One complication that arose in the fall was the department's use of a new "reform" calculus book, Calculus in Context. As we expected, the new and radically different approach to calculus drew a lot of criticism from students (in fact, the department abandoned this book two years later); however, my colleagues pledged to keep student criticism of the book as separate from their evaluation of my teaching as possible.
Here are a few of my teaching experiences from that fall.
9/23/94: There were two interesting points in today's class. First, when I discussed reaction rates as an example of exponential growth or decay (reaction rate is proportional to the concentration of the reactant), one student said, "That's not the way we do it in chemistry!" But then he thought about it a bit and said, "Wait a minute... there's something about taking the logarithm... maybe it is the same thing!" He said that in the chemistry course they just learn a rote technique for finding the reaction rate, without learning why it works. Now he might understand why!
The second point came up when we were discussing inverse functions. As usual, this provoked a certain amount of confusion among the students. I think my way of explaining it is partly at fault. The book has a very nice way, which I will try on Monday. Anyway, another student came up to me after class and started explaining how he learned about inverse functions in high school. To paraphrase: "An inverse function is... you switch x and y, and then you solve for y."
To me, this was another perfect example of how students are taught rote procedures for getting the right answer, without really understanding the concepts involved.
11/11/94: One of my colleagues has started sitting in on my class, and the experience has already been beneficial to both of us. First, she really liked the way I used DERIVEŽ to explain why an unbounded region can have such a narrow "neck" that it has finite area. When you plot a function like y = (1-x)^(-1/2), DERIVEŽ cannot even show the asymptote... the neck is so narrow that the computer can't even "see" it. My colleague said she will always introduce improper integrals that way from now on...
If teaching is a battle for souls, I won one and lost one this week. (Perhaps.) One of the students who has been most critical of the Calculus in Context approach wrote in his journal that he had been thinking about some other subjects over the weekend, and suddenly this approach started to make sense to him after all. He was very vague about it, and wrote, "I will have to think more about this," but that was a very encouraging sign indeed!
The setback occurred this morning. One of my students asked if she could have 5 minutes after class to do a little computer work for one of the problems on the take-home exam, because she hadn't had time to come to the computer lab last night. I said no, and explained, "You're supposed to make time to come to the lab." She got upset, said, "You shouldn't say that, because I worked on this test for nine hours yesterday," and stormed out of the classroom in tears.
There are so many aspects of this incident that I can second-guess myself on. Was it unreasonable to deny her the five minutes? No. A deadline is a deadline. Another student had the same problem on the last test, and lost several points as a result. I have to be consistent. Was my comment insensitive? I don't know. At that point I couldn't have known how much time she had put into the exam already. Some students need a little lecture like that to get the message. Was the exam too long? Apparently most of the students took a very long time to do the first problem. I was very surprised, because the book shows, step by step, how to solve this kind of problem (a logistic equation) and even gives a formula for the solution. BUT... there was only one homework problem on the logistic equation, and it had a typo that ruined the problem, so I didn't count that homework problem. And so, the students, minimizing effort as students always do, may have thought, "Well, the homework problem didn't count, so we won't be responsible for this on the test."
11/16/94: I felt lower than low after this morning's class... I guess I should have stayed away from the [problem] that caused all the emotion on Friday. One student had gotten an unrealistic answer and seemed puzzled about it, so I had written next to it, "Garbage in, garbage out"--meaning that because the equation he had plugged some numerical values into was wrong, the output was also wrong. But he interpreted it, I think, as a comment on his whole solution, and started telling me how long he had worked on it, etc. I got pretty flustered, partly because I knew I had set myself up by writing a comment that could be so easily misinterpreted. Ordinarily I would have patched it up and moved on, but after all my tenure struggles I have gotten so paranoid. "Is this where I lose the student forever? Is this what he's going to write about in his letter to the provost? What are [the two math professors attending my class] going to think?" For about 15 minutes I felt as if my brain was disconnected from my mouth, as I babbled on about that problem...
Every semester has to have a worst class, and I hope this morning's class was it.
Perhaps I was right to be so paranoid: one of the two professors in attendance told me, months later, that this class had made a big impression on him. As for the student, my apprehensions were wrong: I didn't "lose" him, and perhaps he even forgot all about the incident. The last time I talked with him, over a year and a half later, he commented on how much he had learned from my class.
12/1/94: ... Another highlight yesterday was my morning calculus class, which was visited by the chair of the math department and the new provost. I started the chapter on dynamical systems... The timing was fortuitous, because dynamical systems is an area of mathematics the provost knows a lot about, and I think he was probably pleased to see it covered in a calculus course. The chair was also very excited about my class, particularly about the way I pointed out that the computer's drawing of trajectories "slows down" as they approach equilibrium points. He thought it was neat that you could actually get information not just from the curves themselves, but also the way that the computer draws them. Funny, it seemed sort of obvious to me, but I guess it wasn't. Moreover, it wasn't obvious to the students either, since we had never talked about parametrized curves before. One of the students asked me to explain what the chair meant [and why it was so exciting]. Once again, it was a case where having another faculty member attending my class was a help to me and my students and the other faculty member.
