Keith Devlin, Stanford University
The US ranks much worse than most of our economic competitors in the mathematics performance of high school students.
We now have the knowledge to turn that around. We could raise the level of mathematics performance across the board, within a single school generation, so that we are number one in the world. All it would take is a one-time, national investment of $100 million over a five-year period. That’s what it would cost to build and put in place a system that could achieve that change, with the existing school system and the existing teachers. Once built, that system would be self-sustaining.
That sounds like a lot of money for an upfront investment. But thought of as a national initiative, it’s peanuts. The payoff for the nation’s health and future prosperity is far greater than the long term benefits we got from the far greater investment in NASA’s Apollo Program to put a man on the Moon.
I don’t think it’s going to happen in this way, but not because people don’t think it’s a good idea. Rather, it would probably require a combination of nonprofit and for-profit funding that our system does not allow.
The same goal can, and surely will, be attained. But it will take a lot longer.
I’ll tell you, briefly, what the approach is, how I am so sure it will work, and where I got that cost figure. Everything I say is based on work that has already been done.
First, let me tell you who I am.
I’m a mathematician at Stanford who directs a multidisciplinary think tank called the H-STAR institute, that looks at issues involving human sciences and new technologies, with a view to improving technology design and use, including applications of technology in education at all levels. (I’m also the Math Guy on National Public Radio.)
What I want to tell you about is connected with the H-STAR institute, but is based on some work I’ve just completed as an individual, working with a large software company in Silicon Valley.
We have spent the past four years looking to see if we can use the range of today’s technologies to improve the dismal math performance level of the nation’s high school students.
The slide in math performance among US children occurs during the age range 8 to 13. Essentially the middle-school years. That was the target group for our study.
Many attempts have been made to improve US middle-school mathematics education, but all have failed to achieve the desired results. I think the reason is clear. They have all focused on improving basic math skills.
In contrast, I (and a great many of my colleagues) believe the emphasis should be elsewhere. Mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free.
There are two reasons why the focus has been on skills. First, many people, even those in positions of power and influence don’t understand what mathematics is and how it works. All they see are the skills, and they think, wrongly, that is what mathematics is about. (Given that for most people, their last close encounter with mathematics was a skills-based school math class, it is not hard to see how this misconception arises.)
The other reason is more substantial. For over two thousand years, the only way to provide mathematics education to the masses was through the written word. Textbooks. But in order to learn mathematical thinking from a textbook, you have to approach it via the skills. That means you have to master the skills first.
But as I already remarked, mathematics is not about acquiring basic skills or learning formulas. It’s a way of thinking. It’s not about things you know, it’s something you do. And the printed word is a terribly inefficient way to learn how to do something.
The best way for an individual to learn how to do something is, as the Nike slogan says, “Just do it!”
Until now, learning by doing was not a viable approach to mathematics education. It was possible one-on-one, by an apprenticeship system, but not on a broad scale. Now it can be done.
We now have the know-how to raise the mathematical performance of our nation’s schoolchildren in the 8 to 13 age-range to the top of the world rankings in a single school generation.
The method is simulation. That’s the way we train pilots to fly aircraft, the way we train astronauts to fly the shuttle and to work in the Space Station, the way we train surgeons, and the way the US Army trains soldiers before they go anywhere near the battlefield.
And that’s the way we should train young people to think mathematically.
The technology to do that has been provided to us by the leisure and entertainment industries. Basically, it’s videogame technology and Web 2.0 infrastructure.
No one has yet tried to do this on the scale that is required. Yes, there are a lot of so-called math ed videogames out there. Lots of them are very superficial, some are more thoughtfully designed. But they all focus primarily on skills. They use the compelling nature of videogames as a wrapper for conventional curriculum, to try to get kids to learn and practice the basic skills. But as I’ve noted, mastery of skills does not lead to mathematical thinking.
For over two thousand years, mastery of mathematical skills had to come before developing the higher level thinking because we did not have simulators. All we had was books. Now we know how to build simulators.
