Tuesday, May 12, 2009

A Few Thoughts on Teaching

A Few Thoughts on Tests and Testing


I looked at tests as a student for 22 years and I looked at tests as a teacher for 37 years. I’ve looked at tests from both sides now, from years in school and still somehow, it’s test’s illusions I recall, I really don’t know tests all. (Judy Collins, sort of)
I have sensed and heard the frustration of teachers over testing, particularly if they really wanted their students to learn something. Teachers are trapped into playing a game they can’t win. If they give a lot of bad grades, then they are too hard and unfair to their students. If they give a lot of good grades, then they are too easy and aren’t keeping standards high and making it even more unfair to the students who drew the ‘hard’ teacher.
There are no bowls of porridge that are just right.

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As I was walking across campus one day I stepped aside to let a man blowing leaves off the sidewalk pass. It occurred to me that the university hired a lot of people to clean stuff up.
And then it occurred to me that the university hired people to do a lot of work that the faculty and students could well do themselves; for example blowing leaves off the sidewalk (at least a work study job) and cleaning our own offices (at least emptying ashtrays and waste baskets).
And then I wondered where the leaf blowers and janitors came from and what their lives had in common. There was one thing they probably all had in common; they did poorly on tests and left the educational system after high school if not before.
And then I started thinking of all the uneducated people I knew who were really quite intelligent. The character in “Driving Miss Daisy” who drove Miss Daisy was uneducated but fixed the elevator for Dan Akroyd; that is the kind of intelligence I’m talking about.
A guy who lived across the street from me went to a welding school after high school but he could do an amazing number of things besides welding very well. This would seem to imply that he could learn.
On the other hand I know of a lot of students who do well on tests but don’t know how to do hardly anything. I know of a student who learned chair forms in organic chemistry by making up a poem for each form that had nothing to do with organic chemistry, a straight A student in fact.
The correlation between grades and smarts didn’t seem to be real high. I know there are smart kids who get good grades but there are smart kids who don’t.

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I think that the rationales for testing are many and most of them are obscure. The consequences of testing are many and many are unintended. A test is a selection process but what are they selecting for?
One of the consequences of testing is that it gives society a constant supply of unskilled labor. Because of the uncertainty in testing, a lot of people who are quite intelligent get put in that labor pool. Some become the person you go to when you have a problem; some become the guys who rob the corner liquor store.
Another consequence is that some incompetent people get jobs that require skill and intelligence. This circumstance results in disasters of various magnitudes.

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Tests are constructed in such a way that they automatically give a certain percentage of bad grades. This is possible because of the general acceptance of the bell curve.
Usually the tests are about how well the students can memorize, about how well they can work standard problems, about how fast they can work standard problems, or about how well they can write the response the teacher is looking for; all are easily fit into a bell curve.
The bell curve requires right or wrong answers so questions on tests have to have right or wrong answers. I think this is a serious drawback.

Some memorization is needed. A chemistry professor told his class that there was some information that was reasonable to look up but there was also some that you were expected to know, like the chemical formula for water and hydrochloric acid; or 9 x 7.

Standard problems are standard and really fall into the memorization category.

The question of speed is a little trickier.
My school started considering learning disabled students although I never fully understood the criterion a student had to meet in order to fit in that category. (It was interesting how the office that handled learning disabled students moved from the basement and staffed by a couple of people to a full fledged power bloc.)
The idea was that if a student was learning disabled they were to get extra time, 15 minutes if I recall correctly, on a test. One young man’s hands were badly crippled by youthful arthritis and it seemed reasonable to give him extra time. Another student in the class brought me the required notification slip and sat the extra time with the kid with arthritis. Her test papers were close to perfect.
Since the young woman could evidently comprehend the material and seemed to have no physical impairment, I concluded that her disability had to do with how fast she could work a test. It made me wonder how many of the students in the class would improve their grade with an extra 15 minutes.
By setting the time for the test to be 50 minutes a bell curve was introduced. If everybody in the class knew how to work all the problems the scores would still fall on a bell curve. Students who knew the material could still get a bad grade.
The bell curve is one of those commonly accepted facts of life that I think is, to say the least, wrong. In practice I found that my tests scores were bi-modal. There were those who got it and those who didn’t. I had very few C’s.

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A few anecdotes:
Instructors, often unwittingly, lead their students into traps. I was sharing a cab going to the Boston airport with some colleagues when one of them said that she sometimes gave students a break by giving them a C instead of the F they deserved. I made an enemy that day when I pointed out that besides lying to the student and leaving them thinking that they knew more than they actually did, she was putting them in a hole. The student didn’t know enough to pass the next course in the sequence but didn’t want to retake a course they had already passed. I used to see this particularly in College Algebra to Calculus I and Calculus I to Calculus II.
The student would try, say, Calculus I two or three times and then either change major or drop out of school.
I made, after much soul searching, the decision to pass a student if I thought they knew enough to have a reasonable chance to pass the next course. When I didn’t pass a student I always gave them an opportunity to discuss my decision and I would tell him the reason I thought he would fail the next course and would explain the trap.
I did this with a student in Calculus II and explained to him how he had improved but that he wasn’t ready for Calculus III. If he repeated Calculus II, he would solidify his improvement and do well in Calculus III. He came to my office a week later and said that because of the D his average had fallen too low and Electrical Engineering had disenrolled him. So I called Electrical Engineering and pointed out that besides voiding all the good work the student had done in Calculus II, they were missing the whole point of education which was, ultimately, being a facilitator in a student’s acquisition of knowledge.
The student came back the next day and said that E.E. claimed to have made an error in the calculation of his average and he was readmitted. He got a B in both Calculus II and Calculus III.
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I was teaching Math 180 which was the first semester of a two semester sequence in calculus for the biological and social sciences. At the end of the semester I gave my little talk that that I passed people in Math 180 who I thought could pass Math 181.
A student who had attended all the classes but hadn’t gotten a grade above 25 raised his hand and asked, “What’s Math 180?”
“It’s the class you’ve been sitting in all semester”, I replied.
He was stunned. “This isn’t Math 102?”
Math 102 was a very elementary course in statistics and the student was a physical therapy major.
After class I walked the student over to the Math 102 instructor and introduced him to the student who hadn’t been in class all semester.
On the way the student said, “You know, I was really starting to get the hang of your course.”
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Walking back to my office from class, a T.A. stopped me to ask me about one of his students. He said that the student was somehow getting a C but didn’t seem to know anything. He said that the student had the best penmanship that he ever seen and when he graded the student’s tests he seemed to give him a few points on all the problems and they added up to a C.
As it happened I had graded this student’s paper in his two attempts to take College Algebra by correspondence. I failed him both times; beautiful handwriting and absolutely no understanding of mathematics. He had apparently made it through College Algebra and Calculus I based on his penmanship.
There is a short story by Lionel Trilling, “Of This Time, of That Place” about an English teacher trying to grade the paper of a ‘different’ student, who was a main character in the story. The teacher sweated over the grade and at one point wishes that he could give the student “M for mad”.

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A C is probably the most ambivalent of all the grades but it is not clear what any grade actually means.
I had a friend whose daughter had gotten a 50 on a high school final exam in history and flunked the course. My friend complained that 50 should have been a passing grade. I told her that it didn’t make any difference, in a cosmic sense, what number her daughter got on the final; her daughter didn’t know any history and should retake the course.
I told the irate mother that her daughter’s knowledge and the placing of the passing line were independent of each other; putting the passing grade at 10 wouldn’t make her daughter know any more history.

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