Yesterday’s math class won’t prepare you for tomorrow’s jobs.
Math is changing, at least in the way we use math in the context of our daily lives. The way you learned math will not prepare your children with the mathematical skills they need in the 21st Century.
Don’t take my word for it. I am not a math professor. I almost failed out of calculus in high school. I do not claim to be an expert. I write about video games, psychology, education, and philosophy. I understand the importance of math, but it is not my area of expertise.
When I am writing about math education and I need a true expert opinion, I reach out to Keith Devlin. He is co-founder and Executive Director of Stanford University’s Human-Sciences and Technologies Advanced Research Institute. He is also a learning game and app developer who founded a company called BrainQuake (a part of the Co.lab/Zynga.org edtech accelerator). And, of course, he is well known as the “NPR Math Guy.”
About a month ago, I interviewed Devlin for my MindShift KQED series on game-based learning. The enlightening conversation changed the way I think about math education. Unfortunately, I only had space there to share some of that conversation. Here, I offer some of the other gems.
I have distilled Devlin’s thoughts down to five key points that I think everyone needs to know about the future of Mathematics.
1. Math education is stuck in the 19th Century
Jordan Shapiro: You wrote a book called Mathematics Education For A New Era: Video Games As A Medium For Learning. You and I have talked a lot about video games in the past, so I’ll let that rest for now. What is this “New Era” and why do we need a different kind of mathematics education?
Keith Devlin: To most people, mathematics means applying standard techniques to solve well defined problems with unique right answers. They have good reason to think that. Until the end of the 19th Century, that’s exactly what it did mean! But with the rise of the modern science and technology era, the need for mathematics started to change. By and large, most people outside mathematics did not experience the change until the rapid growth of the digital age in the last twenty years. With cheap, ubiquitous computing devices that can do all of the procedural mathematics faster and more accurate than any human, no one who wants – or wants to keep – a good job can now ignore that shift from the old “application of known procedures” to new emphasis on creative problem solving.
Jordan Shapiro: What does this mean for mathematics education?
Keith Devlin: When today’s parents were going through the schools, the main focus in mathematics was on mastery of a collection of standard procedures for solving well-defined problems that have unique right answers. If you did well at that, you were pretty well guaranteed a good job. Learning mathematics had been that way for several thousand years. Math textbooks were essentially recipe books. Now all those math recipes have been coded into devices, some of which we carry round in our pockets. Suddenly, in a single generation, mastery of the procedural math skills that had ruled supreme for three thousand years has become largely irrelevant. Students don’t need to train themselves to do long computations, as was necessary when I was a child. No one calculates that way any more! What they (we) need in today’s world is a deeper understanding of how and why Hindu-Arabic arithmetic works.
2. Yesterday’s math class won’t prepare you for tomorrow’s jobs.
Jordan: But we’ve all seen statistics that show STEM (science, technology, engineering, math) skills are in high demand. Certainly a math degree is still good for job placement?
Keith: It’s still the case that math gets you jobs, but the skill that is in great demand today, and will continue to grow, is the ability to take a novel problem, possibly not well-defined, and likely not having a single “right” answer, and make progress on it, in some cases (but not all!) “solving” it (whatever that turns out to mean). The problems we need mathermatics for today come in a messy, real-world context, and part of making progress is to figure out just what you need from that context.
Jordan: Have you seen examples where people with the old skills are struggling in a new economy?
Keith: In all four offerings of my mathematical thinking MOOC to date, I have had as students, engineers with years of experience who suddenly found themselves out of a job when their employers replaced them with software systems (or sometimes overseas outsource services). Those engineers are now having to retool to learn this other skill of creative problem solving – mathematical thinking.
3. Numbers and variables are NOT the foundation of math.
Jordan: Just one question about video games: You’ve said games are the best way to teach math. How does this tie in with “Mathematical thinking”?
