We first met Conrad Wolfram on his TED speech : ‘’Teaching Kids Real Math With Computers’’. We were so impressed with his speech that we thought we would write to him and see if we could interview him on Skype. We were so afraid that he would reject that we proposed a short version of our interview format, ‘’8 minutes- 8 questions’’. He accepted !
Below is the interview. We hope you enjoy not only the expected and amazing answers of Mr Wolfram but the quality of the questions asked. We spent a lot of time of thinking, writing, discussing, re-writing questions to make them at par with the intelligence we were going to face.
We look forward to your comments.
Who is Conrad Wolfram?
Conrad Wolfram (born 1970) is a British technologist and businessman known for his work in ITand its application.
Conrad Wolfram founded Wolfram Research Europe Ltd. in 1991 and remains its managing director. In 1996 he additionally became Strategic and International Directorof Wolfram Research, making him also responsible for Wolfram Research Asia Ltd, and communications such as the wolfram.com website.
Wolfram has been a prominent proponent of the reform of math education by greater use of information technology and is the founder ofcomputerbasedmath.org. The UK’s Channel 4 news quotes him saying “There are a few cases where it is important to do calculations by hand, but these are small fractions of cases. The rest of the time you should assume that students should use a computer just like everyone does in the real world.”. In an interview with the Guardian he described the replacement of hand calculation by computer use as “democratising expertise”.
He advocates publishing technology with the stated aim of “making new applications as everyday as new documents” claiming that “If a picture is worth a thousand words, an interactive document is worth a thousand pictures.”
In 2009 he spoke about education reform at the TEDx Conference at the EU Parliament and again at TED Global 2010 where he argued that “Maths should be more practical and more conceptual, but less mechanical,” and that “Calculating is the machinery of math — a means to an end.”
1. You look at math as a skill of life rather than a multiple choice subject. This excites us all.
a. Can you change the system? Have you contacted any Ministry of Education or
teachers in schools? Is there a reluctance from the older generation instructors?
Yes it’s a good question. Systems are hard to change. You can’t change it very quickly. This becomes a big problem. In global world it is really hard because everybody feels different. There’s reluctance. Teaching mathematics with the old way is more widespread. However, there’s great enthusiasm.
b. How will you assess mathematical skills? Every subject of lesson is valid for this way of thinking (eg. Physics, biology, even history). But when we have teachers who can think like you they don’t match the demands of the Ministry of Education and the university exams, such as A-Levels, SATs and in the worse case the Turkish University Exams. How do you solve this dichotomy, this conflict of interest? What do you think of the current math exams in international exams such as SATs or GCSEs or A-Levels?
I believe that in the end lessons should make a good simulation. The main problem is they don’t use computers. They are using computers as majors. However, the real world has computers. For example, in Denmark, they use computers but not in mathematics. They only use that in science. It is hard to get the things that people don’t use in life.
c. When do you think your plan will function globally?
Well, it is very hard to predict it. Education is going through a big transformation. In USA, some did this transformation. It can happen in different levels too. Everyone will take computer based mathematics. It doesn’t become the major subject. They have to have a separate subject. They should divide and separate the subject mathematics. People can select rather computer based mathematics or normal mathematics. If we do well everyone should choose computer based mathematics.
2. a) I am curious to know how successful you were in math class during your primary school and high school years.
Did you come up with you way of thinking because
– you hated math when you were a child and you didn’t want other students to go through the same things or
– as you grew up. You understood that most of the things you had learnt in math were useless?
I did pretty well at math. I was better at Physics actually than math. I was a lot worse at French. You usually have to learn French in the first four languages if you like to study in UK. I quite liked math because I could do quite well at it. I actually learned quite a lot from the mathematics, but a lot of it, I realize now, wasn’t very useful. It’s not the idea, it’s the way of thinking. I think I was lucky enough that I learned how to think mathematically. I learned how to analyze the world in a kind of a mathematical way. It helped me a lot. It helped me in many many things, not just mathematics. So, I guess I learned a lot from math but then there was a lot of other stuff like I spent six or seven years learning how to solve integrations by hand and nowadays when you look at, it doesn’t make much sense. Of course to be fair though, at the time, which is about 20-25 years ago, computers weren’t that good yet. Some of the things that don’t make sense to learn it now probably made sense to learn then, if you wanted to do mathematics as a subject.
3. Most of the famous mathematicians had difficulties in their school years. For example, Einstein failed math, Newton was twice not accepted to university. Does this mean that the schooling system was wrong back then? Or does math education start too early?
The first thing I would say is the educational systems usually follow the real world. So I think schools and education have always been somewhere behind from what’s actually needed. At times people like Einstein or Newtonare thought of likeoutliers. I mean Newton was certainly a pretty weird guy and you know the edge between being unfocused or being brilliant usually doesn’t fit very well. So I think that there is always a difference between people who think very differently and those who have trouble with things.
