Category: Computational Thinking

What Is a Computational Essay?

A Powerful Way to Express Ideas

People are used to producing prose—and sometimes pictures—to express themselves. But in the modern age of computation, something new has become possible that I’d like to call the computational essay.

I’ve been working on building the technology to support computational essays for several decades, but it’s only very recently that I’ve realized just how central computational essays can be to both the way people learn, and the way they communicate facts and ideas. Professionals of the future will routinely deliver results and reports as computational essays. Educators will routinely explain concepts using computational essays. Students will routinely produce computational essays as homework for their classes.

Here’s a very simple example of a computational essay:

Simple computational essay example

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High-School Summer Camp: A Two-Week Path to Computational Thinking

The Summer Camp Was a Success!

How far can one get in teaching computational thinking to high-school students in two weeks? Judging by the results of this year’s Wolfram High-School Summer Camp the answer is: remarkably far.

I’ve been increasingly realizing what an immense and unique opportunity there now is to teach computational thinking with the whole stack of technology we’ve built up around the Wolfram Language. But it was a thrill to see just how well this seems to actually work with real high-school students—and to see the kinds of projects they managed to complete in only two weeks.

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Machine Learning for Middle Schoolers

(An Elementary Introduction to the Wolfram Language is available in print, as an ebook, and free on the web—as well as in Wolfram Programming Lab in the Wolfram Open Cloud. There’s also now a free online hands-on course based on it.)

An Elementary Introduction to the Wolfram LanguageA year ago I published a book entitled An Elementary Introduction to the Wolfram Language—as part of my effort to teach computational thinking to the next generation. I just published the second edition of the book—with (among other things) a significantly extended section on modern machine learning.

I originally expected my book’s readers would be high schoolers and up. But it’s actually also found a significant audience among middle schoolers (11- to 14-year-olds). So the question now is: can one teach the core concepts of modern machine learning even to middle schoolers? Well, the interesting thing is that—thanks to the whole technology stack we’ve now got in the Wolfram Language—the answer seems to be “yes”! Continue reading

Launching Wolfram|Alpha Open Code

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Wolfram|Alpha and Wolfram Language logos

Code for Everyone

Computational thinking needs to be an integral part of modern education—and today I’m excited to be able to launch another contribution to this goal: Wolfram|Alpha Open Code.

Every day, millions of students around the world use Wolfram|Alpha to compute answers. With Wolfram|Alpha Open Code they’ll now not just be able to get answers, but also be able to get code that lets them explore further and immediately apply computational thinking. Continue reading

Computational Law, Symbolic Discourse and the AI Constitution

Leibniz’s Dream

Computational Law, Discourse Language and the AI Constitution Gottfried Leibniz—who died 300 years ago this November—worked on many things. But a theme that recurred throughout his life was the goal of turning human law into an exercise in computation. Of course, as we know, he didn’t succeed. But three centuries later, I think we’re finally ready to give it a serious try again. And I think it’s a really important thing to do—not just because it’ll enable all sorts of new societal opportunities and structures, but because I think it’s likely to be critical to the future of our civilization in its interaction with artificial intelligence.

Human law, almost by definition, dates from the very beginning of civilization—and undoubtedly it’s the first system of rules that humans ever systematically defined. Presumably it was a model for the axiomatic structure of mathematics as defined by the likes of Euclid. And when science came along, “natural laws” (as their name suggests) were at first viewed as conceptually similar to human laws, except that they were supposed to define constraints for the universe (or God) rather than for humans.

Over the past few centuries we’ve had amazing success formalizing mathematics and exact science. And out of this there’s a more general idea that’s emerged: the idea of computation. In computation, we’re dealing with arbitrary systems of rules—not necessarily ones that correspond to mathematical concepts we know, or features of the world we’ve identified. So now the question is: can we use the ideas of computation, in very much the way Leibniz imagined, to formalize human law? Continue reading

How to Teach Computational Thinking

The Computational Future

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. There’s always lots of discussion (and concern) about how to teach traditional mathematical thinking to kids. But looking to the future, this pales in comparison to the importance of teaching computational thinking. Yes, there’s a certain amount of traditional mathematical thinking that’s needed in everyday life, and in many careers. But computational thinking is going to be needed everywhere. And doing it well is going to be a key to success in almost all future careers.

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 computational agriculture—success is going to rely on being able to do computational thinking well.

I’ve noticed an interesting trend. Pick any field X, from archeology to zoology. There either is now a “computational X” or there soon will be. And it’s widely viewed as the future of the field.

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