Greg Bales

Knowledge for Teaching

Because it comes very close to what I do IRL, I can’t say very much about Elizabeth Green’s New York Times Magazine article about training teachers, which has been making the rounds through the Intarwebs.1 But I want to highlight a concept springing from the work of Deborah Loewenberg Ball, dean of the college of education at Michigan. Studying mathematics pedagogy, Ball (with coauthor Hyman Bass) recognized that, to be able to teach mathematics well, teachers need a sort of empathetic knowledge that is different from being able to find the derivative of a curve. Green describes it:

It’s one thing to know that 307 minus 168 equals 139; it is another thing to be able understand why a third grader might think that 261 is the right answer. Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it. Then they need to take each mind from not getting it to mastery.

Ball called this knowledge Mathematics Knowledge for Teaching (MKT) and, as education researchers are prone to do, devised a test to measure it. MKT, she discovered, has a strong correlation to learning. That correlation has led other researchers to begin studying the idea of knowledge for teaching in other disciplines, including Pam Grossman in English.

Since I read that last part about Grossman’s research (which, going by her CV, doesn’t seem to be that far along), I have been thinking about what English Language Arts Knowledge for Teaching (ELAKT) might be. Surely it includes sympathy for the traps of argument and the problem of process when writing. It also includes a keen awareness of the ambiguities of language and a willingness to to exploit those ambiguities at all points of learning. But what of teaching narrative, or teaching poetry? To teach fractions well, math teachers must understand why slices of pie are really poor metaphors to use; is there something comparable for teaching voice, for teaching meter? I’m curious what you language teachers think.

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Comments

March 10, 2010

I don’t know what the specifics would be, but I’ve always thought that one of the reasons I was not particularly successful as a teacher of writing is that it’s something I can’t ever recall having to learn to do myself. I do much better when teaching things that I’ve blundered at and worked my own way through. Not everyone will have the same problems and difficulties you did, but if you can at least get a concept of one set of difficulties, it makes it easier to imagine more.

there’s something to your thesis. According to the article, Deborah Ball’s story about teaching mathematics is the opposite of your story. She was a language student and seemed to stumble into mathematics. I’ve met other math teachers who have similar stories: they were able to teach it because for much of their lives, they didn’t get it. After working out the process intellectually for themselves, they were able to turn around and bring their students along a similar path.

March 12, 2010

i’ve actually wondered the exact opposite of ms laura. growing up bilingual and having had very poor language arts instruction from the very beginning—or at least 3rd grade—i’ve always struggled with the written language. an embarrassing admission for a phd in language to admit, i know. but, 3rd grade was in spanish. i entered halfway through 5th grade into an advanced placement class in louisiana that was well above me grammatically and i could not swim well. 7th and 8th were taught by non-native english speakers in the d.r. and then there was the not having gone to anything during 10th, 11th and 12th… so, i’ve muddled my way poorly through both grammar and argument and think that these are subjects that i simply cannot teach well—at least in english. because i feel less than confident in my own abilities to do so.

but, the other thing about those concepts you bring up is that one develops an ear for them over time. maybe math is the same way… but, it takes a lot of reading of different kinds of voices, tones, etc., in my estimation, to get to a point where you can easily identify such things. and, differently than fractions, etc. this type of reading is, by and large, taught in schools much later. and, though one of the things that math teachers have to deal with is a cultural intellectual laziness that allows people to be poor at numbers, language arts teachers have to deal with a culture that doesn´t read. and, you get stuck in a trap where reading for content rather than tone, nuance, etc. is sufficient because, at times, that is all that can be asked.

March 15, 2010

Mathematics might be a special case and a poor comparison because in many ways it’s about learning logic. That can be epiphanic in a way that reading often is not: once you grasp the concepts of equality, substitution, and distribution, you can really comprehend algebra; once you get the various properties of numbers, you can do a lot with it. Moreover, mathematics teaching has long been plagued by really bad rote knowledge at the expense of learning the basic processes that make it work. For example, to this day, I still frequently act as though there is only one real way to subtract a 9 from a 1 (as in 61 – 59 = 2), though that way is incredibly inefficient, because it’s how I was taught to do math. The steps to make it happen were more important than the concept being learned. Students taught like I was don’t really learn mathematics—they learn the shortcuts to apply mathematics instead. I never had a chance to inquire of them much, but I wouldn’t be surprised if the teachers I was referring to in 2 had their epiphanies when they realized that what they really needed to learn wasn’t the steps to apply the concept but rather the logic that the concept relies upon.

It’s because the logic of mathematics matters so much that Deborah Ball (in the article) makes a big deal of saying that teachers really need to know mathematics well to teach it well—and that goes for all math teachers, from kindergarten up. I have no doubt that she is building off of research from the University of Chicago, which I think took place in the 1990s, that concluded that even student teachers in mathematics didn’t know their fields very well. And it makes sense: if the ultimate goal is for all students to learn algebra before they graduate high school, then it’s really important for those teachers teaching arithmetic in primary school to understand how the two are connected so they can help their own students make those connections, too. But historically, they don’t. All arithmetic teachers have known is they need to teach addition and subtraction, multiplication and division. It is the ability to recognize how to move from a crutch to a fundamental understanding of process that I think Ball is referring to with MKT.

Now, I have no doubt that teaching reading and writing has its own shortcuts that can undermine learning, and they have nothing at all to do with what age a skill is taught. One of the best known shortcuts in teaching writing is the 5-paragraph theme structure: teachers have taught it because it’s a fairly adaptable pattern and it yields fairly neat essays that are easily scored. Students learn it at the expense of, for example, more sophisticated structures that meet the demands of the kind of essay they must write (which also requires an awareness of the rhetorical demands of the essay—which teachers also would have to teach). There have been efforts to change that crutch (1980–1990: write about yourself; 2000–2005: everything’s an argument), but just as in mathematics, teachers have managed to replace the crutch with another.

One crutch in reading is the tedious distinctions secondary teachers make about literary themes (a theme is x, not y, and it must be said in z way), which is part of a larger tendency to teach formalism at the expense of rhetoric and the idea that writers write in order to say something to someone. It is “easy” to teach literary terms; moreover, if my students learn to recognize a literary term or a theme, then it is also easy to measure what they know.

Now, a lot of teachers don’t even recognize these kinds of things as problems, but I wager that many students don’t get writing or reading—or they don’t like them, or they find them a drag—precisely because they, too, have been taught to walk with crutches in place of their own two perfectly good legs. Obviously there will always be students who will refuse to play even with the best teachers, but I wager the teachers who teach students to walk might, who have something like high ELAKT (or whatever it might be called), get more students to come along with them than those who do not.

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