We were being a little vague this afternoon. Please tell me: what can I do for, say, first semester Calculus II students that I'm not already doing for them? (An interesting question)
You know I'll fume if you say, "water down the course". Likewise if you say "Teach at their level", for you know I believe I'm doing something close to that. Don't forget that almost every freshman at JHU says that he or she was in the top quarter of the last math class taken, AP in almost all cases, and that is prima facie evidence that they were taught in high school well below their level.
I'd like you to look at some things on my home page. They're in the folder "Mathematics Education":
. . . . . "Teaching at the University Level", Notices of the AMS (8/96)
. . . . . Teaching freshmen to learn mathematics (appended to a book on teaching math in college [author, Steven Krantz; title, "How to Teach Mathematics," 2nd edition, 1999; published by AMS]
. . . . . Myths and Games
The location: http://www.math.jhu.edu/~sz
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From ____@jhu.edu Thu Jan 7 11:54:58 1999
Subject: Re: First epilogue
Hello Dr. Zucker,
I realize it has taken me a rather long time to reply to you. I apologize, and I won't bother you with lame excuses.
I think your desire to teach mathematics to freshmen is noble and should be applauded. Many professors at Hopkins doesn't really care about "teaching" their students. Yes, they do give three lectures a week, write exams and give grades, but they don't seem to have a real desire to see their students learn the material. They simply cover what is outlined in the curriculum and hand out grades on a curve. I think you are of the few professors who wants to see their students master the material, be "fluent" in it, so the knowledge gained could be used outside of the classroom.
Having said this, I must also say that your approach in conveying your desires to your students is misguided. I have read your web pages and agree on most of what you said about level of university education, and student's disinterest in learning on their own--especially their freshman year. But I think the alternative teaching that you suggest--"teach at their level" is not the only one. I know how much you dislike teaching at "highschool level". And I agree, highschool level teaching has no place in university level education. We, the students, shouldn't expect the professors to spoon feed us information that we would later regurgitate on an exam. That is not teaching, and that is not learning, either.
The best professors I've seen motivate their students to learn. They let the students know early on that the course would be demanding and that a lot of work is demanded from the students. The professors also let the students know that they'll do everything they can do help them understand and master the material. They take it as their responsibility to present the material well so the students can understand them. The professor does his/her part, and students do theirs. If one student does poorly on an exam while most of the class does well, then the student is responsible. If most of the class does poorly, then the professor is responsible.
I know you try to do all of the above things. Perhaps mathematics is a difficult subject to give good lectures on. Perhaps the best way to learn a concept is to do a lot of problems. I don't know. But I think you should be kinder to your students. Don't be so condescending and assume everyone in the class wants to be spoon fed. There are students willing to do their share of the work, if they see the professor doing his. Teaching so that the students will understand the material is different from teaching below their level. Not all of the students will understand the material first time around. Give them a chance to come to office hour and ask more questions. If a student feels that the professor doesn't expect much from them, he/she sure won't want to go to office hours.
Perhaps it's because Calc 2 is mostly freshmen that makes things more difficult. Adjusting to university level learning does take time. Perhaps you should teach a more upper level math, say diff eq, and see if students react differently. But I have a feeling that the result would be similar.
I think the best way to get students to motivated to learn on their own is to encourage them to do so, not demand them. Won't it be better if they learned to do it on their own instead of being forced to do so?
I hope I didn't bore you with all these words. It's the best I could do to answer your question.
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[Reply, mid-January, 1999]
I have been out of the country since Xmas. Though I read your message last week, it is only now that I am able to compose a reasonable reply.
> [The best professors I've seen] take it as their responsibility to
> present the material well so the students can understand them. The
> professor does his/her part, and students do theirs. ... I don't
> know. But I think you should be kinder to your students. Don't be so
> condescending and assume everyone in the class wants to be spoon
> fed. There are students willing to do their share of the work, if
> they see the professor doing his. Teaching so that the students
> will understand the material is different from teaching below their
> level. Not all of the students will understand the material first
> time around.
The main issue is to establish what "students doing their part" means. Most freshman have as a model that which they did in high school, and some are less willing to relinquish this than others. This is the reason that I've done all of my orientation efforts. But it's very difficult to address a very diverse group of students with a single presentation. It's like a radio announcer reminding people to vote on Election Day; some will be thinking, "do you claim I'm so indifferent that I won't [vote]?!"
My experience is that only about half of the freshmen want to be spoonfed in mathematics, expect to be able to feel comfortable with the material the first time around; how can one convince them otherwise? In these students' view, the "teacher" sets them up to finish in a routine manner. If they don't understand things moderately well in class (if they bother to show up at all), it's the teacher's fault. [These people are my target;] I'm not so concerned about the students who would instinctively figure out how to deal with college.
I never really care so much what the student can figure out the first time around. There's no quiz at the end of the lecture, you know! It's (many of) the students who expect it. If they picked up a hint of the lecture from looking at the textbook a little before class, as I recommend, then they'd be on their second time around in the lecture! (See letter of Jim Morgan.)
It's this that I find so obnoxious about trying to instruct calculus: there's a tacit expectation that the instructor should excise anything remotely hard from the course because many students can't "get it" in class! (I call that "teaching high school.") How many students would complain then that the course is too easy, eh?
Do you remember Dr. Laugesen, who taught the other lecture [in Fall '96]?
His students adored him. But they did no better than mine did on the
exams. [As I say, students are often looking for the wrong thing in their
math professors; and when they get what they say they want, they don't do
any better anyway.] What do you make of that?
[I'd like to conclude that after a certain threshold of effort, what the
instructor does has little to do with performance by the students. There
may be another
explanation: the other instructor may have made it easier to attain the
same old level of performance that we professors are complaining about.]
Of course, the pass/fail mentality does further damage. However, I refuse to make accommodations for that. Students have told me that P/F allowed them to stay in high school one semester longer.
Students don't go to professors' office hours because they just don't. This is a general pattern. You know, I have a reputation of being very helpful in office hours. If this gem isn't getting passed along to the freshmen---and I can't do it!---then it is beyond my power. If the sophomores and juniors could communicate what they learned about college to the freshmen; if the high schools; if Orientation ....
> Perhaps you should teach a more upper level math, say diff eq, and
> see if students react differently. But I have a feeling that the
> result would be similar.
My reflex was to think about 400-level courses for math majors. In that context, your impression would certainly be wrong. I'm not sure what would happen if I taught 302 or linear algebra, but I think that an audience of sophomores and juniors would have to be more receptive. Even Calc III should go better.
As one student put it, I ran the course in a way that forced her to learn how to learn. That's the bottom line, as far as I'm concerned. (See my "Teaching freshmen to learn mathematics" .) [It is a question of overhauling one's mode of operation. Is it really possible to encourage this?]
Finally, I want to mention that it was essential for me to get away on sabbatical this academic year because worrying about educational issues was sabotaging my research career.
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Steven Zucker
February 12, 1999 (this compilation)