The lesson we created for my grade 9 applied class (late April 2013) took a
page from a lesson that I was involved in an earlier lesson study. That lesson involved experimenting with the
relationship between the volumes of popcorn kernels and popcorn. We decided that in this lesson, rather than
telling them what to do, we would ask them to come up with the question. We would provide
a number of items around the popcorn theme and asked the students to come up
with a good question that could be solved with math and then go ahead and solve
it. Students would work in small groups
of 2 or 3. The groups were based on ability
groupings with social considerations. In
other words, students would be working with other students of similar
mathematical ability who they had worked with before. Each group would be given 100 g of kernels
and the cost in bulk,movie theatre popcorn pages with the price attached for
small medium and large, cubic centimetre linking cubes, a measuring cup and an
instruction sheet. At the top of the
question sheet was a For Better or Worse cartoon with the caption "You can
tell how smart someone is by the questions they ask." They also had access to electronic scales and
an electric corn popper as well as chart paper and markers for recording their
work.
When planning the lesson there was one more critical piece
to consider. What were the teacher moves? What would I be doing to facilitate the
lesson? We had a guest at the table for
that planning session who offered "Do nothing". So we agreed that instead of moving about the
room and encouraging and cajoling, I would sit down and make myself available
for questions.
On the day of the lesson, the observing teachers were given
a list of mathematical terms that they could listen for as evidence of
accountable talk. My introduction to the
students was very short and the students got down to work rather tentatively at
first. I found it incredibly difficult
to just sit there and let things happen.
I answered a few questions and I was pleased when one group eventually
got around to using the corn popper to make popcorn. As it turned out they just wanted to munch on
popcorn as they did their question. In
fact in all the groups the mathematics produced was at a very low level. There was a group of two with the strongest
students. I had little contact with them
until the end of the period. After more
than an hour their chart paper showed that 1000 cm linking cubes fit in a cubic
measuring cup that was 10 by 10 by 10. They
had asked a question and answered it just like I directed.
The questions that seemed obvious to us never
materialized; "How many kernels to
fill a bag?", "What does it cost to fill a popcorn bag?",
"Which size bag in the better deal?". Interestingly the least academic group came
closest to what we had in mind.
In the debrief with the teachers I expressed my
disappointment. How could they not see
what we could see? What a flop! Thankfully one of the observing teachers
picked up on a comment made almost immediately in a group farthest from me. As soon as they saw the price on the bulk
corn kernels and the price on the movie popcorn the comment was "What a
rip-off!". They got it. But why couldn't they parlay that into a good
question?
After some discussion, the thought occurred to us that there
was a huge disconnect between the math classroom and what goes on in the 'real
world'. For their good question, these
students were giving us bizarre random worksheet/textbook style math
questions. They were giving us what they
thought we wanted. We can speculate that
for years they have been subjected to questions that had little context and
even less meaning. Why wouldn't they
mirror that? To quote Pogo, "We
have met the enemy and the enemy is us".
In this lesson the students learned very little. We learned lots. We were blown away by how much we learned
about the how little the students understood about good questions. We knew that we had new challenges
ahead.
Glad to hear you tried the "do nothing" idea.
ReplyDelete