From: Mathematics with Applications by Lial and Hungerford. To the Student: "mathematics is not a spectator sport". You can't expect to learn mathematics without DOING mathematics... There is no way that your instructor can possibly cover every aspect of a topic during class time. You simply won't develop the level of understanding you need to succeed unless you read the text carefully. In particular, you should read the text BEFORE starting the exercises. However, you can't read a math book the way you read a novel. You should have pencil, paper, and calculator handy to do the side problem, work out the statements you don't understand, and make notes on things to ask your fellow students and/or your instructor. ...There is no such thing as a "dumb question" (assuming that you have read the book and your class notes and attempted the homework). Your instructor will welcome questions that arise from a serious effort on your part.
From: "Teaching at the University Level", by Steven Zucker (Professor of Mathematics at Johns Hopkins University, sz@math.jhu.edu). The complete article from the Notices of the American Mathematical Society can be viewed at http://www.ams.org/notices/ - get to the August 1996 issue.
One of the ironies of being a college educator in the US is that one is often rewarded for NOT doing one's job. That sounds like a strange thing to say, but I know that it is true. ... I eventually learned to accept the pretenure save-your-own-hide advice that I give to assistant professors: teach so as to keep your ratings up. From then on, I had good student evaluations. But was I a good university educator ? Were the students learning better ? Not really. Did anyone care ? NOT REALLY. At universities where the standard for reappointment and promotion was quality research and acceptable teaching (or even entirely a research standard), it is obvious why few people wanted to rock the boat over educational matters. The goal was de facto to concentrate one's energies on research and do enough in teaching to keep the students from complaining. That it kept many of them ignorant was not at issue. When I moved to Hopkins, I got as a bonus an improved environment for teaching... I felt that I could comfortably blend into the style that had emerged from my years as assistant professor some of my ideals about teaching calculus to science-oriented students. However, as years went by I started to feel increasing resistance - balking - on the part of a large portion of my class. Since I also felt that my presentation was getting clearer, I became correspondingly irritated over their apparent refusal to take the course seriously. And when I took part in the student-run course evaluation survey, I discovered that the class as a whole rated me only "satisfactory". What was going on ? It took a poke from my department chair and a couple of years of exertion on my part to arrive at the conclusion that I now hold. The answer is so obvious that it is embarrasing.
The fundamental problem is that most of our current high school graduates don't know how to LEARN or even what it means to learn (a fortiori to understand) something. In effect, they graduate high school feeling that learning must come down to them from their teachers... It is unacceptable at the university level. THAT THE STUDENTS MUST ALSO LEARN ON THEIR OWN, OUTSIDE THE CLASSROOM, IS THE MAIN FEATURE THAT DISTINGUISHES COLLEGE FROM HIGH SCHOOL. ...We should be putting our effort into reforming the STUDENTS, not the calculus!...One of my basic tenets is that the students have no right to know what an upcoming exam is going to look like. I aim to prepare them for ANY reasonable exam I might come up with. That is, I'm asking them to aspire for command of the material of the course... Some students think this is "unfair" - it wasn't like that in high school - when in actuality asking for a sneak preview of the exam is nothing but attempted cheating. When the instructor helps them cheat, the students reward him or her with higher marks on the evaluation survey for giving "fair" exams and "relevant" lectures, and the community ends up with the impression that the instructor is a good teacher. I think I've made a good case that such people should be REPRIMANDED, not lauded, for they contribute to the undermining of education at the college level...
( The complete article from the Notices of the American Mathematical Society can be viewed at http://www.ams.org/notices/ - get to the August 1996 issue.)
ADVICES:
1. YOU ARE NO LONGER AT HIGH SCHOOL. The great majority of you, not having done so already, will have to discard high school notions of teaching and learning and replace them by university-level notions. This may be difficult, but it must happen sooner or later, so sooner is better. Our goal is more than just getting you to reproduce what was told to you in the classroom.
2. Expect material covered at TWO or THREE times the pace of HS. Above that, we aim for greater command of the material, especially the ability to apply what you have learned to new situations (when relevant).
3. Lecture time is at premium, so it must be used efficiently. You cannot be "taught" everything in the classroom. IT IS YOUR RESPONSIBILITY TO LEARN THE MATERIAL. Most of the learning must take place OUTSIDE the classroom. You should be willing to put in two hours outside the classroom for each hour of class.
4. The instructor's job is primarily to provide a framework, with SOME of the particulars, to guide you in doing your learning of the concepts and methods that comprise the material of the course. It is not to "program" you with isolated facts and problem types nor to monitor your progress.
5. You are expected to read the textbook for comprehension. It gives the detailed account of the material of the course. It also contains many examples of problems worked out, and these should be used to supplement those you see in the lecture. The textbook is not a novel, so the reading must often be slow-going and careful. However, there is the clear advantage that you can read it at your own pace. Use pencil and paper to work through the material and to fill in omitted steps.