You are right, I guess

And I'm right: you guess

The aftermath of the semester's first exam is often a teachable moment. I frequently assign my students to analyze their results. This usually comes in the form of a two-part prompt, to which I want a written response: (1) What kinds of mistakes did you make? (2) What steps will you take to minimize these mistakes on the next exam?

Most of the responses are dominated by the usual litany of math's most persistent errors and shortcomings:

• I misread the problem.
• I made a stupid mistake.
• I used the wrong formula.
• I made a calculation error.
• I didn't study.
• I didn't do the homework.
• I need to catch up.

The proposed remedies are as predictable: More study. More answer-checking. More diligent attention to homework. More visits to office hours or tutors. All good ideas and apt to be helpful if actually applied.

Occasionally, however, I get the whiny response from someone who is looking to place the blame elsewhere. Why not engage the instructor's sympathies by explaining to him that he is to blame? Most students avoid this approach, but sometimes you get a brave one:

After looking to see if I had done the problem right in which case it was correct but the only thing that I had over-looked was the correct notation.

Ah, yes. Notation. I may be a little stricter about notation than other math teachers, but I refuse to countenance false statements like

4x + 3 = 11 = 4x = 8 = x = 2.

I'm just not crazy about taking the equal sign in vain. Putting an equal sign between things that aren't equal is irksome, sloppy, and—darn it!—untrue.

In the present instance, the student was taking a calculus class and had presented me with solutions that were mostly bits of scratch work and the occasional untrue statement. For example,

6x + 3h − 5 = 6x − 5

is a false statement unless you indicate that you are taking the limit of the left-hand side as h goes to zero (if you would please be so kind). The student got most of the credit for deriving the correct answer, but he lost a few for neglecting correct notation. His tone was a bit pettish, but he came to a correct conclusion in his analysis:

Overall, I think in order to improve myself as a math student in Dr. Z's class, I need to focus on how he wants me to solve or work out the problems so I can meet his expectations. Because it seems to me that I do the work as best as I can but fall short of what is expected of me from him. So my best solution to this dilemma is to find out how he wants things done and pretty much follow his rules in order for me to get an A in his class.

A helpful hint: The best way to find out how I want things done is to watch what I do in class, because I model it in every example I do and in every homework question I solve for the class. And—one more hint—be there when I do it.