To the Editor:
“The qualities of an effective mathematics teacher,” according to your front-page summary of findings from the National Mathematics Advisory Panel’s recent report, are “frustratingly elusive” (“Essential Qualities of Math Teaching Remain Unknown,” April 2, 2008). Must teachers be certified in order to “teach well”? Does it matter how many math courses they took in college? Even more elusive, however, is the answer to a question your article—and possibly the federal panel—doesn’t bother to ask: What does it mean to talk about “teaching well” or being “effective”?
The only hints we’re given are occasional references in the article to students’ “achievement.” But this just sets the question back a step, leading us to ask, What kind of achievement and how is it assessed? My fear is that this concept—and, by extension, the teaching that’s supposed to produce it—is simply equated with high test scores.
Yet, as a group of Michigan State University experts put it in the Review of Research in Education, “many scholars have argued that standardized achievement tests represent a severely limited view of what mathematics is worth knowing,” with “too much emphasis on isolated computational skill” and the mindless application of memorized algorithms, with “little or nothing to assess students’ ability to comprehend mathematical reasoning.”
The question “What tends to be true of teachers whose students get high scores on standardized math tests?” is much less important than the question “What tends to be true of teachers whose students understand mathematical ideas from the inside out and can apply them to new types of problems?” In any case, these are certainly two very different questions, and they’d likely produce two different sets of answers. (While we’re at it, here’s a third question: “What tends to be true of teachers whose students develop a lasting interest in math?”)
Reports, and articles about reports, that ignore these differences are not only frustrating but ominous, because the default assumption is that higher test scores ought to be our primary goal as educators. In fact, this is true not only of reports but also of studies whose primary dependent variable is standardized-test results, rather than more meaningful kinds of learning.
Nor is this limited to the field of mathematics. Whenever we read a discussion of whether a given policy leads to “better” outcomes—for example, more “effective” classroom management or more “successful” schools—we should demand to know how these words are being used, and whether those meanings capture what matters most about education. Not to ask is to be complicit in perpetuating the most disturbing features of the status quo.
Alfie Kohn
Belmont, Mass.
