Dispatches from the Front

Dispatches from the Front

I taught my first calculus course in the fall of 1957 at RPI. Calculus was the lowest level mathematics taught, so first year TAs were given calculus to teach. Calculus I met five days a week and I had two sections. The previous spring they had given me a copy of the first edition of Thomas and told me that this was the book I would use. During that summer I worked all the problems in Thomas; it was the only thing I could think of to do to prepare for my first teaching experience.
On the first day I realized that I would have to teach without notes because I couldn’t hold them with a steady hand; never let ‘em see your notes shake.
The classes had twenty or fewer students. I taught in the same way I had been taught at RPI. I taught the same material and the tests I made up were based on the tests I had taken. I wrote my tests on the blackboard; the only tests that were mimeographed were the three hour finals which were given in the gym en mass.
I found out at the end of the semester that the finals were graded during a marathon session that started right after the final was collected.
My biggest anxiety was making a test that was too easy and yet,not too hard. I ended up with tests whose problems were trivial if you saw how to work them and impossible it you didn’t. Of course the students hadn’t worked on making up the problems all night and so didn’t see how they were obvious. The grades were dismal. I would then add insult to injury by going over the test with the class and showing how easy it was.
This made the class feel bad; it made me feel bad.
“Why didn’t I see that?” they would ask themselves.
“Why didn’t they see that?” I would ask myself.
I would recall that in my Statics and Strength of Materials class there was an A, a B, a C, a D and 16 Fs so giving too many Fs wasn’t a big concern.

I don’t remember what my early grade distributions were. I do remember that a regular faculty member looked over our grades for irregularities before we handed them in. I suppose my grades must have fit some predetermined norm because I don’t recall any bad glances directed my way.
At my next graduate school calculus was taught in a lecture hall to a lot of students and tests were given in the evening in the lecture hall. Two versions of a mimeographed test were made up by the TA and approved by a faculty person. The tests were multiple choice and machine graded. I had nothing to do with assigning letter grades to scores.


I had a student in College Algebra who passed the bi-weekly tests and failed the final dismally. He told me that this had happened all through high school. He’d have an A average going into a final, fail it badly, and get a B in the course.
I told him that he could memorize two week’s worth of material but not a semester’s worth.
But I have had students who could memorize a semester of problems and formulae. And I have seen instructors who would encourage memorization by putting the page and number of the problem whose numbers they had changed to make the test problem.
At the risk of appearing grumpy I think this method of teaching and testing is insane.
One thing that seems clear to me is that the test should be made to fit the course and not the course designed to fit the test.
When I was a graduate student I made some extra money tutoring a high school kid in plane geometry. In New York State one of the requirements to pass a high school class was, and maybe still is, to pass the Regent’s examination in that subject. The previous 15 or so years of Regent’s exams in plane geometry had been compiled into a book and this was the text that the student was using.
The whole point of the student’s course in plane geometry was to pass the Regent’s exam. His course was designed around the exam and not the exam designed around the course.