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Re: Learning and Mathematics: Schoenfeld, Metacognition
Posted:
Apr 7, 1996 4:58 PM
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Gypsyamber wrote about Schoenfeld's example: Reading a problem such as the
one above, most students recognize that the problem is testing their
division. Becuase the students are aware of this agenda to the exam they
want to show the full operation being tested. They want to show they know
how to find the remainder.
So if kids understand that that their answer gives the proper mathematical
procedure but not an answer that would be useful in the real world, why do
they think giving the proper mathematical answer is more important? I think
the answer is largely that their mathematical learning is centered around
test taking-- they learn a set of mathematical procedures (like adding,
subtracting, multiplying and dividing) and a set of clues for when to use
them, so that they can do well on (worksheets and then) standardized tests.
A new twist is word problems- perhaps just a disguise for the usual rote
applying of procedures OR perhaps an attempt to bring real world matters
into the classroom. The children don't know yet so they stick to what they
know-- which is plugging and chugging through the procedures without
thinking about the context. Would discussing the question first make a
difference? Would generating their own "real life" questions or using math
time to actually answer real questions (like how many papers can we post on
the bulletin board, how many buses will we need for an actual school trip,
what grade do I need on my next test to get an 80% average etc.) help bring
this new message home to kids? Finally, are we ready for this to be the
message? Do we want kids to learn that math is only useful if it helps us
with real world things or do we want them to have a place for (blind?)
procedures as well? If so, should they be taught at the same time,
integrated or kept separate-- like one day the kids do real life problems
and one day they do book problems? -Laurie
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