# College Math Teaching

## May 10, 2011

### Non-portability of mathematical skill

On my calculus final exam, I gave two questions about a metal plate of uniform density. The plate was easy to describe: it’s boundary was the $x$ axis and the parabola $y = 1-x^2$. In the first question, I asked for $M_x$ (the moment about the $x$ axis and in the second question, I asked for the center of mass (they could use symmetry to deduce $\overline x = 0$). So to find $\overline y$, they needed to find the area (mass) and $M_x$.

What astonished me is that a number of students missed the question “find $M_x$ ” completely but then went on to solve for $\overline y$ correctly!

This says something about the intellectually immature mind, but I am not sure what is says.