Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



Constructivism Redux
Posted:
Aug 16, 1995 12:34 AM


Perhaps one way to jumpstart 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



