone is never going to change their minds and go down some different route! But what is clear is that it is not an obvious thing how to make those lights go on and off. There is sensible thoughts, proper thinking does go into this, but a team of Melbourne mathematicians including some at La Trobe are currently talking to Vic Roads about trying to make the most of optimising the flow for the existing traffic lights and trying to analyse this mathematically. It's quite complicated. Think why it's complicated, aside from the fact that it's a massive network already it's clearly a difficult thing. You might think well maybe we'll get the main roads all synchronised so everything moves really quickly down there. Well that's great for getting traffic down there, but that road comes to an end at some point, it doesn't go on forever, and it's not necessarily in your interests to get all the cars right to the end of the road very quickly if you haven't then got ways of getting cars out from the end of that road, otherwise you're just going to get a massive traffic jam at the end. And as we know, when you're in a traffic jam the lights don't end up playing much of a role, because you're not going anywhere. So it's complicated. It might be in your best interests, for example, to have the lights not quite synchronised so that there is a bit of stopping and starting, so you don't get all the cars down one end at the same time.

Matt:

So where do the maths come into that? Is it standing at a blackboard trying to work out the equation of timing?

Marcel:

Well there would be someone out there at some stage who would be doing that kind of thing, but mostly it's about finding the appropriate mathematical model. What it's not is the kind of thing that one experiences at a high school level. And you can see it's difficult because you can imagine trying to give a mathematical model for the flow of traffic is not at all obvious how you should go about doing that. But it is perhaps obviously going to be a complicated task, it's like anything in life. You can't expect to be doing the complicated task when you're first learning it, and that's really why we have to do the basic algebra at high school level, because without those thing it's like trying to read the book when you haven't learnt how to read.

Matt:

So how do you go about making maths interesting and engaging students?

Marcel:

Yes, well that's a good question. The main thing is that we try to get students involved in the actual learning process, so typically at university level, and this is also true even at other levels, and commonly in other areas as well. Typically what happens is students get told things. They get told how this works, how to do this. So at La Trobe, we've tried to put the focus on students doing rather than just sitting there listening. It's amazing how easy it is to sit back and write things down based on what someone is saying, and not really take it in at all. You can quickly learn to process through your ears information and transmit that to your fingers to write down information, but you don't actually take or learn anything there. So what we've done is we've reduced the number of lectures. We try not to reduce the material and instead, with the extra time we have with losing one or two lectures a week, we get the students to do problems, we have interesting problem sheets, problem sheets that try to develop the material. But with the students actually doing that themselves. Now of course people get stuck very quickly without some kind of assistance, so while the problem sheets tend to have explanation in them as well, we have lots of staff members who help with the students, so the actual teaching environment is a room where there is one or more helpers depending on the number of students, and the students work through these sheets and the helpers come round and try and correct things. And many students tell me, and they tell everyone this, that this is where they really learn the material. I mean you can learn the material in the lectures, but you just get a very vague idea what's happening. You can't take everything in on the first go, when they start to do the problem sheets then they start to actually engage in that material. And that's really important. Getting back to the analogy I had earlier of reading the book, that's where we're trying to go from the flicking through the pages stage which is the lecture, to the actual reading. And that's the only way you can get value from a book, and the only way you really get to learn things in mathematics. You have to do it yourself, really. You can't just have it told to you.

Matt:

And you've had better results doing it this way?

Marcel:

Yeah, we've traditionally had very positive responses from students. The students seem to really like this method of teaching. A good example of some evidence for this is the CEQ results, the Course Experience Questionnaire that's administered by the Graduate Careers Council of Australia each year, so La Trobe's maths and stats have always come out really well on that. In fact just over the past few years there's only been one instance where La Trobe's maths and stats haven't been ranked top in Victoria, and never outside of the top three Australia wide, and that's in the good teaching scale and in overall satisfaction of mathematics and statistics graduates. So this is really strong evidence that this is the way to go.

Matt:

What sort of reasons do they have for going into mathematics?

Marcel:

Well that's a good question. Well firstly I'll include statistics as part of mathematics because it certainly is a part of mathematics. It's a little bit different to the type of mathematics that I might do but certainly we'll group them together. So yes, there's a huge number of different paths that people take. Only a very small number will go on to be academics. But there's a lot of jobs out there for mathematicians, the thing is that they're really labelled as mathematicians. If you do law, of course there's lots of jobs that call for a lawyer, or a solicitor or something like this, it's very clear what the job is. But that's not really so much the case with mathematics. There's a lot of jobs that actually call for mathematic expertise but won't really call it a mathematician. So it could be a logistic expert, banks for instance, the financial industry employ a lot of people to do mathematical modelling of financial situations. Statisticians, that's a place where there really is a named career path, because there's a lot of jobs that call overtly for statisticians, the Bureau of Statistics for example is going to be some kind of employer of statisticians. In fact we have a problem here that it's very hard to keep students in the system long enough in the statistics area because there's so many companies that want statisticians, there's a real shortage of statisticians at the moment. So I guess the point I'd like to get across is really that there's nothing wrong with the mathematics that people see at high school, but it is unfortunately a little repetitive, and a little bit dreary, but the problem that people have with mathematics is that that's all they see, they don't see the end result of where mathematics can eventually take you, and the variety of different mathematical thinking. Unfortunately it really does take a little bit of work to get to the exciting stuff, but it really is out there, as I've tried to explain, mathematics is used all over the place. It's not surprising, we live in an age where increasing impact by technology. That technology is fundamentally mathematical, I mean, the computers, algorithms, all of these things are analysed and understood in a mathematical language. You can't understand them in other ways. So given the prevalence of these in every day society, it's amazing that mathematics isn't slightly more popular, cause everyone uses the effects of it, but no one seems to want to understand it. Understanding it is an empowering and beautiful thing, but of course it takes that engagement.

Matt:

Dr. Marcel Jackson, thankyou for your time.

Marcel:

Thank you very much, Matthew.

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