Sunday, October 23, 2011

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.


Kathie said...

Would you have accepted THIS?

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

Zeno said...

Of course.

Elipson said...

How about transforming the equation into the Laplace domain, solve it, but now transform it back. Would you accept that? ;)

Karen said...

Good heavens! Whatever happened to listing various versions of the equation on sequential lines?
4x + 3 = 11
4x = 8
x = 2

Are you not leaving enough space on your exams for answers, Zeno?

Zeno said...

Elipson: Yes, of course, for those algebra students who mastered Laplace transforms before taking elementary algebra.

Karen: I provide plenty of space, but this appears not to help certain students; namely, those who (a) grip the pencil with their fists like a two-year-old and write in BLOCK CAPS, (b) start writing two inches from the right-hand margin and continue up or down the edge of the paper, or (c) squeeze their work into one square inch because of some obsessive-compulsive impulse.

Disturbingly Openminded said...

So you want students to not only get the right answer but to also understand what they are doing.

Harsh, man, harsh.

(Cue piano music)

"Oooohhhhh, you can't take 3 from 2, 2 is less than 3 so you look at the 4 in the ten's place....."

Karen said...

Zee, you are my hero. I am probably the only geology MS student who has graduated from my university in recent times WITHOUT doing a stint as a teaching assistant. I didn't need the money and I have NO patience for the stuff you real teachers put up with. You lot are awesome.

p.s. the thesis was submitted today. I'm on track to graduate in December.

Anonymous said...

This: "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."

Should be bloody obvious from the beginning of the first class *anyone* takes at *any* institution. If you want an A, you have to give the teacher what xe wants. You can't expect the teacher to guess what you mean and *hope* they interpret your gobbledygook in the most positive light.

I would have thought that went without saying. What did our friend expect?