12/29/94: [A former student whom I visited with during Christmas break] paid me a compliment that I never expected to hear. She said that, as she was preparing for her student teaching, she looked over her old tests from the calculus course she took from me, and appreciated for the first time the creativity and wit that went into them.
1/29/95: Friday was the day that the student and faculty letters of evaluation for my tenure review were due at the provost's office. The provost's secretary reported to me on Friday afternoon that they had received 36 student letters and all the faculty letters. Quite a change from last year! Lack of information should not be a problem this time.
As I awaited the outcome of the review, an interesting subplot played itself out: the faculty debated and finally adopted a proposal to create a tenure and promotion committee--too late, ironically, to have any effect on my case.
3/31/95: Three people have told me this week that they were glad that I spoke up in the faculty meeting on Monday... I was the first person to speak in the debate on the tenure and promotion committee. I said that I had a unique perspective on the current tenure system, having become the answer to the trivia question, "Who was the last person to be denied tenure at Kenyon?" Then I talked about my view that the departmental input was not great enough, and asked how the proposed committee would affect that; also, I said that a paramount consideration should not be whether more or fewer people get tenure, but whether more or fewer mistakes will be made. I don't think that my little speech was very eloquent, but I guess some people may have thought it was brave for me to identify myself as a person who didn't get tenure.
Finally, four days before the trustees' meeting, I got a hint of the way the wind was blowing.
4/17/95: Once more the same nightmare? Only a nightmare the second time no longer makes the pulse race quite as much... I got a call from the provost's secretary, who had been told to set up a meeting for me with the president and provost on Thursday. The agenda: my tenure decision. Naturally, two possibilities crossed my mind. One was that they may have decided, out of sympathy, to end my suspense and let me know before the meeting that they were recommending me for tenure. However, that doesn't seem likely, as sympathy is a foreign concept to bureaucracies. The alternative explanation is that I am being denied again. Further support for that interpretation came when a German professor met me in the copier room a few minutes later and asked if I had gotten a call to meet with the "diumvirate." I said I had and, with my hopes momentarily rising, asked if everyone who was up for tenure was getting such calls. She said they definitely weren't. So it almost certainly seems to be bad news for both of us. She was distraught, and looked just the way I remember feeling last year: like a tree uprooted. I felt a lot calmer, since I've been through it before and was somewhat prepared.
4/21/95: After all the surprising turns that my tenure saga has taken, one more shocker awaited me on Thursday morning. As I expected, the president told me that I would not be offered tenure. But there was one huge difference from last year: this time the mathematics department recommended that I not be offered tenure. Once I heard that, the wind went right out of my sails. All that I battled for in the grievance procedure last year was the right to be judged by my own peers. Now that has happened...
Since Thursday morning, I have talked with each of the members of the department to find out what caused them to change their minds. I think that [one of them] expressed it best. She said that she went into the re-evaluation determined to find the answers to two questions. First, was there a problem with my teaching, or was it a figment of the administration's imagination? And second, if there was a problem, how could it have escaped the department's observation for so long? She said that after sitting in on eight of my classes, she felt that she had the answers. She saw patterns in my teaching that, in individual classes, had not seemed like serious problems, but when they were repeated she could understand why the average to weaker students were dissatisfied. She commented, for example, that I would give a beautifully prepared lecture with nice examples, get to the end, and she would think, "Great, now all he has to do is tie this up"--and instead I would go on to the next topic. She also commented that when students ask questions, she always tries to figure out what it really is they don't understand--which is not always the same as the question asked, because students often don't realize quite what they are confused about. But she said that too often I would take the question too literally, and answer only what the student asked. Another criticism she had was that, because of my mild-mannered demeanor, it was hard to tell the central points of the lecture apart from the minor points. They were all presented on an even keel. Another colleague saw some other problems, such as my not getting all the students equally involved. Also, he pointed out that I would often ask a question, get a right answer, and then go on with the lecture without making sure that everyone understood the answer.
Maybe none of these problems individually was decisive, but taken all together, they made the department too uneasy to recommend me for tenure. My reaction to them was that all the criticisms had some validity, but it was a shame that no one had brought them to my attention four years ago, or even two years ago. It was a fault that we all shared. I did get a warning, in my second reappointment review, that I should find a mentor to work with me on my teaching. The chair and I talked about having him attend my classes, but we never quite found the time, and I don't think that either of us really believed it was serious enough to warrant the effort. We have all learned that attending each other's classes and talking about them should be a routine part of our business. It should start the first year that new faculty come in, and it should continue even with the senior faculty, because they, too, have to deal with the same kinds of classroom challenges the junior faculty do.
In the above entry I portrayed the math department's change of heart in probably the most favorable light. Other people, including my wife, were not so charitable in their opinion of the department. My wife found support from a somewhat surprising source.
5/6/94: Kay went to the college's ombudsman to talk about my tenure decision and her anger over it. Surprisingly, even though the ombudsman is in the administration, she agreed that I had been badly treated. She had also talked with the German professor who was denied tenure, and agreed that the secrecy of the meetings between the administration and the departments was a serious problem. As the German professor commented on Saturday night [when she visited our house for dinner], the secrecy works completely against the tenure candidate, by depriving that person of the ability to defend him or herself before the decision is announced. I have also commented before that the fact that the department cannot view the candidate's complete dossier was a critical factor in my case. If the department had known how exaggerated were the administration's claims about the number of negative student letters in my [previous year's] dossier, they might have reached a different conclusion.
