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 DOI: 10.3102/0013189X023007004

1994 23: 4EDUCATIONAL RESEARCHERPaul Cobb

Constructivism in Mathematics and Science Education  

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An Exchange:

Constructivism in Mathematics and Science Education PAUL COBB

Educational Researcher, Vol. 23, No. 7, p. 4

The idea for this exchange arose as a response to the fervor that is currently associated with construc­tivism in some segments of the mathematics and sci­

ence education communities. In addressing this topic, it seems important to distinguish between the writings of influential constructivist theorists, particularly von Gla-sersfeld, and the views that have emerged in the two edu­cational communities. As a theory, constructivism is often reduced to the mantra-like slogan that "students construct their own knowledge." Although several theoreticians have stressed that constructivism is a model or a conjecture that might be useful for educational purposes, the charac­terization of learning as individual construction is fre­quently treated as a conclusively proven fact that is beyond justification. Difficulties, of course, arise when one applies psychological constructivism reflexively and attempts to explain how so many mathematics and science educators have individually constructed this supposedly indubitable proposition. It is also interesting to note that a far greater degree of certainty is typically attributed to this proposi­tion than to the apparently fallible and potentially revis-able claims of mathematicians and scientists.

Pedagogies derived from constructivist theory fre quently involve a collection of questionable claims that sanctify the student at the expense of mathematical and scientific ways of knowing. In such accounts, the teacher's role is typically characterized as that of facilitating stu­dents' investigations and explorations. Thus, although the teacher might have a variety of responsibilities, these do not necessarily include that of proactively supporting stu­dents' mathematical development. Romantic views of this type arise at least in part because a maxim about learning, namely that students necessarily construct their mathe­matical and scientific ways of knowing, is interpreted as a direct instructional recommendation. As John Dewey ob­served, it is then but a short step to the conclusion that teachers are guilty of teaching by transmission if they do more than stimulate students' reflection and problem solv­ing. It is disturbing that instructional pronouncements con­sistent with this interpretation of the maxim are sometimes used as absolute standards against which to assess peda­gogical alternatives. In such instances, the judgment that the alternative "is not constructivist" apparently consti­tutes an adequate counterargument. Justifications of this kind thwart the type of discourse that makes genuine in­quiry possible in mathematics and science education.

If we researchers broaden ourjocus, it is in fact possible to challenge the very notion of a constructivist pedagogy. On an alternative reading, the constructivist maxim about learning can be taken to imply that students cpnstrucLtheir ways of knowing in eyenjhe most authoritarian of in-stniSionaT~situations. This interpretation transcends the

dichotomy between situations in which students construct their own knowledge and those in which it is transmitted to them. The critical issue is then not whether students are constructing, but the nature or quality of those socially: and culturally situated constructions. From this latter perspec­tive, the very notion of a constructivist pedagogy or of con structivist teaching is a misnomer that reflects a category error. It is readily apparent, for example, that the various versions of constructivism discussed in this issue do not constitute axiomatic foundations from which to deduce pedagogical principles. They can instead be thought of as general orienting frameworks within which to address pedagogical issues and develop instructional approaches.

An overriding goal of the contributors is to counteract the "political correctness" that frequently surrounds con-structivislnirrmathematics and science education. In our contributions, Driver and I both discuss the need to go be-yond purely psychological, individualistic constructivism and argue that the learning of mathematics and science must be viewed at least in part as a process of encultura-tion into the practices of intellectual communities. The is­sues touched upon include the role of language and the significance of broader social and institutional processes in this current era of reform. Our contributions differ primar­ily in terms of intent. Driver and her colleagues argue that the process of learning science is primarily one of social construction. They then go on to delineate aspects of class room practices that support the reconstruction of scientific concepts. I, for my part, focus on the apparent conflicts be-tween constructivist and sociocultural accounts of mathe­matical development. In doing so, I make a distinction analogous to that between personal and social construc­tivism. However, rather than emphasize one or the other of these two viewpoints, I argue that analyses of mathematics learning as individual construction and as enculturation are complementary.

In his article, Bereiter comments on the first two papers and outlines his own position by drawing on Popper's phi­losophy of science. His primary contention is that" am-structivism cannot adequately account for the immaterial objects that Popper located in his World 3—abstract math ematical and scientific objects. Bereiter notes that his ap­proach is a relatively unfashionable way of regarding knowledge. In the current climate, there might well be a tendency to dismiss his views out of hand. This would be most unfortunate in my opinion because, in taking his ar­guments seriously, we have the opportunity to raise the current level of discourse in mathematics and science edu­cation. I am grateful to Bereiter for initiating this conversa­tion.

PAUL COBB is Professor of Mathematics Education at Vanderbilt University, Peabody College, Box 330, Nashville, TN 37203. His specialization is mathematics education.

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