Wednesday, April 4, 2007

"I don't know" is a good answer

In the summer of 2006, I had the opportunity to teach Math 10A (calculus for the non-technical students) through a fellowship from UCSD's Center for Teaching Development. You can see the syllabus here. I think the format is a little bit clunky, but I'm not very fluent with HTML and making the boxes that resize themselves properly was a big deal for me.

This post is going to highlight the "About Tests" section, which I've copied below:
Tests measure your ability to demonstrate your understanding of the course material.

I have an unusual stance when it comes to exams. You can earn up to 20% credit for admitting that you don't know what you're doing instead of haphazardly guessing at what you should be doing. I want to discourage the "shotgun" method of test taking; that is, I don't think you deserve credit for writing down a bunch of stuff and hoping that some part of it resembles something that might come close to the right answer. The tests attempt to measure how well you understand the material, not your ability to spew information on your paper. This does not apply to multiple choice questions. On the tests, there will a box to mark if you want to take the credit.

Similarly, you will earn credit on your exams for having a good presentation. While the answer is important, it is also important that you are able to demonstrate how you got to that answer. Math reads left to right, top to bottom, just like in English. (It helps to practice good presentation by doing this on your homeworks!) IfI you have questions about the clarity of your presentation, you are welcome to stop by during office hours and I will help you out.
The 20% credit for not randomly guessing was an idea I came up with as a graduate student while I was lamenting the terrible scribbles students left on their paper when they clearly had no idea what was going on. It frustrated me enough to make me want to give negative points. Of course, that's not an option. I don't think it's good to penalize students in that way.

But instead, I think it's appropriate to award students for academic honesty and integrity by giving them the chance to say "I don't know." In real life, I think "I don't know" is a perfectly legitimate answer, and is often the best one when it's true. Too many times I have seen people (myself included) get trapped in difficult situations because they didn't want to admit that they were not qualified to give an answer on the basis of lack of knowledge or experience.

There are a number of positive aspects to this idea:
  1. As mentioned above, it rewards students who are able to give academically honest answers.
  2. It encourages students to evaluate the quality of their work, something which seems to be conspicuously absent, especially among students who are less mathematically inclined.
  3. It prevents students from being penalized inequitably for that one topic that they never quite understood that happened to be the one that showed up on the test.
  4. It makes grading those problems much faster.
As I tried to implement this, I discovered a few problems which I will hopefully be able to address and clean up with some more experience:
  1. The grading must be done in such a way that 20% is a meaningful enough amount to make it worth while for the students to consider it as an option. Many students felt that their wild guessing would get them more points. I can see a two possible solutions. I can increase the value from 20% to 40%, or I can change the grading so that it is harder to earn 20%. I'll have to experiment and see what happens.
  2. Many students don't know how to interact with this option. Their entire academic lives, they have been taught *NOT* to leave questions blank and to always guess something because "perhaps you'll get partial credit." I think students need to be retrained to use this system to their advantage.
  3. The grading must be consistent from problem to problem. It cannot be difficult to earn 20% on one problem, then a piece of cake to earn 20% on another one. I think this can be resolved by making all problems worth 5 points. With a narrower grading system, there is less room for fudging around with -1 for this mistake and -2 for that mistake. What is the difference between 14/20 and 15/20 on a particular problem, anyway?