I also think coming up with new computers has given real opportunities to have much more customized schools. So instead of everyone sitting and learning stuff people can do more individual stuff and what they want to do or what they’re interested in. I think that’s a kind of interesting future that might work.
4. Our generation’s learning methods have changed. We learn more visually, and with fast paced tools (such as You Tube). Do you see this trend as an asset or as an obstacle for thinking/analysing/understanding math? What are the implications of this trend for creating new?
Well I think it’s overwhelmingly a good thing in the world’s history when we have new tools you can use. Obviously, using new tools in good ways; there are always negative aspects in new tools, but on the whole,it is very exciting to have new tools which will offer the modern world interactive learning. I think on the whole , it is overwhelmingly positive. I think many modality tools have come up. I know Youtube as an example. There is also social networking where there is interactivity, which we are launching computable documents to suit. It will allow the reader to drive the example they’re looking at. We have an example of this in our demonstration site where you can actually go and play with examples. Many of you submit new examples at times. These are some new ways to communicate. In a sense we connect the author of the ideas much more directly with the reader or the student and that’s probably a good thing.
Two other ways I look at this: having an equipment, an automation allows you to split the method of what you are doing from the task. I watch this from my young daughter for example, the task of writing by hand and what you say are pretty separate things. When I was learning how to write there were type-writers but they weren’t like computers; so I didn’t write email messages. Now when you watch people learning to write they type email messages at the same time they’re learning to write and they get these new skills. Typing and writing are different; the physical act of holding a pen is a different skill than typing and it is interesting to see the separation of these different modalities. I think of technology as like standing on a hill and looking over a plateau. If you are standing on a top of a thing you can usually see below and I guess that’s how modern technology is for learning.
5.I quit science because there was no visual thinking involved. Most of the visual thinkers in school leave sciences. But when we look at careers of people on the world, we see a lot more lawyers than mathematicians.
Who do you think changes the world?
Hitler or Einstein?
Obama or Zuckerberg?
An interesting philosophical question…I have to say, there are some brave, good and terrible people who are around. In the end, good and bad people change the world.
In terms of leaders, leaders of industries and companies have become very technical in the last twenty years. It is almost a joke…My brother has started a research, with someone with a PhD running a company. Now, it is strange for somebody who is technically educated running large companies. It is a large turn around. In terms of people running countries, it is interesting to know that the German chancellor, Merkel is a physicist. Some of these things are changing.I think there are several things combined here. I think it is partly who decides to go into which subjects and different areas. I think a lot of people put off going into science perhaps for the reasons you are describing, It doesn’t feel creative.
That was certainly the case for science for the time when the current leaders were schooled. I think , it is partly who the intake is and what the jobs demand …The other aspect we need to realize is that the world is vastly going for more quantitative issues, in walks of life, not only in running companies but also increasingly in running countries. People need to understand a lot more about how to analyze technically, much more than they ever did. They need to push people who are more quantitative, who need direction.
In the end people who succeed have different passions, and current leaders actually are people who are interested at the very start and passionate about what they are doing. In the end whichever subject you happen to be excited about, evenbizarre subjects, or practical subjects, can lead you to success.
6. My question is about people who don’t have computers in the 3rd world countries? Have you ever thought which one would be cheaper:
a.To invest aid money to teach them math through teachers?
To invest aid money to buy them computers and teach them how to use it properly and not just for Facebook?
Good question, though I don’t think that they’re mutually exclusive. I mean, I think you’ll have to do to some extent both. I suppose the way I think about this is computers enable new forms of teaching, though I find ‘’teaching’’ a slightly odd term. Teaching suggests one person telling somebody else what to learn. What I mean by teaching is investigation, and understanding; maybe education can be a better term.
Now, I think a lot of that can happen in the future with computers, people discovering new things on their own. In fact, somebody who had the same specialty as me when I gave my TED talk, a guy called SigarDemitra, believes in putting computers all over public domain. I know he’s done this in India for example, he’s put computers into the wall, and he just gives his students some questions to answer and they go off and search the web and figure out the answers and find out a bunch of stuff. I don’t think that’s the only way you can do things. I do believe you need some formal teaching too. But I think there’s a lot further that you can go.
In terms of teaching arithmetic with computers, what’s difficult is, it’s really coming out with the right materials and the right way of using them. I think teachers are very important in making that work, but perhaps not in the traditional way they do. I think that you can immediately get a big result, in investing in a sensible amount of technology, with sensible ideas about how to apply it, but I think you’ve got to invest in some sort of teaching way to help students as well. I don’t really think you can decide that computers will take over. And, in fact, some of the mistakes that governments have made is they’ve decided that they can save money by paying for computers, rather than teachers. So what they’ve done is they’ve made up computers to do the most conventional imaginable thing, to not actually do calculating for example, but to just ask multiple choice questions. And then the computer helps you answer those, and the whole thing degenerates into a robot like world where nobody is really learning anything. So I think that’s a danger, but we can avoid that danger.
