(Mis?)constructing Constructivism

By Clements, Douglas H. | Teaching Children Mathematics, December 1997 | Go to article overview

(Mis?)constructing Constructivism


Clements, Douglas H., Teaching Children Mathematics


Many educators base recommendations for teaching mathematics on "constructivist" thinking. However, they often misunderstand constructivism, so their recommendations may be incorrect or inappropriate. We need to examine what constructivism is and is not, what myths have grown up around constructivism, and what characteristics define it.

We Do Constructivism on Fridays

Do students stop "constructing knowledge" when their teacher lectures? Do they switch over to "absorption" mode, passively soaking in facts? No. Constructivism is not a "type" of learning. It does not make sense to believe that today a student learns in a constructivist way, but tomorrow, in some different way. At its core, constructivism is a philosophy of learning that offers a perspective on how people - all people - learn, all the time.

Constructivism tells us more about learning than about teaching. However, it has important implications for teaching. Certain teaching practices might be more or less consistent with the beliefs of constructivism. For example, we could predict that we would have less success if we simply fed students information with no concern for connecting that information to knowledge they already have.

What Constructivism Is Not

Confusion about what constructivism does and does not mean has engendered a number of myths. Unquestioned, such myths dilute and pollute constructivism.

Myth 1: Students should always be actively and reflectively constructing. One powerful way to construct knowledge is through conscious, reflective construction. As educators, we too seldom give students appropriate time, tasks, and encouragement to think deeply and to talk about mathematical ideas.

Not all constructions are of that type, however, nor should they be. Our minds actively construct ideas without our "working at it" or even being conscious of it. For example, young children construct the idea of flying animals, which at first may include everything airborne, because their minds are actively building connections, with little formal "teaching" and even less "effort" on their part. Even when we are consciously working on a problem, we are not fully aware of all that we are learning.

There are times for many different types of constructing: time for "experiencing"; for "intuitive" learning; for learning by listening; for practice; and for conscious, reflective thinking. During all these activities, students construct valuable, but different kinds of, knowledge. We need to balance these times to meet our goals for students.

Myth 2: Manipulatives make learners active. A related myth is that when students are using manipulatives, then they are "actively learning." Manipulatives can help students actively construct knowledge (Clements and McMillen 1996); however, teachers can also use manipulatives to impose prescribed procedures for routine problem types. Students then learn to use manipulatives only in a rote manner (Clements and McMillen 1996). So teaching with manipulatives is not necessarily "teaching constructively."

Myth 3: Constructivist learners are lonely voyagers. "Constructing their own knowledge" does not imply that students build their ideas in isolation. Rather, the phrase means that one person cannot simply and directly transmit knowledge by means of words into the mind of another person. One can say words with intended meaning, but active listeners have to create their own meanings for the words they hear (Steffe, personal communication). In the words of the poet and philosopher, "If [a teacher] is indeed wise he does not bid you enter the house of his wisdom, but rather leads you to the threshold of your own mind" (Gibran 1989).

So students do not construct knowledge alone, even though each has to modify his or her own ways of thinking and acting. Further, although inventing mathematical ideas together is important, so is learning to better communicate these ideas to others. …

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