An opinion on how one should or should not do testing in a math class.
[Updated to add justifications]
There’s no particular reason for this topic as I’m not teaching at the moment and I’ve not had to deal with anyone else’s testing issues. It just came to mind and I thought I’d get the ideas out.
Here are my shoulds for a major math test (think midterm or final, not quiz):
- It should be out of 100 points. Because it’s easy to understand what the grade means and you have enough room for decent ranges for all the grade groups.
- It should be designed so that it can be graded in whole points; no fractions or decimals. Because if you open the door for fractions, then you just encourage arguments about grades.
- It should be designed so that the average grade is in the 70-80 range (depending on the course and class, of course), and with a reasonable distribution. Because this eases interpretation, avoids crazy curves and gives enough room for distinctive (by grades) scores.
- It should be comparable in style and depth to the way the course has been presented so far. Because that’s the only fair thing.
- It should contain a range of problems covering the topics of the test. Because that’s sort of obvious, but also because the score will be interpreted as the knowledge of all the material.
- It should be take about, but not more than, the allotted time for most students to complete, with an opportunity for quickly checking answers. Because if time becomes too big of a factor, then you are testing other skills and you’ll get strange results (and lots of complaints).
And here are some should nots:
- It should not have unnecessary multi-part questions, i.e. where the answer to part a. is needed for part b. Because then you are stuck deciding what to do with tests where they get a. wrong, and in general it becomes much harder to connect performance to learning.
- It should not overemphasize any aspect of the course or prerequisite knowledge (like algebra for calculus). Because you just have to accept that they’ve passed the prerequisite and not keep punishing them for not making an A in it.
- It should not contain any problems that are intentionally tricky. Because … do I really have to have a reason for this?
- It should not be used to introduce new material to the students. Because, a test is a summary assessment and the pressures and the results of the test don’t relate well to students learning during the experience.
- It should not include extra credit problems to make up for excess difficultly elsewhere. Because then the distribution of the problem emphasis and difficulty is out of balance, and you are putting too much on a students ability to figure out which problems they can and can’t do.
- It should not be used to reward or punish any set of students, e.g. including a special problem covered only on a day that a large portion of the class missed. Because it’s obviously unfair and a bad idea and …
I can’t say that I always follow these, but at least it’s important to be aware of what I’m doing and have some reason for it. And I can’t say that not following these guarantees a bad test. However, it’s not a bad place to start when designing a test, or at least to think about what you expect before designing a test.