Technology in School

Conrad Wolfram: Let’s Build a New Math Curriculum That Assumes Computers Exist

By Tony Wan     Sep 19, 2018

Conrad Wolfram: Let’s Build a New Math Curriculum That Assumes Computers Exist

Has the math brand become toxic? That was the provocative question posed by Conrad Wolfram in a blog post earlier this summer. “Sadly,” he wrote, “I’ve started to conclude that the answer is yes.”

That conclusion may seem startling, especially as Wolfram is the strategic director of Wolfram Research, and one of the brains behind Wolfram Alpha and Mathematica, a system widely used in technical fields to process complex computations and calculations. His critique, in a nutshell: math instruction has become too fixated on computation—solving for x, for example—and removed from real-world applications and data.

Today, Wolfram is the founder of Computers-Based Math, an effort that he described as “building a new math curriculum that assumes computers exist.” In the following interview with EdSurge, he explains what exactly that means. (Note: the interview has been edited for clarity.)

Conrad Wolfram
Conrad Wolfram

EdSurge: How did your interest in math begin? When? And, were you always good at math as a child?

Wolfram: Like many people who kind of enjoy math, the reasons I enjoyed it at first was because I beat my friends at school. I wasn’t interested in the actual structure of it and how it worked. What really interested me was applying it in physics or in other areas. I found it quite fun, and the fact that I seemed somewhat more successful than some of my friends drove me forwards.

Your recent work and writing has focused on math education. Today there are many math instructional software and tools. But in what ways do you think we’re still missing the point when it comes to teaching math or getting kids engaged in the subject?

Fundamentally, I think it’s somewhat the wrong subject. It’s kind of shocking to many people that I would say that. But math to me is a problem-solving system, and with some logic and computation, you can come out with an answer.

Today, computation now gets done fantastically well by computers—better than anyone could ever have imagined 1,500 years ago. But what we’re doing in education right now is making people learn how to calculate by hand, but not learn how to do problem solving at a high level. They’re learning how to do computation, and not leaving that to the machines. Until we fix that fundamental issue, we’re not going to have the subject of math converging with what we need in the real world.

When you bring up the word math, many people tense up. And it got me thinking: Is the brand itself, the word “math,” actually causing us a lot of problems? We’ve got to figure out what people are going to do with math after education. When you think about what math is actually for, and how people really use it in the real world, you realize that people actually use computers to do the calculating to help us solve harder and messier problems.

Your current education effort is called computer-based maths. What is it, in a nutshell?

We’re trying to build a math curriculum that assumes computers exist, and that they can calculate things for you. So what do you have to learn, as a human, in order to be able to use the full power of math?

You don’t necessarily need to learn every step needed to solve a quadratic equation. You probably need to know what a quadratic equation is. You need to know how to set up the equation. You need to know how to verify the results, make sure that somehow you didn’t fooled. But most crucially, you need to know when you’re going to set up an equation, and why—which very few people coming out of school actually know.

Computer-based math is a project to redefine the subject based on computers doing the calculating. Rebuild the curriculum, the pedagogy, the approach. The basic idea is to be able to use technology as you would in real life and solve much harder problems. So, for example, an early module we made was for teenager, asking “Am I Normal?” What does normal mean? Maybe we define it as, how’s my foot size compared to other’s? Can we use math to help us figure that out? Maybe we can’t.

And then a bit later we have questions like, “Are Girls Better at Math?” But what does that mean? What does “better” mean? As you see, these thing are quite fuzzy, they’re not like traditional math questions. What we’re trying to do is get people to tackle hard questions with no clear answer, and that involves a mixture of defining the problem and actually doing calculations.

Are a lot of the problems that you present interdisciplinary by nature?

Absolutely. Math is this general-purpose subject at school, but if it isn’t interdisciplinary, well, why not? If it isn’t serving history, English, geography and all the other subjects, why not? If you study English in school, it’s servicing all of those other subjects.