Based on the work I and my colleagues have done over the last four years, we have a pretty good sense of what it would take to build such a simulator. That’s where I get my figure of $100 million over five years. Building the simulator in the first place would cost around $50 million. (That was the cost of building World of Warcraft.) The remaining amount is what it would cost to build the infrastructure to support and maintain the system for use across the nation. Once in place, it could be self-sustaining through user subscriptions.
I totally agree about simulation, although my experience is much less high-tech.
While teaching at Three Village CSD on Long Island in the early-mid 70’s, I taught many units using Unified Science and Math in the Elementary School (USMES). The unit of teaching metric measurement using cardboard carpentry was taken to a higher level with my fifth-graders.
As a class we discussed what “furniture” we would like to enhance our classroom and its functionality. They suggested tables, bookshelves, storage units, walls and the like. We then broke into five teams of five students each. Each team measured the classroom (metrically), divided the dimensions by ten and drew a scale model of the room on a large sheet of paper. As a team, they discussed what pieces of furniture they would like and determined the size and placement within their scale classroom. Each member then created a scale model of their selected piece using oak tag and slot construction. When completed, a class meeting was held to select pieces to construct for our classroom. There was much discussion and decision-making, as we couldn’t have only tables or only shelves. Once one model from each team was selected, the members multiplied the dimensions by ten, measured, and then drew precise cut lines on tri-wall cardboard. Each team member had the privilege of making a cut with the electric saw and specialized cardboard-cutting blade, supervised one-on-one by their teacher. The carefully cut pieces were then assembled into the furniture depicted by their models, and once painted, were a welcome addition to our busy classroom. In the end, the students not only understood linear metric measurement, but gained valuable teamwork, decision-making and basic construction skills.
Thank you for your recognition that math instruction and student progress is not solely the problem or responsibility of classroom teachers. I teach math to over 21 8-9 year olds every day. I want them thinking; I want them moving past basic skills & memorization. But I HAVE to teach the curriculum and aim for the benchmarks established by my state education dept, my board of education and my administration. The math they work on is budgets and student data from multiple choice testing. The other math concept that impedes what I want to do is TIME. I have to fit SO much into one school day. The exploration and problem-solving methods take more time and frequently, at the moment a connection is being made or a solution is being reached, we are interrupted by scheduling. Keep working on that simulator!!
[...] Keith Devlin wants to build a virtual game on the scale of WoW that helps people learn to think mathematically. He thinks that commercial game developers will not be motivated to spend the necessary money to build an educational game. I’m not so sure that’s true. If it’s a good game, what geeky gamer doesn’t want to be in a world of math? I would play. In fact, I’m very tempted to buy an early reading program, ItzaBitza, because it’s just a really great game. Click the “Try ItzaBitza” button for a 15 minute free trial and you’ll see what I mean. I hope I can spend my gaming dollars to learn things like higher math, physics, and programming someday soon. Possibly related posts: (automatically generated)Confessions of a Twitter ConvertTWG- Vol 11- Pale, anti-social and reclusive: The Gamer (Homo Sapiens Ludus…Summer Gaming PlansFavorite game arguments transcend hobbies Leave a Comment [...]
I admire your goals, but I’m not precisely sure what sort of system you’re calling for. “Simulator” is a broad concept, and while World of Warcraft is mentioned, I’m confused as to how far to take the analogy.
Is there somewhere online where you’ve given a broad overview of how the simulator works, what a single “gaming session” would be like, how the games would improve math skills, etc.?
Dr. Devlin, I enjoyed your thought provoking suggestion. I particularly like that you emphasized the importance of focusing on developing mathematical thinking rather than mathematical skills. For your “plan” to work as you describe it, I think we would need funding to address one important related issue. I am confident we would need to provide the appropriate professional development for middle grade mathematics teachers so that they could effectively use the simulator to help students focus on mathematical thinking, establish relationships, make connections, etc. I think most teachers could handle the mechanics of the simulator – helping them to learn how to draw the important mathematics out of those activities would require professional development for many.
