University Assessment rant
It has become clear to me that assessment at University is rarely aimed at assessing the increase in intelligence of a student due to their participation in the course, but more commonly the ability of a student to memorise one lecturer's methods of teaching. Sadly, various attempts at bringing this to the attention of academic staff have been met with ignorant stubbornness, and it seems more fruitful to play the game. That may explain why I was relatively indifferent when presented with what is typically a very frustrating example of such butt-headedness.
Last week I was marked wrong when I answered that n squared terms were required in an adjacency matrix to fully describe any graph. The answer they were looking for was only n times n-1 divided by 2, which is considerably less than n squared (roughly half). And that would be correct if we only considered undirected graphs. Directed graphs, which certainly belong to the set "any graph" described in the question, do indeed require n squared terms in the adjacency matrix. When I mentioned this to the lecturer, he claimed that yes, that was the correct answer, but when adjacency matrices were introduced in the lectures, directed graphs had not yet been explained. Thus, we were to ignore the truth, and pretend we have no ability to learn outside the classroom. The assessment task then, was to see how well we could parrot the lecture material, even to the point of "forgetting" prior knowledge, and answering questions wrong such that they suit that taught in lectures.
I thought Albert Einstein said something admonishing memorising that which can be looked up, but my searches for the exact quote have proved fruitless. Allow me to be so bold then, as to offer a quote of my own.
"There is no point in memorising that which can be easily looked up, for our minds are capable of so much more than serving as an incomplete and fallible reference book."
And therein lies my greatest disappointment with University education. More and more we seem to be encouraged to stop learning and start parroting. A number of subjects have required no more intelligence to pass than the ability to rote learn formulas, and substitute numbers. It seems laughable in my mind, that we could claim to be educated in the field of, say, information communication theory, because we are able to memorise a number of formulas, and can substitute the numbers provided in the question into the memorised formula. It gets more nutty when the formulas become such gospel, that we are required to perform our substitution dance in completely inappropriate circumstances. That was basically the final exam in last years Computer Networks subject - the substitution of numbers from the questions into a couple of information theory equations. The problem was, those equations did not apply in the circumstances described in the question. I knew that because I've studied information theory outside that course. I let my frustrations be known to the powers that be, and was promptly placed back in the zombie pack and asked to stop thinking so much. At first, answering questions I knew were wrong was very painful. At first it hurt to abuse the equations, which are actually very accurate and important in the situation in which they were proposed, by substituting numbers from a question which does not describe a situation in which they apply. After a while, I guess I numbed a little. The thing that keeps me going is my steadfast respect of the mantra articulated by Mark Twain:
"I have never let my schooling interfere with my education."
A real concern for me is that so many people are happy to accept that formula substitution constitutes skill in a new discipline. Many people are so comfortable with that method of assessment that they never question the equations they are using. And they are comfortable with being so apathetic because that is all University requires. The real danger is when I have to work with these people. I recently had such a situation, where when discussing a new algorithm for sizing a physical phenomena (I'm being deliberately vague to avoid identifying the situation) a colleague was so happy to take a couple of formulas way out of context and still treat them as gospel, that against my wishes I wasted hours of development time implementing an algorithm I knew was wrong. He tried to tell me that attenuation of signal as it spreads out is an inverse square law. I said that's for propagation and you can't apply it here. He said we don't want to get too complicated. Well, the world is complicated, and unlike University assessment, you can't just substitute the numbers from the question into the nearest equation, and hope to get a sensible answer.
I'm reminded of a bit of science folklore, that may have lost some accuracy over the years, but still carries the important information. I'll finish this rant by pasting it verbatim here.
Some time ago I received a call from a colleague who asked if I would be the referee on the grading of an examination question. He was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would if the system were not set up against the student. The instructor and the student agreed to an impartial arbiter, and I was selected.
I went to my colleague's office and read the examination question: 'Show how it is possible to determine the height of a tall building with the aid of a barometer.'
The student had answered: 'Take the barometer to the top of the building, attach a long rope to it, lower the barometer to the street, and then bring it up, measuring the length of rope. The length of the rope is the height of the building.'
I pointed out that the student really had a strong case for full credit, since he had answered the question completely and correctly. On the other hand, if full credit were given, it could well contribute to a high grade for the student in his physics course. A high grade is supposed to certify competence in physics, but the answer did not confirm this. I suggested that the student have another try at answering the question. I was not surprised that my colleague agreed, but I was surprised that the student did.
I gave the student six minutes to answer the question, with the warning that his answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, but he said no. He had many answers to the problem; he was just thinking of the best one. I excused myself for interrupting him, and asked him to please go on. In the next minute he dashed off his answer which read:
'Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula S = at2/2, calculate the height of the building.'
At this point, I asked my colleague if he would give up. He conceded, and I gave the student almost full credit.
On leaving my colleague's office, I recalled that the student had said he had other answers to the problem so I asked him what they were. 'Oh, yes' said the student. 'There are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of simple proportion, determine the height of the building.'
'Fine' I said. 'And the others?'
'Yes' said the student. 'There is a very basic measurement method that you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give the height of the building in barometer units. A very direct method.
'Of course, if you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of 'g' at the street level and at the top of the building. From the difference between the two values of 'g', the height of the building can, in principle, be calculated.
'Finally,' he concluded 'there are many other ways of solving the problem. Probably the best' he said 'is to take the barometer to the basement and knock on the superintendent's door. When the superintendent answers, you speak to him as follows: "Mr Superintendent, here I have a fine barometer. If you will tell me the height of this building, I will give you this barometer."'
At this point, I asked the student if he really did not know the conventional answer to this question. He admitted that he did, but said that he was fed up with high school and college instructors trying to teach him how to think, to use the 'scientific method', and to explore the deep inner logic of the subject in a pedantic way, as is often done in the new mathematics, rather than teaching him the structure of the subject. With this in mind, he decided to revive scholasticism as an academic lark to challenge the Sputnik-panicked classrooms of America.