When I think about math, I quite like the term “computational thinking.” It’s a way of thinking about life. The point about computational thinking is under the surface of any subject, there is a process you can run, and we have fantastic machinery to work out complex computations.

Sometimes you need to come out with a number or specific answer. Sometimes I think you don’t have a clear-cut answer. Sometimes, you need to know how to think about how to weigh risks or assess how, for example, politicians explain different kinds of facts. Most problems in business, or in other walks of life, are not multi-choice questions. You don’t get five choices, one of which is right and the other four are wrong.

We should think about applying computational thinking across different subjects—like computational history, computational English.

What would be an example of a computational English kind of problem?

It might be looking at the linguistics of a novel. Can we do sentiment analysis through a book, to see if we can pick out when it was happy and sad and other things? A colleague of mine, John McLoone, wrote a blog post about this with [“Lord of the Flies”].

We also have an example for history, where we were looking at the most common words used in inaugural addresses by presidents. That could get one thinking: Do these words ultimately reflect what they did during their term in office?

As new technologies like machine learning and artificial intelligence continue to evolve, how do they shape computers-based math, or what students will need to know to be prepared for the future?

What we need to do is to figure out, what’s the tool set that we really need, and how well should people know how use to use them?

One of the big problems is that people learning math are using a very small computational tool set. They’re learning how to solve a quadratic equation, how to stitch a graph, these sorts of things. But the tool set out there right now is massive. There is machine learning. There is calculus of all sorts. There’s data science, of course. The ways in which people will communicate with the computer will change, but we need them to know how to use the technology available.

Today we need people to learn how to code. It’s what I call step two of the problem-solving process. The first is trying to define the problem. Step two is extract to the language of math, which today is usually code. You want to write it so the computer can understand it, but so you can also communicate it. Step three is calculating, what we’ve been discussing, and hopefully you get a computer to do that.

It seems there’s been a lot of momentum, in the U.S. and U.K. to introduce coding into the curriculum. Would you consider yourself a fan or a proponent of this push?

I think it’s great that this has come up as a movement. Coding is crucial. If you think about coding as learning how to abstract a problem, which I think is really hard especially the fuzzier and more complex the problem gets, then I think it’s good we’re seeing this being encouraged.

But I’m not sure we’ve completely got the angle quite right yet. I think we need to make sure that coding education is not too purist. Like in math: if you’re one of the top people who enjoy it, that’s great and wonderful, I’m all for that. But most people don’t enjoy it, and it’s no good writing the whole curriculum assuming that it’s a great piece of enjoyment for everyone.

With coding, we’ve done really well with the people who are already interested. I think we haven’t done quite so well yet with many other people who don’t quite connect with coding, and just want to use it as a means to an end in school.

I think that tying math together with computational thinking and other subjects, and combining it with code, would be the absolutely ideal direction for the future. And I think it will happen in one form or another over time.

How widespread has computers-based math been adopted?

Early on we’ve got Estonia. I think we’ve got interest from some other European countries. We’ve also had project in Egypt, and also some interest in Australia.

One of the issues we’ve had is that, in the end, everyone has to take tests. And the problem is that the assessments don’t match with our vision, because they are basically about how to calculate things. It’s been a slow process because you’re trying to get the tests adjusted, and to get governments and others onboard.

There’s no problem with the idea of a quantitative assessment of computer-based math. We just have to have a different set of questions, where the answer isn’t necessarily “right or wrong” in the traditional sense. Instead of “solve the following quadratic equation,” the questions should be: “Here are two data sets, what can you figure out about them?”

I love asking politicians, “When was the last time you used a quadratic equation?” They all say we all have to do them, but other than helping their kids do their math homework, I haven’t found a politician who actually has used one in their own life.

And then we’ve got teachers trying to teach this, and often they get criticized [when students don’t do well]. But then you realize, maybe the teacher doesn’t quite know why they’re teaching this either, really. It’s tough to teach something if you yourself can’t really understand how or when you’d use it.

