Wolfram Research, a software company with deep mathematical and scientific expertise, is expanding to the broad education market with a range of mobile apps.
But although those apps hold the promise of turning smartphones into sophisticated next-generation calculators, they also raise questions about the best way for students to learn.
Smartphones in school
Should students' smartphones become calculators good enough to do everything up to multivariable calculus?
Wolfram Research got its start with the hard-core A New Kind of Science. It was therefore fitting that the company's "knowledge engine," , took a rigorous approach to facts and data., itself an offshoot of Stephen Wolfram's attempt to explain his mathematical view of the universe embodied in his book,
So perhaps it shouldn't have been a surprise that the company's first mobile application to use Alpha was similarly tailored for a refined audience and came with a correspondingly expensive price tag of $50. No doubt displeased with the response, Wolfram shortly after decided to "focus on ubiquity" and cut the price to $2.
Now Wolfram is showing signs that indicate a deeper understanding of consumer sensibilities, announcing new iOS applications called Wolfram Course Assistants to help students with algebra, calculus, and music theory. They tap into Alpha's Mathematica abilities behind the scenes, but they're focused, packaged, and reasonably priced at $2 for algebra and music theory and $3 for calculus.
Wolfram said on its blog that a lot more course assistants will arrive in coming months, and the iPhone, iPad, and iPod Touch won't be the only hardware to use the apps. "We're working on Android and also assessing other platforms currently," the company told me.
The apps look sensibly crafted and sensibly priced. Here's the bigger question I have, though.
I've been noodling with Mathematica recently, inspired by a foolish desire to explain to my son why I answered "infinity" when he asked me what 100 divided by 0 is. The more I looked at Mathematica, the more it seemed that all that struggling to find the integral of sec^3(x)dx in Mrs. Strong's 12th-grade calculus class was, in a sense, busywork.
Useful busywork, yes, that doubtless has afforded generations of engineers and physicists a deeper understanding of how the universe works, but still busywork.
Nobel laureate physicist Richard Feynman bemoaned how students lost their seat-of-the-pants understanding of logarithms and therefore some of their numeracy with the arrival of calculation devices.
But nowadays calculators are permissible in many schools and even tests for operations such as long division that Feynman doubtless would see as the rudiments of math. And even Feynman and fellow laureate Hans Bethe, sparring in numeric tests of mental agility, benefited from not having to derive everything from first principles.
Clearly, children need some understanding on their own of math, and reliance on a computer has a lot of drawbacks. But computers can also aid those who otherwise would fall by the mathematical wayside, or let people with more advanced abilities bypass drudgery and move on to the challenging material. Graphing calculators can let many students explore curves and functions that realistically they'd more likely ignore if they had to plot them by hand.
And extending beyond the realm of math, spell-check, and grammar-check software, though fallible, can still be a help. Sure, those writing aids may be crutches that enable a certain laziness, but after having seen my son wrestle with the arbitrary, inconsistent arcana of English spelling and reading countless misuses of "its" vs. "it's," I'm not convinced this knowledge truly can be flogged into every brain. I have some sympathy for those who want to permit spell-check software in school tests.
Yes, I'm ambivalent, but overall, I see computer-aided knowledge as an asset. Google and Wikipedia may often substitute for real research and learning, but in my experience they've opened up vistas of knowledge I hadn't realized existed, supplied me with resources I'd otherwise need a major university nearby to find, and helped me innumerable times to gratify my curiosity--and my son's as well.
Wolfram, as one would expect, argues its software augments traditional schooling.
In a sense the ultimate idea of our course-assistant apps is to provide automated expert tutoring for anyone anywhere. They're also a good way to "scope out" what's involved in a course, and work out as many examples as one wants.
For teachers, one of the interesting things is that the course assistant apps don't just do elementary examples: they handle the real-world cases too. So it becomes possible to explore concepts in much more realistic settings.
Though it's not yet clear to me how well the software itself lives up to that sales pitch, I see the merit of the company's education-boosting aspiration.