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Re: Teaching Algorithms
Posted:
Dec 12, 2000 12:25 PM
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Mike,
I agree with much of what you're saying. I think there is a place for
"page-of-twenty-problems" in a constructivist classroom to give
students more practice so they can develop efficiency. TERC stresses
that students need to eventually settle on a small set of efficient
algorithms for each operation that make sense to them, although those
need not include the standard algorithms. Most students are not going
to get quick enough with their facts or with these algorithms unless
they get a lot of practice. How much is "a lot" is a judgment call
that teachers have to make based on observing their students.
My concern with "page-of-twenty-problemsÃÂ is that they shouldn't be
used too early, while students are still in the exploring phase, but
later when they are in the settling on/consolidation phase. This isn't
easy for teachers to pull off, because some students, as you mention,
get through the exploring phase faster than others.
Some research that is relevant here: a 1998 study compared three
groups of 2nd grade students-- some receiving Investigations
instruction, some receiving traditional math instruction, and some
receiving a combination. The three groups did about the same when it
came to basic facts and two-digit addition. But with two-digit
subtraction requiring re-grouping, the Investigations group did best,
the traditional group was next, and the combination group did the
worst. I believe these students in the combination group were
introduced to the traditional subtraction borrowing procedure too
early. (See Study 3 in
http://www.lab.brown.edu/investigations/resources/studresults/iccuwno.html)
I couldn't agree more that leaving the number fact practice and other
consolidating work to parents is a bad idea: an abdication of
responsibility and a big blow for equity for all children. Parents can
do extra work with their students in this area, but teachers should
not be counting on this.
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