Mathematics education suffers from a condition that resembles schizophrenia. One of its personalities is exhibited in the day-to-day realities of classroom learning; another is evident in journal articles, in-service presentations, and other such forums where educators present alternative realities of learning. For the purposes of this article, these personalities will be labeled, respectively, as the practice and theory of mathematics education. This article focuses on the latest form of the theoretical personality of mathe-matics education, constructivism, by asking what is constructivist learning theory and what does it imply for the practice of learning mathematics? How students learn mathematics has long been an area of speculation and controversy. Over the last century, a number of themes have emerged that are discussed in an attempt to place constructivism in perspective. To understand the implications of the various themes for teaching and learning mathematics, pedagogical examples of integers studied at the ninth-grade level are given.
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