Wednesday, July 6, 2011

A manifesto for "Gen X": Mathematica and the future of math education

Well, that's a heck of a post title! I don't have the slightest notion what specific effects Mathematica will have on mathematics education, but I can make some guesses. I just got done participating in a Webinar with Kelvin Mischo from Wolfram on the Wolfram Demonstrations Project. If you've not found this site yet, it is a phenomenal resource. The Webinar itself was organized and hosted by Maria Droujkova of the Math Future 2.0 group. I have played with Mathematica for about a year now, and it is an amazingly impressive piece of technology.

So: what is the "Generation X" doing in the post title? Well, those of us who teach math and who were born sometime from the mid-1960s to the late 1970s have seen technologies both disappear from and enter into our own mathematics educations. I am probably one of the older people who never used a slide rule, for instance (and never even learned how to use one), but my teachers were resistant to the use of calculators, the "replacement" technology for slide rules. I never was allowed to use a calculator prior to my precalculus course in my junior year of high school.

I have decided that this is an advantage. We Gen-X teachers know what is lost when a technology leaves the field (e.g., slide rules), and when one replaces it (e.g., calculators). We are probably the last generation who was almost exclusively taught arithmetic "by hand" and who were expected to master it "by hand" as well. I know, I know - teachers today claim that they do not allow the use of calculators in their classes.  But I also know that students are using them at home, for homework or other practice, and that THAT is what is different now. That, along with testing pressure, the increasing number of special education/504 students, and other issues which I will ignore here.

So here we are, face-to-face with yet another "game-changing" technology, and the powers that be do not know how to respond.

I claim that our generation does. I claim that we "Gen-X"-ers are uniquely positioned to help our students make sense of this new technology. I claim that we can (and must) know how to use these new tools to help our students learn what is important, while at the same time respecting the skills that are being lost. In short, one of our jobs should be to show how the technology can be used in a complementary fashion to the more traditional ways of learning mathematics. And, as students get further along in their math careers (say, from elementary to middle school or from middle to high school), teachers should be able to gently steer students away from the "rote" or "mechanical" calculations beloved by textbooks and into more interesting waters. Not completely, mind you, but to an appropriate extent (appropriate, that is, for a new century).

It is obvious to many that the power of this new technology is having an enormous impact on mathematics teaching. So many of the things that we teach are becoming "Wikipedia-ized" or "Google-ized". Why do students need to know how to factor a 4th-degree polynomial by hand when you can put it into Wolfram|Alpha and get the answer? I've made this point before, but as I learn more, it is apparent that mathematics educators need to change their game or get out of it.

In my "step up or get out" category:
  • The National Council of Teachers of Mathematics
  • The Common Core Standards Initiative
  • The College Board
  • among others.
I don't mean to imply that these groups don't do good work or mean well. But their model of what math is and how it should be taught and learned is largely behind the times, woefully so. Students now have tools at their disposal that even the most optimistic progressive educator of the early 20th century could not have imagined. It's high time that the students be allowed to use them, and it's high time that we educators figure out productive, interesting, challenging, deep, and (yes) meaningful things for our students to learn from them. To help students understand the importance of quantitative thinking, students need to know what their options are, and it's our job to help them out. I believe that those of us who are fortunate enough to be of Generation X are uniquely positioned to tackle this extremely difficult but necessary task.

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