The education establishment commits to fads like group and collaborative learning, but Garelick says they shouldn’t ignore and misinterpret traditional math.
Most discussions about mathematics and how best to teach it in the K-12 arena break down to the inevitable bromides about how math was traditionally taught and that such methods were ineffective. The conventional wisdom on the “traditional method” of teaching math is often heard as an opening statement at school board meetings during which parents are protesting the adoption of a questionable math program: “The traditional method of teaching math has failed thousands of students.” A recent criticism I read expanded on this notion and said that it wasn’t so much the content or the textbooks (though he states that they were indeed limited) but the teaching was “too rigid, too inflexible, too limited, and thus failed to adequately address the realities of educating a large, diverse, and rapidly changing population during decades of technological innovation and social upheaval.”
There is some confusion when talking about “traditional methods” since traditional methods vary over time. Textbooks considered traditional for the last ten years, for example, are quite different than textbooks in earlier eras. For purposes of this discussion, I would like to confine “traditional” to methods and textbooks in use in the 40′s, 50′s and 60′s. And before we get to the question about teaching methods, I want to first talk about the textbooks in use during this time period. A glance at the textbooks that were in use over these years shows that mathematical algorithms and procedures were not taught in isolation in a rote manner as is frequently alleged. In fact, concepts and understanding were an important part of the texts. Below is an excerpt from a fifth grade text of the “Study Arithmetic” series (Knight, et. al. 1940):