Saturday, June 14, 2008

An Idea Whose Time Has Come?

On p. 7 of the current issue of the MAA FOCUS one may read the following, which I presume is presented as biting satire of an event the author would apparently find heinous should it become reality:
Outsourcing Mathematics: Is a News Story Like This Possible?
A nightmare from Michael Henle, Oberlin College.

Dystopia Times

Mathematics Department Shuts Down

Monday, May 3, 2010. Nemesis College announced today the dissolution of its mathematics department. No details were given, only the statement that the future mathematical needs of its students would be met outside the traditional Department of Mathematics setting. We wondered what this meant. Could it really be true that students at Nemesis would no longer be subjected to the universally unpopular subject of mathematics? To find out, we interviewed Professor Earnest, the former chair of the mathematics department. He met us in his old office, surrounded by half-packed boxes of books. We asked first if this action on the part of the College administration had come as a surprise to him or to other members of the mathematics department. “Not at all,” Professor Earnest said. “This has been in the works for some time. For example, we haven’t taught statistics for at least a year. It’s outsourced to economics, psychology and other client departments. They prefer it like that. The last statistician left the Department of Mathematics several years ago.” We were curious about the calculus, that most dreaded of mathematics courses. How would Nemesis students be taught calculus? “Not a problem,” Professor Earnest told us. “Most of our students get their calculus in high school now. The few that don’t will be given workshops. They’ll be shown how to do calculus using a computer algebra system. The Engineering Department will handle this. That’s what they want. Likewise, students who need remedial work in algebra and trigonometry will be trained on software.” What about current members of the Department of Mathematics? Where would they end up? “Well, a few will retire,” Professor Earnest said, “but most of us will be right here. Let’s see. A few colleagues are joining the Computer Science Department and some others will be in Engineering. They’ll teach the workshops I mentioned. Then a few more will work in Information Technology. They will update software, trouble-shoot email problems, replace spent print cartridges, and the like. Oh, and a few lucky chaps are joining Environmental Studies. They’ll teach modeling software. Maybe even a course or two.” All this seemed very well planned to us. Our last question concerned Professor Earnest himself. Where would he be? “I’m fortunate,” he said. “I’ll be in the Physics Department. I get to teach transform theory and advanced analytical methods.” He paused. “There’s only one problem.” For the first time in the interview he looked a little sad. “What was the problem?” we asked. Professor Earnest sighed. “No proofs,” he said. “I have strict instructions. There must be no proofs in my classes.”
Is this a dystopian dream of mathematical hell? Or is it in fact much to be wished by sensible students and educators that teaching mathematics be taken from the hands of mathematicians for whom teaching is too great a chore? 

Let's consider Professor Henle's piece in more detail. He states, "the future mathematical needs of its students would be met outside the traditional Department of Mathematics setting." Why would this be a problem for students? As long as their real mathematical needs are truly met, what student would care about which department was meeting the need? Do students care or think about how academic colleges are structured? At the graduate level, the story is possibly different, of course, but even there, if a student could get the coursework, mentoring and degree s/he desired, would the name of the department supplying any/all of the above matter? 

When I came to the University of Michigan to do graduate work in mathematics education in 1992, one of the first classes I took was a 400 level undergraduate course in mathematical probability, taught by a full professor who came highly recommended to me by his office mate, the fellow in the mathematics department who taught all the mathematics for teachers content courses. I'm sure, in retrospect, that when I was told that Professor S. was outstanding, what was being communicated had absolutely nothing to do with his ability to teach. Rather, I was being told what in fact did not need to be said: that a person with a full professorship at a world-class university mathematics department REALLY knew the mathematics needed to be an expert about one or more tiny twigs on some tiny branch of some larger branch on one of the major branches of the tree of mathematics. And that he had climbed all the requisite branches to get there as an undergraduate and graduate student of mathematics, had done the expected original research needed to be officially accepted into the tribe of professional mathematicians, and had finally dotted all the i's and crossed all the t's needed to reach the plum position he currently held. 

