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

Comments
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.)