You may have heard that San Jose State University's recent partnership with Udacity ended with MOOC-enrolled students passing courses at much lower rates than their on-campus cohorts. Lots has been said about these results (Phil Hill has a good round-up of the coverage) but there's one line that deserves more coverage:
When students did get to the online programs, even navigating the computer systems could be daunting. One of the questions that tutors were frequently asked was how to do exponential notation on a computer.
Again we find computers are not a natural medium for doing mathematics. There's nothing intuitive about pressing Shift + 6 to write an exponent, no inherent connection between the idea and the action. This isn't true for computer science, where the medium is perfectly suited for the course. Or even for English composition, where typing words is only one intuitive abstraction away from writing them with a pen.
I'd wager 90% of people reading this already know how to type an exponent on a computer. They believe it's easy enough to teach and I don't think they're wrong. But this is only one instance of a problem with a lot of reach. Notation makes math difficult on a computer. But notation also makes math more powerful and interesting. That tension will be very difficult to resolve and, so far, online math providers have generally resolved it in favor of the computer at the expense of math's interest and power.
In our relentless transition from classroom-based math to computer-based math, these SJSU-Udacity results offer us a chance to pause and ask ourselves, "What's now missing?"
2013 Jul 26. Okay, taking friendly fire on Twitter, I posed this challenge:
Use a computer to compose a clear proof that a triangle's midsegments create similar triangles and send it to me for assessment.
My guess is you'll find the process a lot less annoying and a lot more clear when you pick up a pencil and some paper.
But on the other hand, the reality is that if our students use math any time later in their life, there’s a really good likelihood it will involve a computer, whether it’s using Mathematica to solve complex problems, doing computer programming, or just entering formulas in Excel. There is value in learning the notation for entering formulas in a computer, and it provides an valuable side benefit of reinforcing proper syntax to ensure proper order of operation.
I’ve slowed down on the Euler Project problems, but last I checked, I was just short of 200. Those problems require a computer to do the math, but you don’t do the math on the computer. I have a notebook (ink on paper) dedicated to that that has a couple hundred pages filled with notes and drawings – that’s the math.