We had the second exams for the term this week. I wanted to have them last Friday, which would have been just at the two-thirds point of the term, but apparently there was some kind of religious holiday or something that many students found distracting. I can be reasonable. The exam scores worked out to be almost identical this exam as the last one, in both classes, although fewer people were taking the tests. I had thought these exams simpler, and with I assume the weaker students having withdrawn I'd expected averages to be higher. So that's a little disheartening. Or I was just writing harder than I figured.

However, there was some moderately alarming news in the Introduction to Algebra class. This is algebra for college students, so, yes, I'm not fully convinced that anyone here has seen an equation before. But I had worked at describing the procedures starting from addition and subtraction of fractions, and going onward, to the point that we were solving such word problems as ``the circumference of a circle is (this), what is its area?''.

One problem is that a lot of students apparently had no idea what the little center dot meant. This is the vertically centered dot used to represent multiplication where one wants to emphasize that it *is* multiplication, without using the x symbol that gets confused for the variable *x*. Quite a few didn't know what to make of it and they seem to have treated it as a subtraction sign.

Worse from my perspective is that they seem not to have gotten the order-of-operations idea. I know we covered this; I went over it in class, and I'm careful to explain the order whenever I do a problem on the board, and I do a lot of problems on the board. This isn't even anything that requires careful thought; it's a fixed procedure whose rules you just have to follow, and if you follow them, you will get the correct answers. But when I have an appreciable fraction of the class turn something like

8 - 5*(2*x + 1)

into

3*6 - 3*x + 1

it's enough to bring despair.

* Trivia: * Apollo 13 Astronaut Fred Haise had flown for NASA since 1959. Source: A Man On The Moon, Andrew Chaikin.

Currently Reading: Pirates of New Jersey: Plunder and High Adventure On The Garden State Coastline, Mark P Donnelly, Daniel Diehl.