Interview | Doing the Math with Conrad Wolfram

Conrad Wolfram is the younger Wolfram of Wolfram Research, a leading software company and powerhouse in scientific and technical innovation. Wolfram Research does Wolfram|Alpha, Demonstrations and the core, underlying technology—Mathematica. After his brother Stephen established a U.S. base, Conrad founded the European Wolfram Research in 1991, where he continues to serve as its managing director. Since 1997, Conrad has also been the strategic director of the worldwide group where he initiates and directs business, marketing, design and a variety of strategic technical projects—everything from the Mathematica Player family concept to webMathematica (which underlies Wolfram|Alpha)—to conceptualizing wolfram.com. Conrad is interested in how technology and computation can move our lives and economies forward and actively campaigns for the reform of mathematics education based on computers. He is an avid photographer, plays the piano and has an MA from Cambridge University, UK, where he reads physics and mathematics. He’s been a featured speaker at the world-famous TED talks. Here, Conrad answers some broad-reaching questions about education, technology and of course—mathematics. While his ideas about math, computers and education are all quite logical, they are also radical and revolutionary—though inevitably necessary—and very well could be the future of education.

Victor: What’s right with math education in America today?

Conrad: First, the belief that math is an important, mainstream subject. And second, the constant wish to improve, and from many a wish to apply technology to the maximum. What concerns me is that we’ve sometimes failed to look at the bigger picture of math education in the computer age, to look at fundamentals of what math is, why we’re teaching it, how we use it, and how it’s metamorphasized outside education in the last few decades. I think we can get America’s great “math energy” and unleash it in an improved direction.

Victor: Are we missing some factors from the equation when it comes to classroom technology and math?

Conrad: Quite a bit, yes.

Victor: What makes you say that?

Conrad: I’d characterize most of what’s happened so far as taking the existing math subject and assisting it with technology. Instead I think we can make a new, much more conceptual and practical subject that’s based on computers. For each piece of content, we need to ask afresh, “what purpose does it serve to teach this now that we have computers?” “How can we make this more life-like, more real, if computers do the calculating?”.

I’d add one other thing. Often the computer is used to attempt to replace the teacher or for doing the teaching rather than doing the calculating. As I often say … a good guide to how and what you should do with a computer in the classroom is what you’d do with it outside. As much as possible, use real-world tools in the classroom in an open-ended way not special education-only closed-ended approaches.

Victor: In your 2010 TED talk, you say, “we have a real problem with math education right now”—how would you characterize that problem in U.S. schools, is it the same internationally? What’s wrong, essentially? Why? What do you suggest we do about it?

Conrad: There are different layers of the problem. Let me try to peel them off from the outside. To start with, most people–parents, employers, students and teachers—aren’t that happy with math education. It’s hard to find people who say “math in America is great” … Why is this? Well, math is more and more important so the pressure on it to deliver has gone up, yet students’ abilities don’t seem to have gone up; and very few find math fun either! Why is this? In my view a key reason, bluntly: we’re teaching the wrong subject. A chasm has opened up between the subject of math in education and math outside. I think of math as having 4 steps:

1. Posing the right questions

2. Real world –> math formulation

3. Computation

4. Math formulation –> real world, verification

In education, we spend perhaps 80 percent of the time on step 3 by hand, yet it’s rarely used outside above the most basic arithmetic. Computers (and don’t forget phones, iPods and iPads) do that bit—and usually much better than any human could!

So let’s do the same in education. Let’s teach the other steps much more, with harder, more realistic problems. There are some cases where hand calculating is still useful—like estimating—but that’s the exception not the rule. The default assumption should be “computers do the calculating”.

This isn’t just a U.S. problem; it’s everywhere; and the country that solves this first will get a great boost in technical competency and its important economic and societal consequences.

Victor: Is a revolution in math education necessary or would an evolution do the trick? (And what would we have to change from and change to?)

Conrad: This is more revolutionary than evolutionary. In the end we need a new curriculum from the ground up—what I call a “computer-based math” curriculum. The mainstream subject of today really is discrepant from the future mainstream math subject we need. The change therefore is a big one and will need some qualitative steps (e.g., computers in exams).

Victor: What is calculating, what is computing, what are students doing in classrooms today when they learn and/or study math?

Conrad: Now they’re primarily learning processes for hand calculating. Sometimes they understand what they’re doing; often it’s pretty much rote-learning of those processes; usually they have no idea why they’d want to do this calculation anyway.

What they should be learning is problem solving. They should be asking the questions, formulating what they’re trying to solve and why then turning that into math, usually getting a computer to calculate the math answer and then interpreting it back to the real work and verifying it. They need to learn to think about the world in a mathematical way—whether for jobs they might have or just being a citizen in today’s ever more mathematical world.

Victor: What is at stake if we do little or nothing to change math education?

Conrad: The economy and some aspects of society. Those who instinctively understand the world mathematically will be far more successful at technical jobs and at many other aspects of being a “good citizen”—managing money, problem solving of all sorts, etc..

Victor: Why do we need students who are fluent in the language of mathematics?

Conrad: Roughly three reasons: technical jobs, everyday living (e.g., calculating mortgage or understanding health statistics), and logical thinking. Chart out any recent century and see the rise of the use math, quantitative techniques and the amazing and accelerating technological revolution that’s depended on it.

Victor: How does Mathematica software fit in to this discussion? How about the Wolfram Alpha knowledge engine?

Conrad: They’re both tools for the computer-based math empowerment I’ve been talking about. What’s exciting recently is how easy they are to use, yet packing huge industrial-strength computational power and data under the hood. They prove that the technology for a complete computer-based math curriculum really is here: in ease of use, power, range of equipment (including many of the new devices). And coming up, we’ll also have complete interactive documents that anyone can make and share with anyone else. Take a look at demonstrations.wolfram.com to get an early idea of what I’m talking about.

Victor: Is there anything else you care to add or emphasize about math, technology and/or computers in the classroom?

Conrad: Computers are the best thing that ever happened to math Let’s unleash them in education like they have been outside and redefine the mainstream subject of math. Wouldn’t it be great if math became one of the most popular subjects? Please do take a moment to go to computerbasedmath.org and join our effort.

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Victor Rivero tells the story of 21st-century education transformation. He is the editor-in-chief of Edtech Digest, a magazine about education transformed through technology. He has written white papers, articles and features for schools, nonprofits and companies in the education marketplace. Write to: victor@VictorRivero.com