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Education & Academic

Flipping Out over Technology in Education

I’ve been interested in education for a long time, and when someone suggests that the software system I’ve been working on for 20 years is bad for education, I take it personally. So I was upset when a New Scientist magazine article “Physics Tool Makes Students Miss the Point,” reported on a study by Thomas Bing and Edward Redish, “Symbolic Manipulators Affect Mathematical Mindsets,” strongly implying that the study concluded that replacing paper-and-pencil calculations with Mathematica was educationally unsound. And I was greatly relieved to find that the study itself says no such thing. Bing and Redish don’t recommend banishing Mathematica; they welcome it in their classrooms and point out many positive things about it, along with one relatively minor pitfall they suggest ways to work around. What mindset led the reporter to jump to such a reactionary conclusion? Why use such an inflammatory headline in connection with level-headed research that showed, when you get right down to it, virtually the opposite of what the New Scientist headline says? The question of what technology to use in the classroom comes up all the time, and the resulting debate often generates more heat than light. People feel strongly about the subject because at its heart it is a question about what it means to be human.
Theodore Gray, Cofounder, Wolfram Research, Inc.; Founder, Touch Press
Education & Academic

Mathematica and the Fundamental Theorem of Calculus

Most calculus students might think that if one could compute indefinite integrals, it would always be easy to compute definite ones. After all, they might think, the fundamental theorem of calculus says that one just has to subtract the values of the indefinite integral at the end points to get the definite integral.

So how come inside Mathematica there are thousands of pages of code devoted to working out definite integrals---beyond just subtracting indefinite ones? The answer, as is often the case, is that in the real world of mathematical computation, things are more complicated than one learns in basic mathematics courses. And to get the correct answer one needs to be considerably more sophisticated. In a simple case, subtracting indefinite integrals works just fine. Consider computing the area under a sine curve, which equals

Oleksandr Pavlyk, Senior Kernel Developer, Algorithms R&D
Announcements & Events

Ten Thousand Hours of Design Reviews

It’s not easy to make a big software system that really fits together. It’s incredibly important, though. Because it’s what makes the whole system more than just the sum of its parts. It’s what gives the system limitless possibilities—rather than just a bunch of specific features. But it’s hard to achieve. It requires maintaining consistency […]

Stephen Wolfram
Products

Gizmos, Gadgets and Gears

I do love gadgets, linkages, clockworks, all that 19th-century cogs-and-wheels technology. So much easier to see than our 21st-century nanotubes and zillion transistors on a chip.

Sándor Kabai has written many Demonstrations illustrating such mechanisms.

What makes these interesting is that playing with the various parameters lets you vary both the geometric setup and the controls that make the mechanism go through its motion.

George Beck, Document & Media Systems
Announcements & Events

Mathematics, Mathematica and Certainty

Not a lot gets written in the general press about foundational issues in mathematics, but this afternoon I found myself talking to a journalist about the subject of certainty in mathematics. It turned out to be a pretty interesting conversation, so I thought I’d write here about a few things that came up. Mathematics likes […]

Stephen Wolfram
Leading Edge

Creating My Website with Mathematica

As readers of this blog might know, I have an unhealthy interest in the chemical elements. And Mathematica. The combination means that all my element-related projects are created using almost no tools other than Mathematica. It’s not that I use it because I feel like I should---I certainly use other programs when appropriate (Photoshop, for example). It’s just that Mathematica is the best available tool for many of the things I want to do. Really. My latest project is the website periodictable.com. Let me say right off the bat that this is a fabulous domain name. It took me months of convincing and no small amount of cash to acquire it. It really deserves to host the definitive online periodic table reference website, not just another run-of-the-mill online periodic table, of which there are thousands. Take a quick look at it here.
Theodore Gray, Cofounder, Wolfram Research, Inc.; Founder, Touch Press
Announcements & Events

Hidden in Plain Sight

Last month, we hosted our annual technology conference here at our headquarters in Champaign, Illinois, where hundreds of Mathematica users from around the world came to show us what they’ve been working on and to see what we’ve been up to. A lot of the conference presentations are now available on our website, so you can take a look at them even if you didn’t have a chance to attend this year.
Nilay Gandhi, Corporate Communications
Computation & Analysis

A Thousand Points of Light

The spinthariscope, invented and beautifully named by William Crookes in 1903, is a device for seeing individual atoms. Or at least, seeing the death of individual atoms. A spinthariscope consists of a needle, similar to a watch hand, positioned in front of a zinc sulfide luminous screen, with a magnifying glass focused on the screen. At the end of the needle is a small patch of radioactive material. Originally radium was used; more recently polonium, uranium and americium have been found to be safer.
Theodore Gray, Cofounder, Wolfram Research, Inc.; Founder, Touch Press
Announcements & Events

The Prize Is Won; The Simplest Universal Turing Machine Is Proved

“And although it will no doubt be very difficult to prove, it seems likely that this Turing machine will in the end turn out to be universal.” So I wrote on page 709 of A New Kind of Science (NKS). I had searched the computational universe for the simplest possible universal Turing machine. And I […]

Stephen Wolfram
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