7. Do you believe every person has the same perspective of math and numeral thinking? (For example I think there are some people who generate their own algorithms and some others who are bound to a single form of algorithm and who can think very fast.)
I think people have innate skills that are very different, you know there is always this debate about nature vs. nurture , you know how much it is your genetics vs. your upbringing vs. other things that surround you in life. I think it is a mixture of both. Some people, both socially and probably genetically, think more in a mathematical way, and some people think more in different ways. But I think both sides can be helped. I think there are a lot of people who currently don’t do mathbecause they perceive math as being calculating and they are no good at following procedures to calculate things. I think there are a lot of other people who are innately perfectly good at quantitative ideas and thinking about the world in a scientific way. But they are put off doing that because of how math is set up. So I suppose not everyone is perhaps that astute, but I think many more people currently set to do math, could be going much further in that kind of mathematical thinking than what the current system allows.
8. We discussed at length your ‘’car’’ example you mention in your TED talk. You say we do not teach people who drive cars the details of the car parts.
What is the objective of math? Are you saying
- a. take the car (ie. Math) and drive somewhere new, so use math as a tool to get to new findings?
- b. Or are you saying take the car (ie. Math) and make another car?
Are you saying:
- a. Math is a tool and you need to use it to get to new places; like people who use computers and don’t know how it works. So, use math in other areas? Or
- b. Math is imagination and you don’t have to learn (memorize) the intricate details to make it work. The computer does it. Understanding math is enough.
I would like to explain better with the example of String Theory (‘’if you bend time enough, you can see yourself in time.’’) Are you saying:
- a. ‘’If we implement the ‘’using’’ math / physics idea, we can use this String Theory to analyze a past genocide, or better, to jump to an old star, or even better to see the creator of the universe. Here, the concept is enough to ‘’use’’ it somewhere else. ‘’
But do we add anything to Math?
- b. Or, ‘’We can use the String Theory to make a new theory. Understanding it is enough. The brilliance of the String Theory is in the idea behind it. The computer does all the calculations anyway.’’
But aren’t you contradicting yourself with this point because wouldn’t this cause people to stop questioning math? For example, to get to know 4+4=?, we have to first know 1+1, then we can question the steps getting to 4+4. Most of the new theories come from questioning the basics and consequently discovering new ways of thinking. How can one properly question the steps going to 4+4, if one does not spend time with 1+1 ?
This is a deep and good question, or set of questions I should say. Let me think about how to answer them…
Look at some level I think that you have got to ask the purpose of life, ok thats generalizing the question even further ,but you what do you want to get out of life, what do you want to get out of education for life.
Now a one-level education is a practical thing to enable you to function in the economy and so forth. In another level, it’s a stringent system. Questioning is a way to help enrich your life. However, what I think doesn’t work is to try to tell somebody that they have to be enriched by a subject which they don’t really care about. So when people are told ‘’math is enriching! You must learn math! Its very good for you’’, if you happen to be interested in math and it can be all forms of math that’s fantastic.
Most people in the world know how to drive cars, but they don’t need to know how to design new cars. I don’t think you should start teaching people about cars and teaching them about the engine design. Basically the main stream subject is driving. Now that’s absolutely not to say that if somebody gets interested in the mechanics of cars, ‘How does a car actually work?’ ‘How does the fuel injection system work?’, ‘how was that designed?, how do I service it?’ that’s fantastic, they should go ahead and study it.
Now if we apply this to math you will get a very small minority of people asking ‘How do you do the calculations?’ or when we have the computer doing the calculations who will ask ‘’how can I get it to do new calculations?’’ I think that if people start to ask those questions and get interested in themthat’s absolutely fantastic. They have a great subject to push on with and overcome the tools like mathematics for example ,or a mathematical software system.
There’s an even more detailed question than that. Some of these villagers I lived with in England make ‘’loops’’, those instruments a little bit like guitars, very ancient instruments and they were saying to me if you think about music, if people were never exposed to music , how could they know there was anything exciting as that, but I think if you expose people to computer based mathematics which I think is also useful, can be conceptionally interesting for many. The people who are interested in how that all works will pursue their dreams. So universities should have numerical analysis courses or courses on how you build computer systems that does mathematics. Those are fine at an abolute level. But that’s no where I would start students at primary school or even secondary school. I hope that’s some answer on the car issue. It’s a pretty deep question and frankly I had wondered why it’s not asked around the world more often.