Math problems!
Joshua Zucker
I appreciate all the introductions, so we have a feel for what kind of
people are here in this discussion and what's going on in their lives,
but I'm even more interested in getting people to talk about math
content for math teachers' circles and for classrooms as well. I'd
also love to hear about the pedagogy of math teachers' circles and of
the problem-solving approach to classroom mathematics. So, here's my
first effort in that direction.
I've recently been mentioned in one of my favorite blogs, Numberplay,
at the New York Times:
http://wordplay.blogs.nytimes.com/2011/05/16/numberplay-danger-of-praise/
There's a bit of a connection to pedagogy there, but what I'm most
interested in is whether you think this problem is good for math
teachers' circles, and/or for middle school classrooms, and why. What
would you do with it in those situations?
You might find a lot of other good material in the archives of
Numberplay, too. Gary Antonick did a very nice series on problem
solving strategies. Here are some links to those.
SIMPLIFY: http://wordplay.blogs.nytimes.com/2010/08/02/numberplay-seat-six/
INCUBATE: http://wordplay.blogs.nytimes.com/2010/09/06/numberplay-a-little-reflection/
(I think I call this strategy "Patience")
INTUITION: http://wordplay.blogs.nytimes.com/2010/10/11/numberplay-the-ultimate-answer/
(What I like here is the way he shows that solving a harder problem
may give you the insight into an easier one, and vice-versa. I first
heard the last problem, about the pills, from Paul Zeitz at a
teachers' circle meeting.)
COLLABORATE: http://wordplay.blogs.nytimes.com/2010/11/01/numberplay-sum-fun/
. Gary definitely does a good job of weaving together ideas from his
commenters into an interesting discussion that often goes beyond the
original problem he posed. Collaboration between school teachers and
university mathematicians is certainly an important part of the
teachers' circles. I'm still not sure I know how to teach this very
well, despite all the research that I've seen and implementation
strategies to go along with it -- how do you get people to see
collaboration as a way of solving problems rather than as something
that a session leader or classroom teacher is making them do? And, as
I just mentioned in my previous post, how do you foster collaboration
between professors and school teachers?
--Joshua Zucker
Joshua Zucker
Gary Antonick, the NYtimes blogger that I referenced in my previous
post, has this to add.
--Joshua
---------- Forwarded message ----------
From: Gary Antonick
Date: Tue, May 17, 2011 at 4:10 PM
Subject: Re: Math problems!
To: Joshua Zucker <joshua...@gmail.com>
a couple thoughts on this:
1. it takes a group to solve group problems. roles are often emergent.
what are those roles and how can they best be filled?
Attached is a graphic I've been tinkering with. The flow diagram is
essentially a smoothed-out bar graph showing the volume of
contribution by reader. Ijnteresting to see that by volume alone you
can tell if the problem is deep or shallow, if it's a debate or
conclusion, etc.
2. it would be interesting to compare your teachers approaches to the
case study method that originated at harvard law school. A kind of
group socratic method incorporating real-life experience and often
wandering into topics of interest outside the original question.