Conrad Wolfram: Let’s Build a New Math Curriculum That Assumes Computers...

Technology in School

Conrad Wolfram: Let’s Build a New Math Curriculum That Assumes Computers Exist

By Tony Wan     Sep 19, 2018

Conrad Wolfram: Let’s Build a New Math Curriculum That Assumes Computers Exist

Has the math brand become toxic? That was the provocative question posed by Conrad Wolfram in a blog post earlier this summer. “Sadly,” he wrote, “I’ve started to conclude that the answer is yes.”

That conclusion may seem startling, especially as Wolfram is the strategic director of Wolfram Research, and one of the brains behind Wolfram Alpha and Mathematica, a system widely used in technical fields to process complex computations and calculations. His critique, in a nutshell: math instruction has become too fixated on computation—solving for x, for example—and removed from real-world applications and data.

Today, Wolfram is the founder of Computers-Based Math, an effort that he described as “building a new math curriculum that assumes computers exist.” In the following interview with EdSurge, he explains what exactly that means. (Note: the interview has been edited for clarity.)

Conrad Wolfram
Conrad Wolfram

EdSurge: How did your interest in math begin? When? And, were you always good at math as a child?

Wolfram: Like many people who kind of enjoy math, the reasons I enjoyed it at first was because I beat my friends at school. I wasn’t interested in the actual structure of it and how it worked. What really interested me was applying it in physics or in other areas. I found it quite fun, and the fact that I seemed somewhat more successful than some of my friends drove me forwards.

Your recent work and writing has focused on math education. Today there are many math instructional software and tools. But in what ways do you think we’re still missing the point when it comes to teaching math or getting kids engaged in the subject?

Fundamentally, I think it’s somewhat the wrong subject. It’s kind of shocking to many people that I would say that. But math to me is a problem-solving system, and with some logic and computation, you can come out with an answer.

Today, computation now gets done fantastically well by computers—better than anyone could ever have imagined 1,500 years ago. But what we’re doing in education right now is making people learn how to calculate by hand, but not learn how to do problem solving at a high level. They’re learning how to do computation, and not leaving that to the machines. Until we fix that fundamental issue, we’re not going to have the subject of math converging with what we need in the real world.

When you bring up the word math, many people tense up. And it got me thinking: Is the brand itself, the word “math,” actually causing us a lot of problems? We’ve got to figure out what people are going to do with math after education. When you think about what math is actually for, and how people really use it in the real world, you realize that people actually use computers to do the calculating to help us solve harder and messier problems.

Your current education effort is called computer-based maths. What is it, in a nutshell?

We’re trying to build a math curriculum that assumes computers exist, and that they can calculate things for you. So what do you have to learn, as a human, in order to be able to use the full power of math?

You don’t necessarily need to learn every step needed to solve a quadratic equation. You probably need to know what a quadratic equation is. You need to know how to set up the equation. You need to know how to verify the results, make sure that somehow you didn’t fooled. But most crucially, you need to know when you’re going to set up an equation, and why—which very few people coming out of school actually know.

Computer-based math is a project to redefine the subject based on computers doing the calculating. Rebuild the curriculum, the pedagogy, the approach. The basic idea is to be able to use technology as you would in real life and solve much harder problems. So, for example, an early module we made was for teenager, asking “Am I Normal?” What does normal mean? Maybe we define it as, how’s my foot size compared to other’s? Can we use math to help us figure that out? Maybe we can’t.

And then a bit later we have questions like, “Are Girls Better at Math?” But what does that mean? What does “better” mean? As you see, these thing are quite fuzzy, they’re not like traditional math questions. What we’re trying to do is get people to tackle hard questions with no clear answer, and that involves a mixture of defining the problem and actually doing calculations.

Are a lot of the problems that you present interdisciplinary by nature?

Absolutely. Math is this general-purpose subject at school, but if it isn’t interdisciplinary, well, why not? If it isn’t serving history, English, geography and all the other subjects, why not? If you study English in school, it’s servicing all of those other subjects.

