I will be starting a teaching assignment in a middle school this August. A few weeks ago, I met with the woman who will be mentoring me for two years. (This is part of California’s licensing requirements for new teachers–sort of like being out on parole from ed school.) As part of some initial advice, she emphasized that students should do math not only in the classroom, but outside–i.e., give examples of real world problems. For example, she said, take fractions–and then added in a hushed confidential tone, “And I wish they would just do away with them, but there they are so we have to deal with them”. Readers of my book “Letters from John Dewey/Letters from Huck Finn” know that my experience in ed school and student teaching has taught me excellent verbal and vomit suppression skills, so I kept quiet. She then went on and described how students could measure a table, say, with fractions of inches and then find the area, or perimeter, etc. She remarked how it is common that many adults say “What on earth did I learn that algebra for?”
I responded that in my experience with word problems or any kind of problems, the relevance to real-life never mattered to me. What was important was whether I could do the problem, and that I noticed with students, if they can’t do something they get frustrated and that’s when they ask “When will I ever use this stuff?”
She stated very matter-of-factly, like a doctor who has heard the complaints of a particular symptom from many patients over many years, that I probably liked math and therefore had an inclination to learn it, but there are some kids who, for whatever reasons, hate it, and have a hard time with it.
What she was saying was a variation of the “you’re the exception” argument. It is offered as a counterpoint to anyone who defends learning math in a traditionally taught manner. Usually, such conversations focus on misrepresenting traditionally taught math as “rote memorization of facts and procedures” with no understanding, and no connection to previously covered ideas–it is all tricks and mnemonics with students “doing” but not “knowing” math. Such mischaracterization is picked up by supposedly objective education reporters who do not question their source’s assertions, but take it on faith.
Those who did well in math taught in the manner so derided and mischaracterized are thus put in a category of “You’re smart; you would have learned it any way it was taught.”
In light of such discussions, I find it interesting therefore that Jo Boaler who has become the cause celebre of math education of late with her latest book “Mathematical Mindsets” (incorporating the ideas of Carol Dweck’s “growth mindset” thesis) says the following at her You Cubed web site:
“When mathematics is taught with an attitude of elitism and is held up as being harder than other subjects and suitable only for the gifted few, a tiny subset of those who could achieve in mathematics—and the scientific subjects, which require mathematics—do so.”
So, using Boaler’s own logic, the idea of “giftedness” or exceptionalism is harmful, since everyone is capable of learning math. But if the idea of giftedness is so overused and abused, then those people who benefited from traditionally taught math should not be viewed as “exceptions”. Doing well with the old style of math does not necessarily signify giftedness.
She (and others) then do the usual mischaracterizations of traditional math. Her underlying premise is that math be taught the right way. And “the right way” means “not the traditional or conventional way”.
She concludes: “It is imperative for our society that we move to a more equitable and informed view of mathematics learning.”
All you need is the right “mindset”, I suppose. That and “full inclusion” classrooms” so there are no special classes for students who may in fact be gifted. A positive “I can do it attitude” is great, so nothing against Carol Dweck’s theories. But such mindsets need to be coupled with good instruction, study habits, initial worked examples and problem sets with well-scaffolded and increasingly difficult problems that stretch thinking beyond the practice problems. It also takes hard work.
What I’m finding is that the “exceptional” students in various classes I’ve taught are those students who benefitted from solid instruction–acquired in school, but often via traditionally taught math by parents, tutors, or learning centers.