To the Editor:
鈥淭he qualities of an effective mathematics teacher,鈥� according to your front-page summary of findings from the National Mathematics Advisory Panel鈥檚 recent report, are 鈥渇rustratingly elusive鈥� (鈥淓ssential Qualities of Math Teaching Remain Unknown,鈥� April 2, 2008). Must teachers be certified in order to 鈥渢each well鈥�? Does it matter how many math courses they took in college? Even more elusive, however, is the answer to a question your article鈥攁nd possibly the federal panel鈥攄oesn鈥檛 bother to ask: What does it mean to talk about 鈥渢eaching well鈥� or being 鈥渆ffective鈥�?
The only hints we鈥檙e given are occasional references in the article to students鈥� 鈥渁chievement.鈥� 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鈥攁nd, by extension, the teaching that鈥檚 supposed to produce it鈥攊s simply equated with high test scores.
Yet, as a group of Michigan State University experts put it in the Review of Research in Education, 鈥渕any scholars have argued that standardized achievement tests represent a severely limited view of what mathematics is worth knowing,鈥� with 鈥渢oo much emphasis on isolated computational skill鈥� and the mindless application of memorized algorithms, with 鈥渓ittle or nothing to assess students鈥� ability to comprehend mathematical reasoning.鈥�
The question 鈥淲hat tends to be true of teachers whose students get high scores on standardized math tests?鈥� is much less important than the question 鈥淲hat tends to be true of teachers whose students understand mathematical ideas from the inside out and can apply them to new types of problems?鈥� In any case, these are certainly two very different questions, and they鈥檇 likely produce two different sets of answers. (While we鈥檙e at it, here鈥檚 a third question: 鈥淲hat tends to be true of teachers whose students develop a lasting interest in math?鈥�)
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 鈥渂etter鈥� outcomes鈥攆or example, more 鈥渆ffective鈥� classroom management or more 鈥渟uccessful鈥� schools鈥攚e 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.