When I think about math, I quite like the term “computational thinking.” It’s a way of thinking about life. The point about computational thinking is under the surface of any subject, there is a process you can run, and we have fantastic machinery to work out complex computations.

Sometimes you need to come out with a number or specific answer. Sometimes I think you don’t have a clear-cut answer. Sometimes, you need to know how to think about how to weigh risks or assess how, for example, politicians explain different kinds of facts. Most problems in business, or in other walks of life, are not multi-choice questions. You don’t get five choices, one of which is right and the other four are wrong.

We should think about applying computational thinking across different subjects—like computational history, computational English.

What would be an example of a computational English kind of problem?

It might be looking at the linguistics of a novel. Can we do sentiment analysis through a book, to see if we can pick out when it was happy and sad and other things? A colleague of mine, John McLoone, wrote a blog post about this with [“Lord of the Flies”].

We also have an example for history, where we were looking at the most common words used in inaugural addresses by presidents. That could get one thinking: Do these words ultimately reflect what they did during their term in office?

As new technologies like machine learning and artificial intelligence continue to evolve, how do they shape computers-based math, or what students will need to know to be prepared for the future?

What we need to do is to figure out, what’s the tool set that we really need, and how well should people know how use to use them?

One of the big problems is that people learning math are using a very small computational tool set. They’re learning how to solve a quadratic equation, how to stitch a graph, these sorts of things. But the tool set out there right now is massive. There is machine learning. There is calculus of all sorts. There’s data science, of course. The ways in which people will communicate with the computer will change, but we need them to know how to use the technology available.

Today we need people to learn how to code. It’s what I call step two of the problem-solving process. The first is trying to define the problem. Step two is extract to the language of math, which today is usually code. You want to write it so the computer can understand it, but so you can also communicate it. Step three is calculating, what we’ve been discussing, and hopefully you get a computer to do that.

It seems there’s been a lot of momentum, in the U.S. and U.K. to introduce coding into the curriculum. Would you consider yourself a fan or a proponent of this push?

I think it’s great that this has come up as a movement. Coding is crucial. If you think about coding as learning how to abstract a problem, which I think is really hard especially the fuzzier and more complex the problem gets, then I think it’s good we’re seeing this being encouraged.

But I’m not sure we’ve completely got the angle quite right yet. I think we need to make sure that coding education is not too purist. Like in math: if you’re one of the top people who enjoy it, that’s great and wonderful, I’m all for that. But most people don’t enjoy it, and it’s no good writing the whole curriculum assuming that it’s a great piece of enjoyment for everyone.

With coding, we’ve done really well with the people who are already interested. I think we haven’t done quite so well yet with many other people who don’t quite connect with coding, and just want to use it as a means to an end in school.

I think that tying math together with computational thinking and other subjects, and combining it with code, would be the absolutely ideal direction for the future. And I think it will happen in one form or another over time.

How widespread has computers-based math been adopted?

Early on we’ve got Estonia. I think we’ve got interest from some other European countries. We’ve also had project in Egypt, and also some interest in Australia.

One of the issues we’ve had is that, in the end, everyone has to take tests. And the problem is that the assessments don’t match with our vision, because they are basically about how to calculate things. It’s been a slow process because you’re trying to get the tests adjusted, and to get governments and others onboard.

There’s no problem with the idea of a quantitative assessment of computer-based math. We just have to have a different set of questions, where the answer isn’t necessarily “right or wrong” in the traditional sense. Instead of “solve the following quadratic equation,” the questions should be: “Here are two data sets, what can you figure out about them?”

I love asking politicians, “When was the last time you used a quadratic equation?” They all say we all have to do them, but other than helping their kids do their math homework, I haven’t found a politician who actually has used one in their own life.

And then we’ve got teachers trying to teach this, and often they get criticized [when students don’t do well]. But then you realize, maybe the teacher doesn’t quite know why they’re teaching this either, really. It’s tough to teach something if you yourself can’t really understand how or when you’d use it.

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