Are Mathematicians Smarter Than Math Teachers?

Are Mathematicians Smarter Than Math Teachers?June 6, 2006 04:45 PM
Maybe. But math teachers know things that are (1) useful for teaching math and (2) difficult for non-teaching mathematicians to grasp, according to Deborah Loewenberg Ball, a University of Michigan researcher who spoke recently to a gathering of AFT leaders and staff.
Here’s an example of a task* at which math teachers outperform mathematicians.
Three students were asked to multiply 35 by 25. The answer is 875. Each came up with the wrong answer, but for different reasons. (Click on the links to see if you can figure out the thinking behind the errors.)
Ball reports that math teachers were much better than mathematicians at identifying where students went wrong–an important fact to know to help put students back on track.
In “Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough To Teach Third Grade, and How Can We Decide?” a 2005 article in American Educator, Bell and co-authors Heather C. Hill and Hyman Bass conclude that there is a body of knowledge math teachers need to be effective. They created test questions that captured this body of knowledge, tested teachers, and used the results to accurately predict which teachers’ students would learn more.
Ball told AFT leaders that the finding that there is a body of knowledge teachers need to have to teach math can be extended to other subjects. As the drumbeat for “content knowledge” becomes louder and louder, this research answers the questions “Which content?” “Which knowledge?”
*Ball notes that this type of thinking, error analysis, is not only a teacher thing but an important area of mathematics
Posted by John on June 6, 2006 04:45 PM | Permalink
Understanding the source of error is very important. A math teacher needs to have extensive experience analyzing mistakes. This requires a strong, strong handle on arithmetic.
But I would be careful before dismissing the math professors. They don’t teach, that is true. They don’t know error analysis, and some other things math teachers need.
But when they get outraged, there is usually a reason. Such as not teaching standard algorithms at all. Avoiding fractions. Not teaching long division. Placing so much emphasis on concept that skill is overlooked (each year I get incoming freshmen from a progressive district who have a real solid understanding of what multiplication is, the variety of meanings it might have, etc, but who have difficulty with facts, eg, 7 x 8.)
Pedagogy and content are both important. Some of the education people and the ‘modern’ curricula privilege pedagogy over content. Back to basics folks tend to emphasize content and ignore pedagogy. Good math teachers, experienced math teachers, we know that we need to pay attention to both and defend our work from either extreme.

One thought on “Are Mathematicians Smarter Than Math Teachers?”

  1. I am a mathematician. Certainly, when I taught my first elementary education course in math last fall, I learned a number of things I had not been aware of. However, I feel that teaching such courses and a lot of reading of the relevant literature enabled me to understand much better what math needs to be taught for elementary school teachers. Recognizing typical errors is just one skill. Others are being able to see what the fundamental and important topics are, and what can or should be skipped (since the current curricula are too full of things of minor relevance); understanding what and how to teach so as to avoid some of the typical mistakes in the first place (since many of them stem from bad teaching); insistence on precision instead of letting everyone “invent” their own algorithm; and the ability to quickly generate a set of problems to specifically clear up a student’s confusion about an item. It is these points I emphasize when I teach math teachers, and my being a mathematician helps here.

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