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Improvements in number sense
Posted:
Apr 25, 1999 10:38 PM
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Using the Investigations lessons has really shown me how limiting a
traditional approach to teaching and learning mathematics can be.
When I started the school year, I had students who would approach a
math problem like 100-11= by writing it vertically, and immediately
crossing out and borrowing in order to perform the standard
subtraction algorithm. Never mind that every child in my fifth grade
class could tell me that if they had $100 dollars and spent $11, they
would have $89 left. When math problems were presented to them in
"naked number" format, their math sense seemed to fly out the window
and they would revert to strictly doing it "how they had always been
told to do it." When we talked about why they did it that way, many
students said it was the only way they thought they were allowed to do
it. Because many of my students had made it to the fifth grade with
very little number sense, we tried some of the 4th grade activities
before jumping into the 5th grade materials. They absolutely loved
Close to 100, and many students asked for decks of cards to take home
to play with parents or siblings. That activity was a real eye
opener! I highly recommend it for any 5th grade teacher who is
starting with students who are unfamiliar with the Investigations
curriculum. (One pair of students who drew the digits 4,7,4,8,6, and
6 assured me that 84+74=158 was the absolute closest they could get to
100. Looking back on their work now, they can't believe they ever
thought that was the best they could do.)
As the year progressed, more and more students seemed comfortable
with trying their own strategies for solving problems. For some kids,
there seemed to be an almost immediate quantum leap in their ability
to come up with their own strategies, and in understanding the
strategies of their classmates. For other students, it has been a
slower and more gradual process. What I have seen is improvement in
the number sense of every child in my classroom, from the clas "math
whiz", to the self-proclaimed "math hater". In every operation, my
students are much more likely to look at the reasonableness of their
answers given what they know about the numbers.
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