I am a mathematician. I am a college professor. I am a mother. From
all three perspectives I have been following with interest the
controversy over the current mathematics education reform. Last year I
had an experience that finally brought clarity.
My husband, who is also a mathematician, and I had a sabbatical at
the University of Utrecht in the Netherlands. We enrolled our eight
year-old son, Robert, in a local Dutch school. In doing so we were
unconsciously starting a very interesting experiment. At home Robert had
been experiencing a traditional mathematics curriculum where a great
deal of time and effort is spent on learning the carrying and borrowing
algorithms for addition and subtraction. The mathematics curriculum at
his Dutch school was very different. The students were working on
problems at the same level, but they were encouraged to develop their
own techniques for doing the problems. They were not taught the carrying
and borrowing algorithms. This approach has been used successfully in
Holland for almost thirty years.
At the same time Robert was adapting to a new curriculum, I was
studying at the Freudenthal Institute at the University of Utrecht—a
world-renowned center for research on mathematics education. I was
learning that the curriculum he was experiencing is called Realistic
Mathematics Education (RME). In RME, the mathematics is introduced in
the context of a carefully chosen problem. In the process of trying to
solve the problem the child develops mathematics. The teacher uses the
method of guided reinvention, by which students are encouraged to
develop their own informal methods for doing mathematics. Students
exchange strategies in the classroom and learn from and adopt each
other’s methods. I also learned that much research has been done on this
approach, that it is based on what we know about child development and
the development of numeracy, and that it is this body of research that
is driving the math education reform in our country.
When we first arrived in the Netherlands and I began to learn about
RME, I spent a little time quizzing Robert on how he would solve a few
addition and subtraction problems. I was shocked by the rigid attitude
he had developed at his school in the U.S. When asked to do any addition
problem with summands larger than 20 he would always invoke the
addition algorithm. He would sometimes make mistakes and then report an
answer that made no sense. He was putting all his confidence in the
procedure and little in his own ability to reason about what might be a
sensible answer. When I suggested there was a simpler way he could think
about the problem he became upset and told me, “You can’t do that!”
After a few months in Holland, I began to see an amazing difference
in Robert’s number sense. He was able to do the same problems more
quickly, more accurately, and with much more confidence. For example, I
asked him to solve 702 minus 635. He explained, “700 minus 600 is 100.
The difference between 2 and 35 is 33, and 100 minus 33 is 67.” When he
tried using the algorithm he made a borrowing error and became very
frustrated. I asked him to compute 23 times 12. He explained, “23 times
10 is 230, 23 times 2 is 46, 230 plus 46 is 276.” This multiplication
problem was much harder than anything in the curriculum at home. I was
very impressed with the flexibility and range of methods he had
developed in only a few months.
What happened to Robert in those few months has had a profound effect
on my perception of learning and on Robert’s understanding of
mathematics. My child learned to think. He learned he could think. He
was encouraged to think. He learned to see mathematics as creative and
pleasurable. This independent attitude towards mathematics will remain
with him forever and serve him well. It is this fact that has convinced
me of the value of de-emphasizing algorithms in the elementary years.
Unfortunately, Robert is once again back in a school that focuses on
the teaching of algorithms. The other day as we were driving to soccer,
out of the blue Robert asked from the back seat, “Mommy, wouldn’t it be
crazy to do 5000 minus 637 using borrowing?” I smiled proudly at him and
said, “Yes, honey, it would.”
Source: http://mathematicallysane.com/realistic-math-makes-sense-for-students/
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