## Sunday, 15 November 2015

### The One Thing that my College Gets Wrong About Exams

I'll be honest. Despite it's shortcomings, many of the courses that are offered actually do contain material that I find interesting. In fact, when you're learning something at the level of a college course, there are few subjects that aren't interesting. It's like Richard Feynman said; everything is interesting if you go deep enough into it. My biggest complaint about the system isn't the lack of depth in the courses or for that matter the professor's depth of knowledge (although I have had a fair share of instructors who had a less than optimal grasp of the course material themselves). My biggest complaint is the focus of the examinations that they conduct that are supposed to evaluate how well the students know the material. The exams  - in addition to having a low correlation to the students' grasp of the material - also actively discourage them from gaining a true understanding of the course material.

Typically, the exams I've written (particularly exams of courses that are highly mathematical) test only the ability of the students to memorize two things: derivations and formulae. I'm not saying that people should be exempted from memorizing formulae. There are plenty of formulae that are so important that they must be memorized. The problem is when you have to memorize formulae that look like this:

$L_F = -10 log(\cos{\theta} \{\frac{1}{2} - \frac{1}{\pi} p(1-p^2)^{\frac{1}{2}} - \frac{1}{\pi}arcsin(p) - q[\frac{1}{\pi}y(1-y^2)^{\frac{1}{2}} + \frac{1}{\pi}arcsin(y) + \frac{1}{2}]\})$

$p = \frac{\cos{(\theta_c)}(1-\cos{(\theta)})}{\sin{(\theta_c)}\sin{(\theta)}}$

$q = \frac{\cos^3(\theta_c)}{(\cos^2(\theta_c) - \sin^2(\theta_c))^\frac{1}{2}}$

$y = \frac{\cos^2(\theta_c)(1 - \cos \theta) - \sin^2(\theta)}{\sin{(\theta_c)} \cos{(\theta_c)} \sin{(\theta)}}$

For anyone interested it's a formula that tells you the coupling loss between two fiber optic cables when they're misaligned by an angle theta. The book doesn't even attempt to derive this formula because the authors know that the derivation on its own doesn't really add to a person's understanding of fiber optics. It may be a nice exercise that tests the student's algebraic manipulation but that's pretty much it. In the real world, if there is a situation in which this formula needs to be used, it's pretty much guaranteed that the engineer will just look it up. It's completely pointless to memorize it.

Why is this focus bad? Firstly, it does not actually test understanding and leads to students not getting the score that they deserve. There have been countless instances where I knew  how to solve a problem but didn't get any credit because I had to remember some stupidly long equation. Secondly, it forces examiners to limit their questions to really simple ones because they know that remembering the formula or it's contrived derivation is half the question. So the number of questions that test my understanding of the material is next to zero. Thirdly, it actively discourages students from trying to understand the material. Once people figure out that they can get scores by just memorization, they will start focusing on memorization. Sometimes, there is so much to memorize that there isn't enough time to try and understand even if I wanted to.

If I were the person who was in charge of the setting the examinations, I would do the sensible thing and give every student a booklet full of the formulae that need to be used for the questions. This allows the questions to be far more interesting and test how the student is able to use the information at his disposal to solve actual problems that practicing engineers face. The brain is a processor with a limited amount of cache! It's not a hard disk! Introducing this simple change of focus will go a long way towards courses that are actually useful. It will also give the professors the freedom to ask tougher questions!

Now I know that this approach actually works! Before college I did my Cambridge IGCSEs and A-Levels. Both these exams were very focused on understanding rather than recall. Exams either had all the required formulae included as part of the questions or (as was the case for Further Mathematics at A-Levels) a large booklet of formulae. This didn't affect the difficulty of the exam at all. It's no use knowing formulae if you don't know how to use it. This might sound a bit strange but I actually enjoyed writing my IGCSEs and my A-Levels. The exams were designed well enough that sometimes I came out of the exam hall with a new understanding of what I had learned. I still feel that I understood and learned more in class during my high school than I did in most of my college courses. Any understanding that I have about my course material is a result of my independent reading and efforts rather than the course instruction.

Now I'm not the first person to talk about this. People have been complaining about the education system for a very very long time. And many have even tried to change it by approaching the administration. Invariably though, I've seen that - at least in my college - the people in charge are very reluctant to bring about any of these changes. The biggest roadblock is probably the fact that a lot the of the professors in my college disagree with what I have said above. They believe that memorization is very important perhaps because that is how they were taught. I've seen that things are changing, but not nearly fast enough. I don't really think that the changes that I've suggested will be implemented any time soon. So why am I writing all this down? I really just really needed to vent. XP