Constructivism in mathematics and science education
Cobb P. (1994) Constructivism in mathematics and science education. Educational Researcher 23(7): 4. Available at http://cepa.info/2951
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 science education communities. In addressing this topic, it seems important to distinguish between the writings of influential constructivist theorists, particularly von Glasersfeld, 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 revisable claims of mathematicians and scientists.
Pedagogies derived from constructivist theory frequently 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 proactivelysupporting 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 our focus, 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 construct their ways of knowing in even the most authoritarian of instructional 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 constructivist 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 constructivism in mathematics and science education. In our contributions, Driver and I both discuss the need to go beyond purely psychological, individualistic constructivism and argue that the learning of mathematics and science
must be viewed at least in part as a process of enculturation 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 classroom practices that support the coconstruction of scientific concepts. I, for my part, focus on the apparent conflicts between 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 constructivism cannot adequately account for the immaterial objects that Popper located in his World 3 – abstract mathematical 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.
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