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What is Constructivism?
"Students need to construct their own understanding of each mathematical concept,
so that the primary role of teaching is not to lecture, explain, or otherwise
attempt to 'transfer' mathematical knowledge, but to create situations for
students that will foster their making the necessary mental constructions.
A critical aspect of the approach is a decomposition of each mathematical
concept into developmental steps following a Piagetian theory of knowledge
based on observation of, and interviews with, students as they attempt to
learn a concept."
It's not surprising that constructivism has a strong voice in the current dialogue on math education. Many are concerned about the success  or lack of success  of math education. Constructivism cuts a nice path between the main ideas that have influenced how math has been taught: the concept of math as facts to be transmitted to the student, and the view that some people have it and some people don't, where the educator's task is to figure out how "smart" students are and choose the right tasks for them to perform. Questions remain, however, about whether these offer rich information for developing different ways of teaching. And what's to be done for the students who aren't succeeding? In contrast, constructivism focuses our attention on how people learn. It suggests that math knowledge results from people forming models in response to the questions and challenges that come from actively engaging math problems and environments  not from simply taking in information, nor as merely the blossoming of an innate gift. The challenge in teaching is to create experiences that engage the student and support his or her own explanation, evaluation, communication, and application of the mathematical models needed to make sense of these experiences. Given this view, there are many approaches to improving teaching: look for different ways to engage individual students, develop rich environments for exploration, prepare coherent problem sets and challenges that focus the model building effort, elicit and communicate student perceptions and interpretations, and so on. We'd like to explore here the theory and applications of constructivism in math education. We invite you to submit your favorite readings, projects, and classroom materials that either point out the pitfalls or demonstrate the opportunities of this theoretical framework.
Constructivism in Math Education

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