Yesterday at the ASEE conference, I attended mostly sessions run by the Liberal Education Division. Today I gravitated toward the Mathematics Division, which is sort of an MAA-within-the-ASEE. In fact, I recognized several faces from past MAA meetings. I would like to say that the outcome of attending these talks has been all positive. Unfortunately it’s not. I should probably explain.
The general impression from the talks I attended is that the discussions, arguments, and crises that the engineering math community is dealing with are exactly the ones that the college mathematics community in general, and the MAA in particular, were having — in 1995. Back then, mathematics instructors were asking questions such as:
- Now that there’s relatively inexpensive technology that will do things like plot graphs and take derivatives, what are we supposed to teach now?
- Won’t all that technology make our students dumb?
- Won’t the calculus reform movement dumb down our curricula with all this nonsense about graphs and multiple representations and so on?
- How can you seriously call a person a mathematician/engineer if they can’t [insert calculation here] by hand? What if they are in a situation where they don’t have access to technology?
And yet, I actually heard all of these questions almost verbatim from mathematics and engineering professors this morning, multiple times. (To the great credit of the speaker who was asked the last question, he replied: If an engineer is ever in a situation where he is without access even to a calculator, we have a lot bigger problems on our hands than just bad education. TRUTH.) I was having serious third-year-of-grad-school flashbacks.
These questions aren’t bad; they’re moot. In 1995, mathematical technology was just at the level of expense, accessibility, and functionality that these questions needed to be dealt with. Students could conceivably purchase calculators for a couple hundred dollars that were small enough to slip into a backpack and could calculate \(\int \ln(\cos x) \, dx\) symbolically. Should we ban the technology, embrace it, regulate it, or what? Should we change what and how we teach? The technology could be controlled, so the question was whether we should, and to what extent, and these were important questions at the time.
But that was 1995. What the TI-92 could do in 1995 can now be done in 2010 using Wolfram|Alpha at no expense, using any device with an internet connection, and with functionality that is already vast and expands every other week. (This says nothing about W|A’s use of natural language input.) The technology is all around us; students are using it; there is no argument against expense, accessibility, or functionality that can reasonably be made. It’s going to affect what our students do and how they accept what we present to them regardless of what we think about it. So I’d suggest that questions such as What do students need to know how to do in an engineering calculus course? and How do we ensure they can do those things? are better questions for now (and might even have been better then).
Some of the conceptions of innovative teaching and learning strategies I saw also seemed stuck in 1995. I won’t name names or give specific descriptions in order not to offend people who probably simply don’t know the full scope of what’s gone on in mathematics education in the last 15 years. (Although I must call out the one talk that highlighted the use of MS Excel, and claimed that there were no other tools available for hands-on work in mathematics. Augh! You should know better than that!)
I will simply say that people who concern themselves with the mathematical preparation of engineers simply must look around them and get up to speed with what is happening in technology, in the cultures and lives of our students, and in what we know now about student learning that we didn’t know then. Read some seminal MAA articles about active learning. Talk to other people. Read some blogs. Something! We can’t stay stuck in time forever.