Incidentally, my colleagues in the mathematics
department were also very distressed about the secrecy issue.
In mid-January, when they made the decision not to
recommend me for tenure, they had intended to inform me
immediately, but the provost directed them not to.
This resulted in three very awkward months for them.
Was the department's change of heart justified? I have
talked with colleagues who called it "criminal"
and "immoral" to support me one year and recommend
against me the next, without giving me a clue until
the day I met with the president and provost. A year
after the decision, Len told me that the department's
flip-flop was, to him,
the most surprising aspect of the whole case. One
could, of course, put a very simple interpretation on it:
when my colleagues actually took the trouble to attend my
classes, they found them
On the other hand, from my previous experiences I have learned
that things are not always so simple. The jury's decision
depends on the charge given to the jury (in this case, my
departmental colleagues). In this case that
charge was (to paraphrase): we have already found Mackenzie's
research and collegiate citizenship to be satisfactory, but if
his teaching is not up to snuff then he should not be
recommended for tenure. Moreover, crucial information
was withheld from the jury: the actual contents of the
student evaluations. Only one person in the department, the
chair, ever heard Len's crucial comment that the letters were
positive enough already for me to get tenure,
and that he himself would be happy to come up for tenure with
such a dossier. The rest of the department was left with the
belief that the students were very critical of my
teaching. (Note that they also did not get to see the
grievance panel's finding that the administration had
misrepresented the student letters.) Even the chair never got
to see the students' letters, and may have dismissed Len's
observation as a rhetorical flourish.
Finally, although the mistakes made in the first evaluation
were the administration's, it was I
who was subjected to increased scrutiny of my teaching.
One time this scrutiny clearly affected my teaching was the
dreadful class I described on November 16. To summarize,
I believe that
the unavailability of key evidence, the changing of the
rules of evaluation, and the shifting of the burden of proof
were more than enough to cause fair-minded people to make the
I will end with the story of another individual who was
forced to turn his back on
a career he had given his heart to.
Was the department's change of heart justified? I have talked with colleagues who called it "criminal" and "immoral" to support me one year and recommend against me the next, without giving me a clue until the day I met with the president and provost. A year after the decision, Len told me that the department's flip-flop was, to him, the most surprising aspect of the whole case. One could, of course, put a very simple interpretation on it: when my colleagues actually took the trouble to attend my classes, they found them unsatisfactory.
On the other hand, from my previous experiences I have learned that things are not always so simple. The jury's decision depends on the charge given to the jury (in this case, my departmental colleagues). In this case that charge was (to paraphrase): we have already found Mackenzie's research and collegiate citizenship to be satisfactory, but if his teaching is not up to snuff then he should not be recommended for tenure. Moreover, crucial information was withheld from the jury: the actual contents of the student evaluations. Only one person in the department, the chair, ever heard Len's crucial comment that the letters were positive enough already for me to get tenure, and that he himself would be happy to come up for tenure with such a dossier. The rest of the department was left with the belief that the students were very critical of my teaching. (Note that they also did not get to see the grievance panel's finding that the administration had misrepresented the student letters.) Even the chair never got to see the students' letters, and may have dismissed Len's observation as a rhetorical flourish. Finally, although the mistakes made in the first evaluation were the administration's, it was I who was subjected to increased scrutiny of my teaching. One time this scrutiny clearly affected my teaching was the dreadful class I described on November 16. To summarize, I believe that the unavailability of key evidence, the changing of the rules of evaluation, and the shifting of the burden of proof were more than enough to cause fair-minded people to make the wrong decision.
I will end with the story of another individual who was forced to turn his back on a career he had given his heart to.
5/10/94: When Michael Jordan decided to return to basketball this winter, after spending the last year as a minor-league baseball player, his basketball coach, Phil Jackson, said, "Michael Jordan didn't fail baseball--baseball failed him." I can say the same thing about academia. The only way the analogy breaks down is that I can't go back to being the world's best basketball player, as Michael Jordan can!
Len, who did such a marvelous job as my advocate and taught me that a few well-chosen words can be more effective than pages of arguments, received one of the two Trustees' Distinguished Teaching Awards in 1996. Ironically, a mathematician won the other one--a vindication for him, as he had been distressed by receiving criticism on his second reappointment review (in 1993) quite similar to the criticism I had received on mine.
Are you conducting a job search, and have applications from people who were denied tenure? In today's competitive job market, I know that there is a strong temptation to pass over any candidate who has any negatives on his or her record, such as an adverse tenure decision. Try looking at that candidate differently: this may be your chance to profit from another institution's huge mistake. You may be getting a very experienced professor who just didn't fit in that other place, or who was denied for reasons having little to do with his or her qualifications.
If you would like to comment on these essays, or if you would like permission to reproduce or republish them in print or on the Web, feel free to e-mail me at "email@example.com."