The Elementary School Journal, 93(2):163–177, JSTOR, 1992.
Valerie Taft's goal is to prepare her fifth-grade students to use mathematics in everyday life. Like the authors of California's Mathematics Framework, Valerie wants students to appreciate the usefulness of mathematics for solving problems. What Valerie considers as useful, however, is what she calls the "hows" of mathematics- knowing how to carry out various computational procedures. This emphasis on mechanics, along with limitations in Valerie's mathematics knowledge, is reflected in 2 lessons described in this article. In the first lesson, taken directly from her district's new textbook, Valerie introduced students to the concept of average. She emphasized the steps of the averaging procedure, providing few opportunities for students to think about the mathematical concepts involved. In the second lesson, Valerie conducted a number of class surveys to provide data for computing averages. Because of the emphasis on the steps of the averaging procedure and lack of reflection on the reasonableness of solutions, however, Valerie and her students unknowingly computed incorrect averages. Valerie has firmly held beliefs about what students should learn and the nature of mathematics. As a result, her mathematics teaching is relatively impervious to pressures from the state and district to change.
@article{putnam1992thm,
abstract = {Valerie Taft's goal is to prepare her fifth-grade students to use mathematics in everyday life. Like the authors of California's Mathematics Framework, Valerie wants students to appreciate the usefulness of mathematics for solving problems. What Valerie considers as useful, however, is what she calls the "hows" of mathematics- knowing how to carry out various computational procedures. This emphasis on mechanics, along with limitations in Valerie's mathematics knowledge, is reflected in 2 lessons described in this article. In the first lesson, taken directly from her district's new textbook, Valerie introduced students to the concept of average. She emphasized the steps of the averaging procedure, providing few opportunities for students to think about the mathematical concepts involved. In the second lesson, Valerie conducted a number of class surveys to provide data for computing averages. Because of the emphasis on the steps of the averaging procedure and lack of reflection on the reasonableness of solutions, however, Valerie and her students unknowingly computed incorrect averages. Valerie has firmly held beliefs about what students should learn and the nature of mathematics. As a result, her mathematics teaching is relatively impervious to pressures from the state and district to change.},
author = {Putnam, R.T.},
interhash = {1dcf0fccf701bc6e63472e62e26554cf},
}