Education

Creativity and computers in math: Q&A with Conrad Wolfram

Posted by: Ben Lillie

In his talk at TEDGlobal 2010, Conrad Wolfram championed a radical new way of teaching mathematics: removing the notion that math is the same as calculating, and completely redesigning the curriculum around the new possibilities opened by computers. He’s now launched a website to collect ideas, and in November he will be hosting The Computer Based Math Education Summit to kick-start the project.

We caught up with him in his office near Oxford, England to talk about education reform and the importance of creativity in technical fields.

How did you get interested in reforming math education?

We’ve been building software for 20+ years, software to do computations. One place I’ve seen this applied, or really not applied, is in math teaching. I got increasingly frustrated. What is it that they’re teaching? Is it really the best thing that we can be teaching under the circumstances? And ten or fifteen years ago I was asking these questions, but realistically although a lot of the underlying technology was there, the interaction with it wasn’t, and it wasn’t ubiquitous. People didn’t have computers everywhere and it was hard to see how one could practically put that in. Now, it seems so obviously discrepant with what one needs to do. So, I can’t really point to an individual time, it’s been growing over a long period and observing what’s happened, and seeing these discrepancies build up between education what’s happened outside education.

You had no previous education background, right?

No, I’ve not gone and taught people. Now, that’s a mixed blessing. Obviously I don’t know some of the practicalities if you’re a teacher every day. On the other hand, it’s tricky to see what one would do differently if you’ve been teaching inside the curriculum that we currently force everyone to do.

The reaction to my talk has been very positive, perhaps more so than I expected. People have managed to come out of their boxes of what they’re doing, and say, “Yeah, I’ve been doing this for twenty years, but I can see there’s a problem.” I think that’s great, when we can encourage people to think outside like that, but not everyone can do that.

That seems to be one of the key questions, how do you get buy-in from the teachers and policy makers?

There are several steps. One is to build a community of people who are interested, and who can contribute ideas.

But the second major step, which we’re doing in parallel, is to build what I call a blue-skies curriculum: consider what you would do if you were starting with a blank sheet or a blank computer, cut all the baggage from the past with what’s been done with math, start again and start writing some modules. Try to work out, what would you do with the student, the teacher, and the computer to optimize the output one wants?

Now, these modules may not be immediately implementable in today’s schools. I’m trying to go to the far extreme, to go up into the stratosphere and figure out what you’d ideally do. I think that hasn’t been done very much. Most of what’s been done with math education reform, and I understand why this is, is people saying, “We’ve got computers now, what can we imagine doing next semester?” That’s also a valuable exercise, but it’s not what I want to do. I want to put up a beacon of what could be possible.

Once we’ve done that, the next step is to find a place where one can pilot that. I think there are countries, or states within countries, which are interested. In the end, I would love to see some of the major countries do this first. I expect that we’re going to see a smaller country really take this on-board fastest, because quicker decisions can be taken. But I’d love to be proved wrong on that, too.

There really isn’t anywhere in the world where math education looks like this.

That’s correct. We are starting from scratch. Every math curriculum in the world is based on the idea of hand-calculating, and most of what you’re teaching is how to calculate. And I think the resistance to this is very variable. In some places it’s, “I basically agree with you, but how are we ever going to get this implemented?” Other places it’s, “This has been an ancient thing, we need to go on teaching the ancient tradition.” They don’t put it in quite these words, but that’s the gist of it. Other places are saying, “This is interesting, let’s form an idea of what we can do here.” And we’re starting some of those discussions now.

One of the huge barriers is the question of standardized testing. It feels like this is something that, here in the USA at least, would take 20 or 30 years to get enough support.

I wouldn’t count on it, but neither would I claim this is anything other than a long, hard road, particularly in a developed and large country like the US. What’s the exact timeline? I wouldn’t like to predict. I think the world moves faster now than it did fifty years ago.

One of the key problems is that everyone teaching math today was brought up with the current system of math education. Now, people argue to me, “Don’t you have to wait for a whole new generation of teachers to make this change?” And I don’t think that’s true. There’s certainly an issue of helping teachers to move to a new way of thinking about things, but there are also new methodologies one can employ. You don’t have to have the teacher teaching the whole lesson. There are remote links, there are specialists, you can pull them in. There are things you couldn’t do twenty years ago that you can do now.

So, I wouldn’t want to put a time-frame on it, but I think we’re at a particular point now where there’s more will to change things than I’ve seen in my lifetime. People see the problem and they see the necessities and they see the rise of China, and they think, “Hang on, we’ve got a real problem we need to deal with here.”

Another problem is that there’s an integrated system assuming certain math education. Have you had a response from teachers at the university level?

Yeah, very much so. At the university level, computers have slowly been adopted more in everything outside the pure mathematics curriculum. So, although they wouldn’t have immediately suggested the theory in my TED talk, ways to improve mathematical understanding are very welcome.

One thing is for sure: most of the people admitting candidates to universities for technical subjects are pretty dissatisfied with the level of math education. Most countries would say the same thing.

In the cases I’ve talked to, we’ve had a very positive reception to the idea that: “Well, we’re going to be using computers with the folks when they get here. We’re trying to teach them engineering, or physics; we don’t need them to know the theory of proving this particular relationship. What we need them to do is be able to apply the mathematics.”

They can see that being able to do that, with or without a computer, is what really matters, and they can see that what I’m suggesting gets a lot further towards that than the traditional way has.

It’ll clearly be a driver of reform if those admitted to the best technical courses in universities studied computer-based math rather than traditional math. That will be a good way to build on initial successes and draw people through to doing computer-based math.

So getting the universities on board could lead the way.

