Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

3
Charting a Course for Secondary Geometry

Daniel Chazan

Michigan State University

Michal Yerushalmy

Haifa University

Fortunately, I see mathematics as a very big house, and it offers teachers a rich choice of topics to study and transmit to students. The serious problem is: how to choose. ( Mandelbrot, 1994, p. 80, emphasis added)

Traditionally, in the United States, geometry instruction is concentrated at the secondary level; high-school students study Euclidean geometry in a concentrated, year-long course that emphasizes deductive proof. Even though educational policy is a local matter theoretically decided school district by school district, teacher by teacher, there are nonetheless strong commonalities in the mathematics education offered to many students; their opportunities to study geometry are limited.

In the past, many arguments were advanced to support the traditional Euclidean geometry course. For example, Moise ( 1975) touted the traditional Euclidean geometry course as "the only mathematical subject that young students can understand and work with in approximately the same way as a mathematician" (p. 477). For Moise, mathematicians work deductively; studying Euclidean geometry gives students an opportunity to experience the deductive development of an axiomatic system. More recently, others (e.g., Malkevitch, n.d.) objected to the study of Euclid. They claimed that limiting students to the study of Euclid misrepresents modern geometry. Is the traditional geometry course a defensible and effective "rudimentary version" of geometry well suited to a wide range of secondary school students, or is it an anachronism? As we near the millennium and as technological tools provide new types of geometrical representations, should Euclid be replaced in the secondary mathematics curriculum, or should the traditional course be maintained or modified?

These questions interest us because we do not see curriculum as fixed; in our view there are curricular choices to be made. In making such choices, we take seriously Bruner's suggestion "that children should en-

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