Past Exam Vision

Students have just been told their exam results for Semester 1, and some of them are facing replacement exams. So we’ll be trotting out our standard suite of exam advice again, which will be all the more poignant now because these people tried to do it last time and failed!

One piece of advice we give is not to use past exams as your main study tool. So many students study for their exams by taking a stack of past exams and systematically working their way through each question and making sure they can do all the intimate details. This is a bad idea for several reasons. I’ll list some in dot point form:

  1. The course may have changed over time, so some of the questions will not be relevant to your course content anymore, while still other questions just won’t have appeared in past exams.
  2. The lecturer probably changed, so the style of the exam questions may be quite different to the exam you are about to do.
  3. No one exam can cover every concept in a whole course, and even several exams will miss something between them.
  4. Lecturers are not stupid, and so will generally always put something in that has not been done in an exam for the past several years, in much the same way that they don’t use yesterday’s questions today on a TV quiz show!
  5. You need to save at least a couple exams to do as proper timed exams in exam conditions or you won’t practice the skill of doing exams in exam conditions.

But there is one more reason I myself had never really known fully until this last semester. It’s related to point number 3 above, but it’s even more pernicious:

  1. Questions in past exams are often cut-down versions of full problems designed specially to be dealt with in exams, and so will not necessarily help you actually understand the material.

Let me explain how I fell into the trap of this peculiar kind of “Exam Tunnel Vision”.

I never studied Differential Equations in a formal course as part of my degree. I managed to avoid all applied maths beyond first year by instead studying statistics, pure maths and Chinese. This means that pretty much everything I know about differential equations has been learned while helping students in the MLC. I have learned a remarkable amount, but there is a problem with my approach: I only see the parts of the course that students ask me about. And since students often study using past exams, the parts of the course I see do not necessarily represent the full picture. Now I do know full well that I should ask questions like “What would happen if it were this way instead?” and “Is there more stuff related to this?” and “Where does this fit in the bigger picture?” and indeed I do ask these things, but sometimes no matter how hard you ask, sometimes you can’t find this information without asking an expert.

Case in point is the Frobenius method for solving differential equations. What happens is you are supposed to make an indicial equation, which for second-order equations will give you two solutions for r. Then for each value of r, you are supposed to do a process to find a solution. But here’s the catch: this final process is quite long, and so in exams and assignments the lecturer only ever asks students to do one of the solutions. Since my learning about differential equations was based entirely on helping students, I had never seen what you were supposed to do after this point! No-one ever asked, so I didn’t know.

I had fallen into the very trap I warn students about: I had developed “Past Exam Vision” and couldn’t see beyond the exam to get the full understanding. In future I’ll be more careful, and now I have a good story to tell them to warn them about it. If I can fall into the trap, then anyone can!

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