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Topic: nctm-l-digest V1 #91
Replies: 1   Last Post: Jul 16, 1995 6:27 PM

 David Van Slyke Posts: 12 Registered: 12/6/04
Re: nctm-l-digest V1 #91
Posted: Jul 16, 1995 6:27 PM

I am writing in response to Kent's concept of "crowd control".

In my mind, running a classroom of "cooperative learning" is something I
learned to do when playing role-playing games (I refer to Dungeons &
Dragons, RuneQuest, and the many others I've used over the years).

In these role-playing games, all the participants but one play the part
of characters in a story. The other person plays the part of "everything
else", describing what their characters see, hear, and experience as a
result of what they say their characters are doing. This other person
also plays the part of every other person or thing they encounter.

When done badly, these role-playing games resemble internet MUD sites:
characters exist mostly to fight nasty monsters and have negligible
personailities.

Since childhood, the games I was in charge of instead involved the other
people slowly acquiring information. The information would allow their
characters to solve puzzles and gain influence in the fantasy setting.
The fearless heroes did not do so much conquering, but the characters did
more growing.

Similarly, when I am teaching math in a cooperative learning setting
there definitely is crowd control. My job exists because this material
cannot be learned by reading a book. Students need some guidance when
first encountering much of K-12 math. The style of guidance differs with
the occasion, but I definitely am being manipulative.

For example, when I last taught arithmetic in different bases, I started
the lesson with asking six students to come to the front of the room. I
handed out papers with 1, 2, 4, 8, 16, 32 on them and as the rest of the
class called out numbers the six students would have to figure out how to
hold up their papers above their heads to add up to the given number.
Then the students were shown MBA blocks, and worked on some activities
pretty much on their own; my role then was to pace the groups and make
sure they were not going too quickly for some of their members, or
believing they were understanding when they were not. Then I came to the
blackboard and lead a discussion of how arithmetic works, doing problems
correctly or incorrectly and having the class tell me and each other what
was right or wrong and why. I was there to guide what they were focusing
on: I knew how to think about the math well, and by observing what they
were trying to do could help them past points of confusion.

The setting is different from when the band of fearless heroes slowly
discovered that the nobleman visiting the prince was actually an assassin of
the grey brotherhood, but the idea is the same: my job is to pace the
flow of information to the students so that their experience is
interesting and memorable, and so that each bit they learn builds off the
last in a structured way.

But the important part of the analogy is yet to come. Anyone who has
also lead a role-playing game knows he/she can never plan for what the
fearless heroes will decide to do. Similarly, I don't design a lesson
plan with "do this then do that then do that", but instead preparing how
to help guide an understanding of some things to understanding new
things. My students often want to use the manipulatives in a way I have
not planned on or seen before. Often an explanation that I thought would
make things clear does nothing for them. No problem - I've spent my time
preparing how ideas relate and not how the class day should go, so I can

I am in charge, but my job is to respond to where they are taking the
plot. I provide a setting, and they are writing the story.

I've met people who believe any form of manipulation is bad. I'm sure
this teaching philosophy would upset them. But from experience I've seen
that students of any age normally can't learn many math topcis (for
example-probability) on their own no matter how well the workbook is
written. Some information needs to be given to students carefully. For
me, this is what teachers are for.

-David L. Van Slyke