An all-round approach to problem solving

Until the 1970s, the colleges of the University of Cambridge offered students benefits known as Entrance Scholarships and Entrance Exhibitions.  These were monetary awards to supplement other sources of finance that the student was receiving.  With inflation, the significance of the value declined, although there continued to be kudos for having obtained a scholarship or exhibition.   Eventually the colleges changed the system.  When I sat the scholarship examinations in 1967, I took exam papers in mathematics and physics.  One of the physics examination papers was designed to test one's ability to bring together many aspects of physics, and did not simply test whether you knew about light rays, or how an electric motor worked.  They were all, of course, unseen.  Even at this distance, I can recall some of the questions, either from the questions that I tackled to win my scholarship, or from those that I used as preparation. 

So dear reader: "A copper plate is placed on the north bank of the River Thames at Greenwich where the river is tidal.  A similar copper plate is placed on the opposite, south, bank.  The north bank is connected by a copper cable to the positive terminal of an ammeter, and the negative terminal is connected to the south bank plate.  What readings will the meter show over a twenty-four hour period?"

Another, which I am reasonably sure was in the questions I answered read: "Explain what happen when a balloon is burst with a pin, drawing attention to the reasons that the balloon goes 'pop'".  Tina and I have been talking about this, because we have had to perform a related experiment.  Three or four weeks ago, we started to make two papier-mache eggs for a sermon illustration at Easter, using balloons as the former.  So we pasted strips of newspaper onto the balloons, allowed the paper to dry, and added further layers of paper soaked in dilute paste.  Eventually we decided that the eggs were firm enough.  So last night we burst the balloons.  But, we had talked in advance about what we expected.  Would the glue hold the balloon in shape?  Would the tension in the latex tear it away from the papier-mache?  Would there be any "pop"?   So what happened?  The air gradually escaped through the pin-holes with a quiet hiss.  The glue held the balloon firmly in place.  Over the weeks, the air pressure inside the balloons had reduced, but had not reached the air pressure outside.  Now comes the next stage of decorating these large eggs!

Part of my postgraduate programme in operational research was examined in a similar way, with a question which was designed to bring together material from across the syllabus.  The Lancaster "Jumbo" examinations were eight hours long.  At 9am, one was presented with a case study to analyse and report on by 5pm.  They were artificial case studies, based on a hidden model, and there was no indication of how to approach each one.  Setting them was an art.  Later in my academic life, I devised two similar case studies, which we used in a different setting to examine undergraduate students in the Mathematical Statistics and Operational Research degree at Exeter as part of their communications skills course.  They are hard work to create!  Mine were both based on queue models, but brought in statistical analysis and cost-benefit analysis.

It strikes me that both examinations - Cambridge scholarship and 8 hour case study - are testing something which is desirable for all students to have achieved, and that is an understanding of their material without the artificial boundaries of one area of their subject material.

ps: The ammeter will show a current.  It will follow a sine wave (approximately) over time with a wavelength of about 12.5 hours.  This is because the salty water is a moving conductor passing through a magnetic field (the earth's magnetic field).  As the tide goes in and out, the direction of the flow of electrical current will reverse.


Popular Posts