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Topic: Constructivism Redux
Replies: 9   Last Post: Aug 25, 1995 1:25 AM

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Kreg A. Sherbine

Posts: 26
Registered: 12/6/04
Constructivism Redux
Posted: Aug 16, 1995 12:34 AM
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Perhaps one way to jump-start this thread is to examine how contructivism
plays out in the classroom. First I must point out that constructivism
is definitely a theory, as opposed to a practice; it may therefore seem
that classroom constructivism is a contradiction in terms. However, the
induced separation of theory and practice that has pervaded education for
decades is, fortunately, waning; it has always been appropriate, and is
now becoming politically correct, to speak of theory and practice as
inextricably intertwined.

What does constructivism look like in a classroom?

In an earlier post I promised/threatened to elaborate on this topic, but
now I find myself tragically/blessedly in a different position. How, for
example, might the recent discussion of division of fractions look in a
constructivist light? What actually is being constructed when students
encounter these techniques for fraction manipulation?

An extremely radical constructivist might say that the way to teach
division of fractions is to teach the concepts of division and fractions
(in some other constructivist way) and then to give the students some
division of fractions problems and tell them to have at it.

Certainly a good teacher could facilitate discussions, leading errant
conceptualizers back to a more appropriate path while encouraging those
who approach the problem appropriately. Taken to an extreme extreme, a
constructivist approach would have this as the only role of the teacher;
the students, such a person might argue, must discover for themselves a
complete and consistent way of dealing with these problems, for only by
doing it themselves will they actually contruct the knowledge of how to
divide fractions.

But if the teacher were to ask no leading questions, to restrict no line
of thinking, and to ensure that every single student in the classroom
goes through the same constructive process, the students who are easily
frustrated would drop out early, the others would be figuring out how to
divide fractions for weeks, and there would be so many and varied lines
of reasoning that the appropriate ones might get lost in the shuffle.
Under extreme conditions (highly motivated students, unlimited time),
this extreme technique might actually be useful. Of course, under
extreme conditions, I can travel a mile in under two minutes with no
sustained mechanical aid. Jumping out of an airplane, for example.

So what about the conditions in which most teachers work, which can be
classified as extreme in many ways but not usually in the ways described
above? How can we unhypocritically claim constructivism as our
philosophy of choice and still teach math every day?

Kreg A. Sherbine | To doubt everything or to believe
Graduate Student | everything are two equally convenient
Vanderbilt University | solutions; both dispense with the
sherbine@math.vanderbilt.edu | necessity of reflection. -H. Poincare







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