After this recent post on the state of mathematics education, I was pointed to this response by Al Cuoco (HT: former guest blogger Corey Andreasen). Here is the introduction:
A recent editorial in the New York Times:
puts forth a plan to “fix math education.”
The arguments presented are variations on themes that have surfaced (and been debunked) several times over the past century. The ones in this NYT piece are especially weak examples of this genre.
Cuoco then proceeds to deal with the article point by point, and correct what he feels are incorrect characterizations of the real standards. At the end, he concludes:
In the field tests of early versions of our precalculus course, we held an advisory board meeting of high school juniors and seniors (many of them “very weak” in terms of traditional measures). This was at the end of the first term; up to that point, students had been experimenting with recursively defined functions, modeled in a CAS on their calculators, finding closed forms for such functions, proving that their closed forms and the recursive models were equal on the non-negative integers by mathematical induction, and then doing a bit with Lagrange interpolation. At the meeting, Wayne Harvey asked the question, “What’s different about this course from others you have taken?” Four kids answered, almost in unison, “It’s more realistic.” That response was startling, even to us, because “realistic” is usually taken to imply everyday or other “real world” contexts, and this was purely mathematical. But what the kids meant was that it felt more like real work, more like the kind of thinking they must do when they are solving a real problem—what mattered was that they got a chance to exercise their own creativity. What mattered was how, not where, their mathematics was used.
This issue of viable and engaging contexts is complicated for a couple reasons. Many of the students in my high school classes came from situations that many of us would find hard to imagine; the last thing they cared about was how to balance a checkbook or figure the balance on a savings account. But they loved solving problems. For another thing, reality is relative. The authors claim that “it is through real-life applications that mathematics emerged in the past, has flourished for centuries and connects to our culture now,” and I agree. But the best mathematicians and scientists I know, and the students in my classes who really got it (and these were not necessarily the “good students”)—who saw the power and satisfaction one can derive from doing mathematics—all see mathematics as part of their real world.
You can read the full response here.
Once again, I’m not really an expert on high school mathematics education, so I am willing to admit that I might have “fallen” for the misrepresentation of the standards. Andreasen certainly seems to be endorsing the view expressed by Cuoco. We have plenty of departmental alumni out there teaching, and many of my friends from the AP Statistics work that I do teach in the high school setting. Any of you want to offer your perspective to help me understand the discussion better?