Thanks again for sharing these thoughts!
This sounds really great to me.
I hope that careful thought is given in serving the needs of the visually impaired. They, also, are quite capable of learning to think mathematically.
Are OERs safe? The model seems to be to get people committed to something, then either make it “for pay” or offer a for pay Pro version, which causes the free version to stagnate. Specifically, I love GeoGebra, but fear that Google financial support may affect the direction of GeoGebra. Certainly, if Google is pulling the strings, they will not push to solve the issue of GeoGebra not running on Apple’s iPhone and iPad.
Dear Keith, there is at least one flaw in your argument. The pilots, the astronauts, the surgeons become such after passing rigorous selection process. And the selection is a necessity, not everyone could become a good pilot or a surgeon.
Why not to simply admit that there is absolutely no reason to expect everyone’s math mastery. What reason there might be? Do not you agree that the fact of widespread innumeracy logically contradicts the claim that somehow people need math to make a better living.
Your simulator may give a better chance to some. There is little doubt it will leave many as nauseated as if they were in a flight simulator.
Prove it. Get some school to allow you to run their math curriculum for a number of years with a well-designed evaluation to assess results. Then you will have earned the ability to make the claims you make in the above article.
Here are my 2 cents…
Many of us want to transform the system and there are many ideas but in my view we need to look at the needs of the teachers. The teachers are the key. the 1-1 communication in the classrooms. The sacred moments of understanding… the ahha experiences…
I think we should encourage Keith Devlin and include him in the universal effort that we are doing collectively but not see this 100 million dollar adventure as the only way. In my opinion GeoGebra is already a Billion program project that needed no money but just a few committed individual who were guided to create this and probably there are other things going on right now that some of us are aware and others are not but the main point is teachers. How to give us (them) back the freedom and the responsibility also.
–Dani
I agree with many of you. Thinking mathematically and exploring, investigating and to learn by doing is so valuable. The problem is, where do we get the time? As a teacher I feel very pressured to get through the text book and “drill and kill”. It may not be as fun as using manipulatives and talking in groups about what they think, but I usually don’t have much choice in the matter. The the mathematical performance of our nation’s schoolchildren is not as good as it could be. A lot of the time upper grade teachers spend time going over basic facts and skills that the kids did not learn in younger grades, which is another problem. As a Kindergarten teacher, I am doing my best to give the kids the basics while also letting them explore so they are prepared when they move on to upper level math.
I think the “simulator” is a great idea and would love to see how it works! As Anne said, see if you can get a school to allow you to run their math curriculum and evaluate it and report the results!
You have said something interesting about creating a game. But, I think there is a flaw. Instead of making one game with subscriptions. There should be more, competing with each other with a fixed subscription rate to ensure continuing progress and innovation. Each of these games should be able to cater to the entire audience (girls/boys, individual likes/dislikes, etc.)
Furthermore, I don’t think that you have to make an all out game. Maybe sticking with concepts that work (flash video games), but in a ‘Open Graph Framework’ (think facebook). You can even introduce game dynamics (like in SCVNR) to create a dedication closer to that of Farmville.
I think these ideas should substantially cut costs and increase the practicality of the Apollo Program for Math.
Remember, build on existing models that work! Build cheap, fast, many, and make it scalable!
More on game dynamics:
http://www.ted.com/talks/seth_priebatsch_the_game_layer_on_top_of_the_world.html (sorry, I don’t know where the TED shortener went)
Now all you have to worry about are those pesky/useless Teacher unions and publications (McGraw Hill, etc.)
[...] Keith Devlin has proposed a “simulator” to teach mathematics via an integrated videogame world. Essentially he wants to tap the same effect seen in a study of Brazilian street mathematics where mathematics done in a natural environment gives a high success rate even when the exact same test subjects do badly on a formal test of the same concepts. [...]