Yesterday I finally got my calculus test results for the test I took last week. My grade was 90% (plus 3 percentage points for extra credit work I did). That the class average was under 64% is irrelevant. As a perfectionist with a 4.0 GPA, my grade is unacceptable. The question is, how am I going to make sure it doesn’t happen again?
The first step is a critical analysis of where I went wrong. The second step is to figure out what was wrong with my learning and test preparation strategies, and the last step is to adjust my learning and test preparation strategies so it doesn’t happen again.
It has been my experience that errors I make on a math test fall into three different categories:
- Format errors
- Calculation errors
- Conceptual errors
The first, format errors, occur when you don’t obey the formatting rules outlined or assumed by the professor. For example, if you’re asked to show work and you don’t or if you’re supposed to call a nonexistent limit “DNE” instead of “it no work”, I would call those formatting errors. The second is calculation errors, and those are caused when you don’t pay attention to detail, or you fail to check your work. The third is the worst kind of error because it signals a conceptual misunderstanding of the material the test is testing you on.
- Format errors: Sloppiness, failure to follow guidelines
- Calculation errors: Failure to check work or pay attention to detail
- Conceptual errors: Failing to understand the material at the conceptual level
Before the test, our professor repeatedly told us that we have to show work in order to receive credit. Well, silly me, on a two-part problem which required the same kind of thinking on both parts, I decided it would be sufficient to show work on one part and just do the next part in my head. Ouch, -1 point. On another problem, I got a -2 for not being explicit enough with my answer. I answered “discontinuous at x = 3 because undefined”. The correct answer was “f(3) is not defined”. I think my professor was getting tired or something when she graded that one. On another one I used absolute value bars when I should have used brackets and a negative sign. I still got the right final answer–my method was just not the traditional one. All in all, 4 out of 10 of the negative points I got was due to avoidable sloppiness–format errors.
On two of the problems, I demonstrated a failure of understanding at the conceptual level. I lost 5 points for mistaking a tangent line to a curve at a specific point for the derivative function of the curve. It took me an hour to figure out where I went wrong–a definite failure at the conceptual level. The one other point loss came from an inability to remember (or to figure out) whether or not a function is differentiable at a removable discontinuity.
To fix errors of the first kind (i.e. format errors) I need to pay more attention to my professor’s guidelines, and I need to follow them to the letter. It wouldn’t hurt to show way more work than I think is necessary. It probably would be a good idea to give my answer in multiple ways just to make it obvious that I know what I’m doing. I didn’t make any calculation errors, but these are fairly easily fixed by checking work religiously and by at least two different methods. Errors of the third kind (i.e. conceptual errors) can only be fixed by analyzing my learning strategy and adjusting it to reinforce and check whether I’m actually understanding the material at the conceptual level. A good review done prior to the test should also help keep the conceptual stuff fresh come test time. So here’s how to fix each of these math test errors:
- Format errors: Pay attention to and follow your professor’s guidelines and generally accepted math syntax. Don’t forget your units.
- Calculation errors: Check your work as you’re going along then later come back and double-check it with a completely different method.
- Conceptual errors: Study, study, study. Constantly review to keep the conceptual stuff fresh in your mind. You need to know the “definitions” so you have a conceptual foundation to fall back on.
That’s it. We’ll see what my grade is on the next calculus test…