Keith: The traditional symbols of math were developed to do mathematics on a sheet of paper. Actually, they were originally developed to do it in the sand, on clay tablets, later on parchment, and then paper (and blackboards). But in all cases, it was a static representation of something fundamentally dynamic – namely a form of thinking! Tablet computers and video games provide interactive, dynamic representations, which means you can get closer to the thinking, and break through the Symbol Barrier.
Jordan: So you’re not only saying that technology renders basic procedural mathematics skills obsolete, you’re also suggesting that it offers new forms of dynamic representation?
Keith: Yes, and a more efficient representation can make a dramatic difference for students. Take a look at the example below from the iOS/Android App Wuzzit Trouble. These are two representations of the very same problem!
What I and a small number of other math learning game developers are doing, but most are not, is viewing the game as a representation of mathematics that replaces the traditional symbols with one that takes advantages of the many different affordances that video game technology offers, particularly tablet screens.
4. We can cross the Symbol Barrier.
Jordan: So, mathematical thinking is the abstract logic that underlies the procedures, right? Does this mean the symbols–numbers as we know them–could change?
Keith: No one, least of all me, is saying we should abandon the traditional symbolic representation for mathematics. You need to master that language if you want to go on to a career in science or engineering, and many other careers as well. Most advanced mathematics is inherently symbolic, and I cannot see any current technology changing that. What I do say, based on a lot of hard evidence, is that, because of the Symbol Barrier, we should not make the symbolic representation the entry pathway into mathematics. It disenfranchises too many otherwise able people. What video game technologies can do is provide a User Interface to mathematics that much better suited to beginner-level learning. Today, study of the symbolic representation can be postponed until after the student has mastered the basic mathematical thinking in a more efficient way.
Jordan: I’m having some trouble grasping what this means in practical terms. Can you give me a real world example?
Keith: The same thing happened in computing. Starting with the Macintosh, then Windows, now (to some extent) tablet touch-interfaces, we have made computing accessible to everyone. That does not mean it is no longer useful to learn how to code. But in my day, the only way to use a computer was to begin by learning how to code. Today, you first learn how to use a computer, then you learn to code. That opens up computing (and coding) to far more people.
5. We need to know math’s limitations.
Jordan: You once wrote a book called Goodbye Descartes: The End of Logic and the Search for a New Cosmology of the Mind. Of your work, it is certainly among my favorites. Can you briefly explain the argument you make in that book? Why would a mathematician make an argument for the end of logic? And what does Descartes have to do with this?
Keith: In today’s world, where our Cartesian-based sciences and technologies play such a huge role in our lives and our societal structures, it is just as important to make people aware of the inherent limitations of mathematics as of its powers. Mathematics is like fire. We need it’s power to live. But it can also be unbelievably destructive, and must always be treated with immense respect.
Just as we have made great progress in the natural sciences and engineering, so too other researchers have made great strides in the sciences of the mind and in the social, psychological, and learning sciences. (Those latter three are, by the way, the true “hard sciences”. Referring to them as “soft sciences” is misleading, unless you understand the word “soft” in the William Burroughs sense of “The Soft Machine”, i.e., us.).
Jordan: It seems like you’re saying we need more interdisciplinary communication. I often write about how important it is to understand that there are many different kinds of truths, many different ways to make sense of our experience in the world.
Keith: When I moved to Stanford in 1987, I did so thinking I would benefit from being in one of the world’s leading technology research centers. And I did. But what changed me far more, was coming up against the world class expertise in the human sciences that Stanford also has. It was after working with (actually, mostly listening to) leading human scientists, and philosophers who consider those issues, that I was forced to reassess the role that mathematics can play in the human sciences.
Jordan: It is dangerous to believe that one particular way of seeing the universe can offer all the answers.
Keith: In the natural sciences, mathematics is the absolute ruler. If you break the mathematical rules, you are no longer doing physics, or astronomy, or whatever. But in the human sciences, mathematics is just a tool. A useful one to be sure, and getting more useful all the time, but still and all, just a tool. My book Goodbye, Descartes was an attempt to articulate what I saw as the inherent limitations of the mathematical approach (the “Cartesian approach”) in the human sciences.