Hung-Hsi Wu

Last night I found the website of a professor at Berkeley who has been quite prolific in the area of Mathematics education.  I've only had a chance to read one of them (here), but I found it very timely and interesting.  I look forward to reading the rest.

I bring this up today, because Wu's comments on "order of operations" and other vocabulary like domain and range meshed perfectly with some of my observations thus far.  The first sentence:

One of the flaws of the school mathematics curriculum is that it wastes fruitless exercises in notation, definitions, and conventions, when it should be spending time on the mathematics of substance

Wu goes on to explain order of operations, the Please Excuse My Dear Aunt Sally mnemonic, and how all conventions like this are artificial.  My favorite example was

Evaluate 4+5*6/10

"Now, one never gets a computation of this type in real life, for several reasons.  In math the / sign (in the paper it's the divide sign with two dots, but i'm not going to the trouble of encoding it properly here) basically disappears after grade 7.  Once fractions are taught, you almost always see 6 * 1/10.  Moreover, if anyone wants you to compute that, he would certainly make sure that you do what he wants done, putting parentheses in the right spot.  The original problem is therefore a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules."

Or, at least I thought it was my favorite example until page 9, when I ran into "most beginning algebra texts still devote pages to teaching the concepts of the domain and range of relations which are not functions, and teachers are known to proudly drill their students on learning htese terms.  But these concepts are not used in any part of mathematics except for rare circumstances such as the discussion of correspondances in algebraic geometry.  There is not much to gain by spending valuable classroom time on this topic."  Our friends the domain and range return!  

The point of all this was mostly just to make a record of these math education papers.  Check back later to see if I've reviewed any more.  Ciao for now!