Wolfram Alpha Widgets

You can now customize your Wolfram Alpha (W|A) queries using a W|A widget right on your web site. It's currently in the Beta stage. You'll see a widget,which I cooked up in a few minutes, below this post. I was able to control the output to just what I wanted. I did not need all sorts of complex number representations and other stuff that comes with the standard W|A query for a simple derivative. Also, with the widget, you don't leave the web site you're on. I plan to put some of these on my class web pages.


Here's another one.

Teaching teachers to teach

An article in last Sunday's New York Times discusses the complex issue of teacher preparation. The writer of the article includes a lengthy discussion of math teaching in particular. I found it to be quite interesting - the work of math educators doesn't usually make it to mainstream media. Hopefully the Times will continue its coverage of key education issues such as this one.

Not so Elementary Mathematics

A thought provoking article on mathematics for elementary school teachers appeared in the recent issue of the American Educator. It was written by Dr. Hung-Hsi Wu, Professor Emeritus of Mathematics at UC- Berkeley. He writes that the basic operations of addition, subtraction, multiplication and division involve more conceptual processes than most people realize, and suggested that there should be separate fourth and fifth grade teachers in math.

Of note in his article is the very basic notion that mathematical thinking involves breaking up a complex task into several easier components. To add 15+16, it is conceptually easier to break up the numbers into 10's and 1's. Even if the rote algorithm is taught at some point, teachers definitely need to understand the ideas behind place value that are inherent in the standard algorithms for arithmetic. I mentioned to my students, in my graduate level math course for high school teachers, that 79*85 can be rewritten as 79(80+5), which leads to the distributive property used in algebra.

Many had never thought it about that way. They quickly pointed out that students are less likely to make errors when calculating 79(80+5) as opposed to the standard way of multiplying. Both methods require the same number of arithmetic operations. The partial products method simply requires a little more space. At any rate, it does require some organization of thought for the student, which is another aspect of mathematical thinking.

I should note that the same issue of American Educator also has an excellent article on the "science wars" and sheds some light why one needs both content and reasoning in science. That is, scientific reasoning cannot exist without content. Likewise, understanding mathematical concepts cannot exist without sound mathematical content.

Some articles on faculty development

The March 2009 issue of PRIMUS, a journal for undergrad math education, focuses on faculty development. The articles are an interesting read for those who want to learn more about student centered math classrooms and varying types of assessments.

Also, the January 2009 issue of PRIMUS has three articles on the use of wikis in math classes. The one on the use of wikis in a senior capstone course was authored by me and the other two articles are on the use of wikis in a general math course and in a real analysis course.