[plt-scheme] Guzdial: "I heart HtDP"

From: Todd O'Bryan (toddobryan at gmail.com)
Date: Wed Mar 10 18:16:43 EST 2010

Why is it, my dear colleagues, that people are so generally stupid?

My school district has invested oodles of energy, money, and marketing
in inquiry-based, constructivist approaches to science and math
education. Apparently, kids who have struggled with math previously
just love it--they work in groups a lot, answer questions about how
the problems make them feel, and don't get tested all that much, so
they don't realize how little they understand.

By way of contrast, the teacher next door to me attended a workshop
for math teachers last year and the presenter asked how teachers
present logarithms. The choices were: (a) you teach the rules that
logarithms follow and drill students on the rules until they are
logarithm-solving machines, or (b) you teach the concept of a
logarithm and force the students to derive the rules based on what a
logarithm is. Fully one-half of the teachers in attendance chose (a).

Especially in K-12 education, we're continually forced to choose
between false dichotomies. "Teach them concepts. Don't drill and kill.
If students understand *how* to do the math, they'll be able to do the
math." At the other end is a method I call cookbook math. "You don't
need to understand why it works, just do what I say. If you see a
problem like this, do this. If you see a problem like that, you can
change it into a problem like this by doing these steps."

We need both/and. Students have to understand what they're doing, but
they also have to have fluency at just doing it. Most 14-year-olds
understand *how* to drive a car, but we don't let them drive cars
because they haven't had enough practice to be good at it. Knowing how
to solve a quadratic is a lovely thing, but it's useless if you can't
actually do it.

The classes I've enjoyed the most manage to straddle this divide very
well. What students can figure out on their own, they figure out,
because teachers provide very carefully chosen examples. But even when
students can't figure it out, they're shown how something works and
why. You see lots of examples and you work through lots of examples
before you're asked to do something on your own. And regardless of
what brilliance or drivel students come up with on their own, the
teacher takes the time to get the "real answer" out there and to
develop it with a sufficient level of formality that students know
what they're supposed to have learned.

I think both Shriram and Kathi, the two people who initiated me into
the HtDP cult, are masters of this technique. When they teach, it
feels like all the ideas are coming from the students and the class is
creating its own little view of the world. It feels like "discovery"
and "inquiry," but don't be fooled--they know exactly where they're
going and their questions and examples are designed to get from point
A to point B. If you come up with an idea that would take the class on
a detour to point C, they'll come up with an example that will make
you think point C is probably not a good place to visit.

I think all of HtDP has this feel. We're "discovering" things that are
self-evident, but they're really not self-evident, and the people who
came up with them are brilliant because they make them seem so.

OK. I can breathe again and go on with my life.


On Wed, Mar 10, 2010 at 5:18 PM, John Clements
<clements at brinckerhoff.org> wrote:
> In a blog post reprinted in CACM, Mark Guzdial draws attention to a 2006 paper by Kirschner, Sweller, and Clark (Educational Psychology, not CS-specific), that suggests that project-based / constructivist teaching theories are junk.  Guzdial draws a broken conclusion (that we should not have students program), but the basic message of this research is that books like HtDP that work directly to provide students with the long-term memory structures that will help them categorize problems and solutions are much much better than the alternative.
> John
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