Steve Willoughby taught mathematics for 59 years at every level from elementary school to graduate school. He is a keen and perceptive observer and a witty and talented storyteller. And, man, after 59 years does he have some stories to tell in Textbooks, Testing, Training: How We Discourage Thinking.
From a fourth-grade book on a page titled “Divided By 6”:
Twelve turkeys. Six turkeys in each cage. How many cages?
There was a picture on the page with the right number of cages so that exactly six turkeys could be, and were, placed into each with no leftover turkeys. The teachers’ guide directed that any student who wrote the answer without writing “12 ÷ 6 = 2” was to be marked wrong. Fortunately, because of the title at the top of the page and four years of intensive schooling, no child would have an urge to read the problem. There are two numbers. One is 6. Certainly 12 must be divided by 6 and the problem is solved to the satisfaction of all concerned without a single thought passing through the head of anyone involved or of any child making the heinous error of counting the cages depicted.
Did the authors really suppose that if somebody wanted to know how many cages there were, he would count the turkeys, count how many are in each cage, and, upon discovering the unlikely fact that the same number were in each cage, would divide the first number by the second?
Steve served a term as president of the National Council of Teachers of Mathematics, and his opinions are thoughtful, cogent, and firmly held. His book, really an extended essay as it’s only about 50 pages long, addresses the problems he sees with our current textbooks, teacher preparation programs, and testing regimes.
But it is more than that. Steve’s book throbs with a deep understanding that the act of teaching is a deeply human interaction between student and teacher. The book is also irascible, opinionated, and sometimes funny: the story of the zealous editor of a national standards document who changed half of the occurrences of “real number” to “actual number” still makes me laugh.
Like a good teacher, Steve’s stories carry you along and drive you to ask the questions he’s been asking himself for decades: Why do we do things this way? Why can’t our textbooks be better? What can we do to make things better for students?
At the center of this essay is a compassionate, and passionate, core that will resonate with every passionate, and compassionate, teacher—which I suspect means just about everyone reading this magazine. It will, at times, make you laugh; it will, at times, make you angry; and it will make you think about what we do and why.
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