Beliavsky wrote:
> http://www.nytimes.com/2008/04/25/science/25math.html
> Study Suggests Math Teachers Scrap Balls and Slices
> By Kenneth Chang
> New York Times, April 25, 2008
>
> 'One train leaves Station A at 6 p.m. traveling at 40 miles per hour
> toward Station B. A second train leaves Station B at 7 p.m. traveling
> on parallel tracks at 50 m.p.h. toward Station A. The stations are 400
> miles apart. When do the trains pass each other?
>
> Entranced, perhaps, by those infamous hypothetical trains, many
> educators in recent years have incor****ated more and more examples
> from the real world to teach abstract concepts. The idea is that
> making math more relevant makes it easier to learn.
>
> That idea may be wrong, if researchers at Ohio State University are
> correct. An experiment by the researchers suggests that it might be
> better to let the apples, oranges and locomotives stay in the real
> world and, in the classroom, to focus on abstract equations, in this
> case 40 (t + 1) = 400 - 50t, where t is the travel time in hours of
> the second train. (The answer is below.)'
>
> <rest at site>
>
> If the study is correct, I wonder which math curricula are most
> consistent with it. It appears to contradict the philosophy of
> Everyday Mathematics (EM), which our public school use. The EM site
> http://everydaymath.uchicago.edu/about.shtml#curriculum
says
>
> "Students acquire knowledge and skills, and develop an understanding
> of mathematics from their own experience. Mathematics is more
> meaningful when it is rooted in real life contexts and situations, and
> when children are given the op****tunity to become actively involved in
> learning. Teachers and other adults play a very im****tant role in
> providing children with rich and meaningful mathematical experiences."
I see all sorts of possible issues with this. First,
I'm not sure I buy the notion that you can generalize easily
from college students to elementary students. Developmentally
they're in different places when it comes to abstract thinking.
That, however, is obviously an empirical question that could
be tested.
Second, I believe there is other evidence on the table
that some students learn better inductively and some better
deductively, and that some have more need of concrete representations
than others in attempting to understand concepts. That said,
I do think that this notion that everything is best *taught*
through a consistent emphasis on concrete examples is hogwash,
and I'm not at all surprised by the results of the experiment.
The task they measured the students on required the students
to think more theoretically--they had to get the theory to
be able to apply to the specific situation. It seems likely
to me that the students who were specifically taught the
theory would do better than those who had to induce the theory
from the specific examples.
Third, while it's im****tant for the kids to know the
theory, for the overwhelming majority of them the im****tance
of knowing the theory is so that they can apply it. Therefore,
the "two trains" problem is still an im****tant component
because a student who has mastered the material should be able
to apply the theory to figure out the answer to the problem.
That's a separate issue from how best to get students to learn
and understand the theory.
Best wishes,
Ericka
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