[O.C.T.O.B.E.R. IV-4] What should an exam test?

Today, I am grading my Calculus I first exam (there was also a zeroth exam–the gateway).  I’m noticing something nice–people are doing MUCH better on this exam than they did on the gateway, and sometimes even on the first homework assignment!

It’s told me quite a bit about how exams should go from here on out.

I was listening to my music while grading (yes, I guess grading means I have to Face the Music…) and something interesting came up.

My music collection contains many things other than just songs–there are radio talk segments that I have recorded, blog posts that I have transcribed vocally, and then there are psychology lectures from when I took PSYC-350 eight years ago at UNL.

And so one of the early lectures came up: talking about researcher- versus self-selection into psychological (and other) studies. After an example that forced us to do a lot of thinking, the professor said the following (including a few curse words that have been masked into brackets:

And it’s an example of something that I won’t do to you on the exam.

All the really nasty [Z = hyperbolic sine integral with an argument of time] happens on the homeworks and in the laboratory. By the time we get to the exam, what I’m focusing on is, ‘Can you see something if it’s there?’ not ‘Can I make up something that you can’t decode?’

Cause the answer is yes–I can write a [Z*t*y] test, grade it badly, and give you a bad grade–no problem! That’s not the point.

(Yes, there actually is a math function that might be written like a curse word, as seen in this picture…)


Well, I think that my gateway quiz for Calculus I was a [Zty] test, as well as Homework 1 in both Calculus I and College Math II. Basically, in each of these, I expected too much of the students in terms of their background and how I conceptually explained the material intended as review.

Well, each time that I screw up, I learn something new! I think that classes have been going better since then.

However, it brings up a good point, and is part of my philosophy.

Timed exams should not be difficult or have twists and turns around every corner. It is fine to have a difficult problem at the end, but I think the time for students to struggle is on the homework when they have resources available to them.

Exams should be primarily for basic application of the concepts and techniques, without a huge amount of thinking involved.

So many people have test anxiety, which may not translate to homework assignments. Then again, since I remain green in this field, I could be just blowing smoke here.

Tests should not be cruel and unusual punishment, and the real thinking and learning should occur without the additional pressure of 50 minutes to do it!

Granted, I have had a lot of tests for myself in a month and a half!


Today is the fourth day of the fourth round of O.C.T.O.B.E.R.

Memorial Stadium: 20 days.

Thanksgiving Day: 53 days.

Joint Mathematics Meetings: 94 days.

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P.S.: The P.A. announcer at the UW-Stout football game didn’t read my blog post from yesterday! He gave scores from around the WIAC, and then said, “And in the Big Ten, the Badgers lose to Iowa 10-6. And Northwestern shuts out Minnesota, 27-0.”

I watched the game on DVR anyway when I got home.


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