What I wasn't being told anything about whatsoever was this professor's ability to help non-experts learn the smallest thing about mathematics. And in fact, he would rate as the single worst teacher, from a technical perspective, I've ever had for mathematics. That he spoke with a heavy accent I can't blame him for, though I did not get the impression that he had made much effort to work on his pronunciation. But he spoke consistently in a very soft voice, frequently spoke while facing away from the students, and often let his voice trail off at the end of sentences in an essentially inaudible manner, usually coupled with a little grin that, after a few weeks, became particularly annoying given that it almost seemed like he knew that he wasn't communicating very well. I made it a big point to get to class early so I could always have a front-row seat, but nothing helped. On the one occasion I went to him for help at his office, I left more confused than when I entered. He assigned homework problems from the text that he'd used for more than five years for which the book gave the wrong answer but didn't bother to mention this to us. I spent a tortured couple of days trying to figure out why I was consistently coming up with a different answer to a (for me) difficult problem in combinatorics than the one the book provided only to discover that my answer was in fact correct. Since the numbers involved were sufficiently large that it would have been impracticable to do the actual counting as a check, I wound up wasting a lot of time that could have been better spent doing problems for my other classes. Of course, Professor S. did not apologize for his thoughtlessness. I'm sure that for him it was no big deal at all. And his final outrage was to offer an optional review session before the final during which something a student asked led him to lecture briefly on something not covered during the course. He then put a problem on the final that was drawn directly from that topic. Not that my having been at the session prepared me for this problem, but imagine the shock it gave students who chose to miss the "optional" session. All in all, a horror show. 

I felt even worse when I was told by a senior mathematics major I'd become friendly with in another class that the same course was offered every semester in the statistics department, that the book they used was vastly more comprehensible and student-friendly, and that the professors who taught the course were generally considered to be much better teachers than those who did so in the mathematics department. It was too bad we hadn't met before I was already past the point of no return in Professor S.'s class.

Of course, I don't really wish to suggest that all mathematics professors, full or otherwise, are so unskilled in the classroom. Some are gifted and dedicated teachers. But the notion that having research mathematicians moved to various departments would be a bad thing for students as far as the teaching and learning of undergraduate courses is concerned simply is laughable. 

Dr. Henle later quips, through the mouth of the imaginary Professor Earnest, "Most of our students get their calculus in high school now. The few that don’t will be given workshops. They’ll be shown how to do calculus using a computer algebra system." Hmm. Doesn't THAT sound like a slasher movie? Not that I am a great believer in the necessity or desirability of teaching calculus in high school, of course. In fact, I see very little advantage to students in trying to complete a lot of calculus before students enter college. Or at least having it be the sole or primary option to seniors who are ahead of the curve in terms of state or district mathematics requirements. A course in discrete math, especially one that involved proofs, would be both more practical and potentially more challenging. It would likely provide a better sense of what mathematics majors are expected to do. And it would undoubtedly connect better with many common real-world applications that high school students are interested in. But then, I'm heretical in so many regards. 

And then there's the gratuitous and predictable pot-shot at computer algebra systems. This despite the fact that research mathematicians use a variety of high-end software that includes, of course, computer algebra and the ability to crunch a lot of difficult integrals and other calculus computations. I'm sure that those researchers COULD do the calculations by hand, though perhaps not as quickly or as accurately in all cases, but then they consciously choose not to, and to take advantage of the power of software like Maple and Mathematica despite the attitude of nay-sayers and, well, Luddites. I don't know if our satirically-minded Oberlin professor is in that camp, but I assume my sides are supposed to be split by laughing at the notion of college kids doing a lot of calculus number crunching with the aid of computational tools. Perish the thought. 

I'm afraid I just don't find the scenario Professor Henle offers us particularly scary. When it comes to teaching mathematics, at least at the college level, I suspect quite a number of high-level mathematics professors would be well-employed replacing printer cartridges as he suggests. Or, perhaps, just doing what they do well and actually wish to do passionately: creating new mathematics. Solving challenging problems of both theoretical and applied math. And communicating to the small number of folks with whom they are capable of so doing. Those professors who actually have both a gift and a desire for teaching should of course be allowed and encouraged to do so. I have been privileged to learn from a few such people and to know others professionally. I doubt very much that any of them would be troubled by Henle's satire. I can't imagine that many students would be. And I know for certain that I'm not. I want teaching to be done by those who not only know their subject but who have the ability to teach it well to real students, and not just one or two who happen to think and learn exactly the same way they do. No watering down of the material, but definitely shoring up the quality of the communication and pedagogy. Imagine that! And who would really care under the auspices of which departments such teaching came?

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