On Apr 25, 6:18=A0am, Ericka Kammerer <e...@[EMAIL PROTECTED]
> wrote:
> 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) =3D 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#curriculumsays
>
> > "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."
>
> =A0 =A0 =A0 =A0 I see all sorts of possible issues with this. =A0First,
> I'm not sure I buy the notion that you can generalize easily
> from college students to elementary students. =A0Developmentally
> they're in different places when it comes to abstract thinking.
> That, however, is obviously an empirical question that could
> be tested.
> =A0 =A0 =A0 =A0 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. =A0That 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. =A0It 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.
> =A0 =A0 =A0 =A0 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. =A0Therefore,
> 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- Hide quoted text -
>
> - Show quoted text -
I agree with Erika's statements but I would add one other potential
flaw for the study. The "concrete examples they use are not in any
sense real world. The students have never had cups of liquid that
behave as they do in this study so its is obvious that the "concrete
examples" would confuse the students just as much as a cat that
barked. We build from REAL world concrete examples that the students
have experience with or at least have intuitions about. The findings
of this study might be valid but this styudy does not prove them and I
am surprised it got past the referrees.
Nevertheless, we should take one lesson away from this study. We
should not use examples or analogies for which the students do not
have experiences or intuitions. Those can be misleading and confusing.
I remember always hating the song "love is something..." which had the
following analogy,
"its just like a magic penny
hold it tight and you won't have any
lend it, spend it, give it away,
and it comes right back to you."
There is no such thing as a magic penny and nobody has an experience
with one, so using it as an example clarifies nothing and in fact
confuses the situation since people start trying to incor****ate thier
knowlege of ordinary pennies into their understanding.
Michael Michalchik
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