This is an edited excerpt from “How to Teach Computational Thinking,” first published by Stephen Wolfram on Sept. 7, 2016.
Pick any field “X,” from archaeology to zoology. There either is now a “computational X”, or there soon will be. Doctors, lawyers, teachers, farmers, whatever—the future of all these professions will be full of computational thinking. Whether it’s sensor-based medicine, computational contracts, education analytics or agriculture—success is going to rely on being able to do computational thinking well.
Computational thinking is going to be a defining feature of the future, and it’s an incredibly important thing to be teaching to kids today. But where does it fit into the standard educational curriculum? The answer, I think, is simple: everywhere!
One might think that computational thinking is somehow only relevant to STEM education. But it’s not true. Computational thinking is relevant across the whole curriculum. To social studies. To language arts. To music. To art. Even to sports. In every one of these areas there are very powerful—and often very clarifying—things that can be done with computation and computational thinking.
For instance, you can talk about a Shakespeare play and try to get a general sense of the flow in it. Well, with computational thinking you can imagine creating a social network for the play (for instance, who “knows” who through being in the same scene). And pretty soon you have a nice summary, that’s a place to launch from in talking about the nuances of the play and its themes.
Imagine you’re talking about different language families. Well, you can just take some words and use WordTranslation to translate them into hundreds of languages. Then you could make a dendrogram to show how the forms of those words cluster in different languages—and you can discover the Indo-European language family.
You could be talking about styles of art—and pull up lots of images of famous paintings that are built into the Wolfram Language. Then you could start comparing the use of color in different paintings—maybe making a plot of how it changed over time, seeing if one can tell when different styles came in.
You could be talking about the economics of different countries—and you could immediately create your own infographics, working with students to see how best to present what’s important. You could be talking about history, and you could use the historical map data in the Wolfram Language to compare the conquests of Alexander the Great and Julius Caesar. Or you could ask about US presidents, make a timeline showing their administrations, and compare them using economic or cultural indicators.
Let’s say you’re teaching English grammar. Well, it certainly helps that the Wolfram Language can automatically diagram sentences. But you can also let students try their own rules for generating sentences—so they can see what generates something they think is grammatically correct, and what doesn’t. How about spelling? Can computational thinking help with that? I’m not sure. It’s certainly easy to take all the common words in English, and start trying out different rules one might think of. And it’s fun to discover exceptions. (Does “u” always follow “q”?)
Everyone would like what’s learned in one class to be applied in others, but it doesn’t happen all that often. Most fields are taught in intellectual silos, with nothing learned in one even being referenced in others. With computational thinking, though, there’s vastly more cross-connection. The social network for the Shakespeare play involves the same computational ideas as a network for international trade, or a diagram of the relations between words in different languages. The visualization technique one might use for economic performance is the same as for sports results. And so on.
Computational thinking is really about thinking. It’s about formulating ideas in a structured way, that, conveniently enough, can in the modern world be communicated to a computer, which can then do interesting things.
There are facts and ideas to know. Some of them are about the abstract process of computation. But some of them are about how things in the world get made systematic. How is color represented? How are points on the Earth specified? How does one represent the glyphs of different human languages? And so on. We made a poster a few years ago of the history of the systematic representation of data. Just the content of that poster would make an interesting course.
So if one knows something about how to represent things, and about the processes of computation, what should one learn how to figure out? The fundamental goal is to get to the point where one is able to take something one wants to know or do, and be able to cast it into computational form.
Often that’s about “inventing an algorithm”, or “inventing a heuristic.” What’s a good way to compare the growth of the Roman Empire with the spread of the Mongols? What’s the right thing to compute? The right thing to display? How can one tell if there are really more craters near the poles of the Moon? What’s a good way to identify a crater from an image anyway?
It’s the analog of questions like this that are at the core of making progress in basically every “computational X” field. And it’s people who learn to be good at these kinds of things who will be the most successful in these fields.
Yes, once the algorithm or the heuristic is invented, it’s up to the computer to execute it. But inventing it is typically first and foremost about understanding what’s wanted in a clear and structured enough way that it can be made computational. With effort, one can invent disembodied exercises that are as abstract as possible. But what’s much more common—and useful—is to have questions that connect to the outside world.
Even a question like “Given a bunch of x,y pairs, what’s a good algorithm for deciding if one should plot them as separate points, or with a line joining them?” is really a question that depends on thinking about the way the world is. And from an educational point of view, what’s really nice about questions of computational thinking is that they almost inevitably involve input from other domains of knowledge. They force a certain kind of broad, general thinking, and a certain application of common sense, that is incredibly valuable for so much of what people need to do.
Computational thinking is something that I think can be successfully taught to a very wide range of people, regardless of their economic resources. And because it’s so new, countries or regions with more sophisticated educational setups, or greater technological prowess, don’t really have any great advantage over anyone else in doing it.
Eventually, much of the world’s population will be able to do computational thinking and be able to communicate with computers using code—just as they can now read and write. But today we’re just at the beginning of making this happen. I’m pleased to be able to contribute technology and a little more to this. I look forward to seeing what I hope will be rapid progress on this in the next year or so, and in the years to come.
