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Mathematics Education

Constructivism in the Classroom

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The Forum's Internet Mathematics Library provides a page of links to sites on Constructivism. A few selections are offered below, and we also offer a page of selected Internet sites with a constructivist orientation or that offer readings on constructivism.

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."
- Calculus, Concepts, Computers, and Cooperative Learning (C4L)


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

  Applications and Misapplications of Cognitive Psychology to Math Education - Anderson, Reder, Simon
A critical view of constructivism by three leading cognitive psychologists at Carnegie Mellon University. Decomposition and decontextualization; ... more>>

  Constructivism and Education: A Shopper's Guide - Moses A. Boudourides
A brief review of the various streams of constructivism in studies of education, society, science and technology: philosophical, cybernetic, ... more>>

  Constructivism - Classroom Compass
The winter 1994 issue of Classroom Compass explores this theory of learning, including a brief literature summary and suggestions for the ... more>>

  Constructivism in Science and Mathematics Education - Michael R. Matthews
Matthews discusses constructivism, its scope and influence, and looks at the particular case of New Zealand, in this article from the 99th Yearbook of ... more>>

  Constructivism: Vygotsky and the Internet - Mathematics Education at The Math Forum
The ideas of Lev Semenovich Vygotsky have sparked considerable thought on the topic of constructivism. The Math Forum has collected a list of links to ... more>>

  Constructivist Mathematics and Unicorns - Lee V. Stiff
The then-president of NCTM lays out distinctions among various forms of constructivism, and how they relate to the Principles and Standards, in this ... more>>

  Constructivist Views of Learning in Science and Mathematics (ERIC Digest) - Drew K. Ishii
An examination of constructivism and its implications for the classroom, with web and print resources for additional ... more>>

  Essays on Constructivism and Education - Tom O'Haver; Maryland Collaborative for Teacher Preparation
An extensive collection of articles on constructivist teaching strategies, change in education, technology in the classroom, hypertext and cognitive ... more>>

  Kinds of Constructivism: An Annotated Bibliography - Annie & John Selden; The Math Forum
A bibliography prepared by Annie and John Selden as a supplement to "Constructivism in Mathematics Education - What Does It Mean?" - a talk they gave ... more>>

  Mathwire.com - Terry Kawas
Standards-based activities and worksheets that support a constructivist approach to learning mathematics. Browse resources by NCTM standard or math ... more>>


For more, search or browse Constructivism in the Math Forum's Internet Mathematics Library.


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