TITLE: Open Mind, Closed Mind
AUTHOR: Eugene Wallingford
DATE: April 28, 2007 12:55 PM
I observed an interesting phenomenon working in a group this
Another professor, an undergrad student, and I are at Duke
University this weekend for a
on peer-led team-learning in CS courses. This is an idea
borrowed from chemistry educators that aims to improve
recruitment and retention, especially among underrepresented
populations. One of our first activities was to break off
into groups of 5-8 faculty and so a sample session PLTL
class session, led by an experienced undergrad peer leader
from one of the participating institutions. My group's
leader was an impressive young women from Duke who is
headed to Stanford this fall for graduate work in biomedical
One of the exercises our group did involved Soduku. First,
we worked on a puzzle individually, and then we came back
together to work as a group. I finished within a few minutes,
before the leader called time, while no one else had filled
in much of the grid yet.
Our leader asked us to describe bits about how we had solved
the puzzle, with an eye toward group-writing an algorithm.
Most folks described elements of the relatively naive
combinatorial approach of immediately examining constraints
on individual squares. When my turn came, I described my
usual approach, which starts with a preprocessing of sorts
that "cherry picks" obvious slots according to groups of
rows and columns. Only later do I move on to constraints
on individual squares and groups of squares.
I was surprised, because no one seemed to care. They seemed
happy enough with the naive approach, despite the fact that
it hadn't served them all that while solving the puzzle
earlier. Maybe they dismissed my finishing quickly as an
outlier, perhaps the product of a Soduku savant. But I'm
no Soduku savant; I simply have had a lot of practice and
have developed one reasonably efficient approach.
The group didn't seem interested in a more efficient approach,
because they already knew how to solve the problem. My
approach didn't match their own experiences, or their
theoretical understanding of the problem. They were
comfortable with their own understanding.
(To be honest, I think that most of them figured they just
needed to "go faster" in order to get done faster. If you
know your algorithms, you know that going faster doesn't help
at all with many, many algorithms! We still wouldn't get
After making this observation, I also had a realization. In
other situations, I behave just like this. Sometimes, I have
an idea in mind, one I like and am comfortable with, and when
confronted with something that might be better, I am likely
to dismiss it. Hey, I just need to tweak what I already
know. Right. I imagine
asking in his Texas drawl, "How's that workin' for ya?" Not
so well, but with a little more time...
When I want to learn, entering a situation with a closed mind
is counterproductive. This is, of course, true when I walk
into the room saying, "I don't want to learn anything new."
But it is just as important, and far more dangerous, when I
think I want to learn but am holding tightly to my preconceptions
and idiosyncratic experiences. In that case, I expect that
I will learn, but really all I can do is rearrange what we
already know. And I may end up disappointed when I don't
make a big leap in knowledge or performance.
One of the PLTL undergrad leaders working with us gets it.
He says that one of the greatest benefits of being a peer
leader is interacting with the students in his groups. He
has learned different way to approach many specific problem
and different high-level approaches to solving problems more
generally. And he is a group leader.
Later we had fun with a problem on text compression, using
Huffman coding as our ultimate solution. I came up with an
encoding targeted to a particular string, which used 53 bits
instead of the 128 bits of a standard ASCII encoding. No
way a Huffman code can beat that. Part way through my work
on my Huffman tree, I was even surer. The end result? 52
bits. It seems my problem-solving ego can be bigger than
warranted, too. Open mind, open mind.