Absolutely. Again, this sort of thing varies a lot between countries. The detailed system of how you get a new course established, who’s got the push and the pull in that, how involved is the government?

Another interconnected piece is obviously teachers and their training. On this topic, it’s an interesting idea that there are teachers in subjects outside math itself: other STEM (Science, Technology, Education, and Mathematics) subjects, maybe even things like geography, social sciences, and so forth that might well be able to teach the kind of math I’m talking about and can’t teach the traditional sort as well. It’s not all in one direction– that we’re going to lose a group of teachers that aren’t able to teach this new kind of math, and we won’t pull them in from anywhere else. I think there are opportunities, just like there are with students. There are students who will be able to do computer-based math much more effectively than the current math, there are teachers who will be able to do that too.

What would be the consequences of not changing the curriculum, if we keep going with the status quo?

I think what will happen is that math at school will become more marginalized. I see it going a bit like latin, where it ended up becoming a very specialist, niche subject. Now, the funny thing with latin, and the reason I brought up greek rather than latin in my talk, is that the use of latin in the world outside education was declining. The case with math, which is so frustrating, is that the use of math is massively increasing. So, there is a subject that is very mainstream, which we should be teaching, and then there’s the subject we’re teaching which is becoming less and less mainstream.

If we go on along this path at some point people are going to say, “This math, that no one likes doing, that we’re spending hundreds of millions of dollars teaching, and that universities and others don’t really want: you can’t justify doing that for everyone.”

It could become a niche subject that folks who go to fancy schools will study. Or alternatively—which is often happening now— it gets dumbed-down into purely a vocational subject : just teaches essential “math procedures” that are supposed to get you through life, but aren’t providing you deep understanding that you can really apply or use as a key skill. So, that’s the long-term danger.

It’s like everyone has started speaking Italian, and they’re still teaching Latin.

Yeah, that’s right, but the two are even more unrelated than that.

Just to emphasize, I’m sometimes accused of saying that we should stop anyone from learning current math, what I call the history of hand calculating. I’m not saying anything of the sort on an individual basis. If an individual student gets excited about the history of hand calculating (as I call much of our current math curriculum), that is a great thing for them to study. It’s a very interesting field. It just isn’t the mainstream field that the majority should be pushed to take

There’s been a trend of people learning to use abacuses recently.

If folks, and particularly kids, get excited about getting good at something, whether it’s learning their times tables, or playing with an abacus, or playing a didgeridoo, I think that’s great, I think they should be encouraged—just because it’s fun, it’s exciting. It doesn’t have to be “useful” per se. But it’s no good believing everyone should be force-fed this traditional kind of math in case a small number happen to find it fun.

I noticed you’re a photographer and a piano player, and I wonder if that’s influenced your approach to math education?

No, I’d put the whole thing the other way around. I’d say that, because I’m a mathematical kind of guy, the way I look at the world is a math/physics kind of way, and that definitely influences everything I do. So, when I look at a business problem, I’m running the scientific process on the whole business problem. That’s my way of thinking about it. If I’m looking at playing something on the piano, I like thinking about that in a fairly logical way “what’s it saying if I go louder of softer at this point” even if it’s an emotional thing I’m thinking about. So, I do feel math and feel science, and that’s the way I look at the world. And I think it’s quite a good way to look at the world, as long as you understand its limitation. It’s also probably led me to things that I think I can understand from that point of view. Photography is one of those: I can understand the theories of lighting. For example, if you put big lights next to a small object then you’re going to get a nice diffuse light. Things like that where I can understand how it fits together I find fun. Perhaps that helps me to be creative, perhaps not.

I would say there’s another interplay, which a lot of people since the talk have mentioned to me. They say that what you’re really talking about is not math, or even STEM subjects, it’s really creativity in education. I think there’s a lot of truth in that. Don’t teach people the processes of calculating, teach them the creativity of problem-solving in a math arena. In a sense that’s no different from teaching them creativity in the study of history, or any other subject.

It’s surprising for people, because we’ve been brought up to think that science and math are unemotional. The kinds of things you’re proposing here are about building a visceral connection to math as well.

There have been very noticeable scientists and mathematicians who show a lot of emotion. One that always comes to my mind is Richard Feynman.

But that’s different from the way it’s presented in schools.

Absolutely by most teachers. But part of the problem is, in testing, a calculation is often right or wrong, but that’s not true of wider questions of education. What’s the best way to represent this data? How does that communicate the idea of the data? or skew it one way or the other? To my mind those are math questions, but they’re not questions which have a definitive answer. So if you turn everything into a multiple-choice question, and you can do this with English as well, it becomes a kind of unemotional process. So, although I believe the world is in a sense a quantitative place, in practical terms with the data one has, the world’s a qualitative place, and one needs to make judgments and apply intuition one’s built-up without precise quantification.

Certainly also true that people have emotions to things that are built using math. I mean people now days have a lot of emotions about technology. But, for example some people are very emotional about their cars — now, are they emotional about how the spark plugs works in the engines? Well, you may find some geek who is, but it’s a much smaller fraction.

And so I think, if you zoom in to the mechanics of everything, that tends to limit the number of people who are emotionally attached to it.

It reminds me of diagramming sentences in English class. That’s the same mechanics, and where I was brought up we almost never did it. I don’t think I’ve suffered.

I had a strange thing with that, which is that the only English grammar I know is from learning latin. It’s slightly weird we were taught latin and it’s grammar in great detail, but never ever English. Now, I would have found English grammar somewhat useful. But in the end, you’re right, it’s a mechanism which is useful for the end, which is “how do I communicate in English?” One needs to get the goals clear from the mechanics. In my view that’s the biggest thing that got lost in Math. Computers affect other subjects too, but the effect in math and STEM subjects is so dramatic.