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All strategies are not equal
Posted:
May 9, 1999 10:15 PM
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One of the big questions I've struggled with in assessment has been
just what I'm assessing. Traditionally we assessed the student's
ability to get the right answer. We believed if the student got the
right answer, s/he understood the mathematics. Clearly with this new
curriculum we're interested in more than the right answer, but what?
I've just finished evaluating some student number work. I noticed
that I am considering three different aspects: their understanding of
operation, their accuracy, and their efficiency.
Regarding understanding of operation, I'm looking to see if their
strategy matches the problem they are trying to solve. Accuracy is
the right answer, which is still an important goal! Efficiency is the
area I grapple with. I've come to realize that all strategies are not
equal. The fifth grader using tally marks to solve a two-digit
addition problem isn't using a very efficient strategy. It may be
appropriate for a first or second grader to use that strategy, but as
the numbers get larger and the student's understandings develop we
expect their strategies to change as well. To know how a student is
doing, I have to first think about the strategies students use and put
them on a continuum. As I begin to think about multiplication
strategies, for example, my continuum looks something like this:
grouping tally marks, repeated addition, using some multiplication and
some repeated addition, breaking the problem into smaller
multiplication problems and then combining the partial products,
breaking the problem into smaller multiplication problems using
landmark numbers. When I see where a student falls on this continuum,
one of my questions is whether this is the right place for her at this
time or whether she is ready to move on. Getting to the higher end of
the continuum has to be done carefully. When we use to just teach a
procedure we were trying to jump to the end without building the
understanding along the way.
This sounds as though I've thought it through much more specifically
than I really have. It is more an idea about assessment that I'm
beginning to use, than a final yardstick to measure by.
Nancy
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