Livingdeb recently threw down a gauntlet on how math textbooks and the pedagogical approach of discovery-based learning sort of suck. Despite my efforts to be brief, I basically wrote an entire blog post worth of response on her site. (But really, I did only say a fraction of what I could have said!) Check it out.
It's a hugely complicated issue, and there are valid arguments/criticisms on all sides of the debate. And the discussion is so dominated by anecdotal arguments that it can be difficult to have any sense of where the preponderance of the evidence lies. I can counter the experience using an exploratory-based math program of the novice (and short-timer) math teacher Livingdeb cites with a dozen teachers who have found such an approach very effective in their classrooms (and who have TAKS scores to help bolster the claims), but the teachers I know from the curriculum development project I am working on are likely to be unrepresentative of math teachers at large. They seem a strikingly intelligent, motivated, passionate group of people who have what it takes to lead kids successfully through a journey to mathematical enlightenment. (Sounds grandiose, doesn't it? But these people think big.) It's not clear whether this can be replicated with run-of-the-mill teachers.
Thoughts?
3 comments:
As with many things, I'm sure this depends somewhat on both the teacher and the student. I've always been better at learning/remembering how to arrive at an answer versus rote memorization, so anything I can re-discover on my own that I may have forgotten is great. It does require a deeper level of understanding for the teacher, though, and also a realization that the thought process can vary for individual students... so two students may arrive at the same right answer different ways. It's harder to use a one-size-fits-all approach that way, I'd suspect, versus just saying hey memorize this particular thing for the test.
There are so many interesting avenues to explore, and so many empirical questions that I don't know the answer to. I agree that there can be a difference between an approach that ends with a kid knowing how to solve a lot of math problems now, and one that leaves the kid with a lifelong interest in math.
I tend to feel that too many people are turned off from math by the way it is taught, but at the same time, it could be that those exact methods are the most fruitful ones for cultivating math talents in the most talented, which leads to another obvious question: Is it better for a curriculum (in general) to lead to some superstars or high performers, or to encourage a general literacy? (Are those ever actually opposed? Perhaps.)
This area is pretty much endlessly fascinating to me. I should probably take that as a sign to learn more about it.
Tam, if you decide you want to pursue a PhD in math education, I can hook you up ;)
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