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Faculty Teaching Guide

Preparing a Syllabus

It is important that you provide a syllabus for your courses, preferably  online, at the beginning of the semester.  This should include:

  • your name, office number, phone, e-mail, and office hours for the semester. (Note that university regulations require that you have at least two hours of regularly scheduled office hours every week)
  • prerequisites for the course
  • the title, author and publisher of all book(s) you plan to use, and a rough idea of the chapters you plan to cover;  also mention that the book is (or should be) available at the Columbia bookstore.
  • The administrative mechanics of the course:  Is homework collected and graded (the Mathematics department has agreed with the School of Engineering that in each Calculus class some written homework will be collected and graded each week)?  Does it count towards the final grade? How many midterms?  What percentage of the grade do they count?  It is a good practice to announce the date of the midterms and the final. All math courses follow the University Master Exam Schedule.

The university Courseworks system allows you to create web-pages and post material for your course.  You can also create course web-pages on the departmental web-server,  for more information see the department computer FAQ.

More information, including sample syllabi, is available on the Calculus Classes web-page.  It would be best for you to just use these as general guidance for the material to be covered, making your own choices of exactly which sections to cover at how much length, and to make your own choice of assigments. You may also want to consult the course web-pages of other faculty who are teaching the same course or who have taught it recently to get an idea of what material is typically covered and what course policies different people have adopted.

For the Calculus classes, the department has an online homework system called WebAssign, and you can assign a mixture of written assignments and WebAssign assignments.  Keep in mind that detailed answers to ALL problems in the Calculus course textbook are available online from commercial services.  One advantage of the online homework system is that it uses different values for the homework assignments of different students, encouraging them to actually work out the problems themselves.

Special Notes on Calculus III

  • Calculus II is not a prerequisite for Calculus III. Many of the students who take Calculus III have taken only Calculus I. These will be primarily prospective Economics majors, who need differential calculus of one and several variables. (However I, II, and III are prerequisites for Calculus IV.)
  • Instructors in Calculus III should therefore not assume the material of  Calculus II, and (the sample syllabus for III mentioned above notwithstanding) should not assign problems which require integration by parts or trig substitution or series.

Meeting Classes and Exams

You are expected to meet every class or to obtain the necessary coverage. Please minimize your absences, especially from undergraduate classes.  Continuity is very important to the students.  It is next to impossible to reschedule large classes without creating insurmountable conflicts for some of the students.  It is much better to get a colleague to replace you at the scheduled time.  You should never use an undergraduate T.A. as your replacement.  It is best to use a faculty member as a substitute. If you must use a graduate student, it is your responsibility to make sure that he or she does a competent job. You MUST provide the Director of Undergraduate Studies and the Undergraduate Office (i.e. Mu-Tao Wang: mtwang@math.columbia.edu) with the dates of your absence and the name of your replacement.  In this way, we can avoid problems if misunderstandings occur about the day/time of the course or location of the class.

Some faculty like to use their TAs or other graduate students to proctor  their exams.  This can however pose several problems.  First, if there is any ambiguity (or error) in your exam, and the TA is unable to advise the students, you run the risk of disaster.  To avoid this possibility, make sure that the TA understands exactly what you want in the exam (and hope that you have proofread it carefully!).  Second, remember that you should  do at least as much grading as one of your (full-time) graduate student TAs and, of course, you should grade the more challenging questions. Undergraduates are not permitted to grade exams or quizzes. Finally, if issues of academic integrity arise, it may be difficult for a graduate student to deal with them, and occasionally students will view the absence of a professor as an invitation to cheat.

Giving and Grading Exams

It is an art to give an exam appropriate to the level of a class, which  contains both easier and harder problems, is feasible to take in the allotted time, and can be graded efficiently. Exams should be graded promptly, fairly, and consistently. Students need to get rapid feedback from their exams, and so the graded exams should be returned to the students within a week. Similar comments apply to homework and quizzes. If possible, it is also helpful to prepare written solutions to the exam problems. If done beforehand, this can also help you to gauge the length  and difficulty of the exam and to find potential errors or ambiguities.

Grading Policies

The determination of grades is both the prerogative and the responsibility of the individual instructor. For reasons of equity, however, it is important to attempt some consistency in grades from section to section   and from year to year in the same course. Of course, there will inevitably be stronger and weaker sections of a course and the grades should reflect this fact if need be. Grades should also be assigned in a fair and consistent manner within a section. The Department periodically collects  historical information about grades within the Department and for the University as a whole and will try to make this information available.

Evaluations

Every course is automatically evaluated through on line evaluations given toward the end of the semester. Information concerning these evaluations  is emailed directly to the students by the University. Copies of these evaluations (including student comments) are available to the instructors shortly after the end of the semester, as well as to the Mathematics Department (which keeps copies on file). Sometimes, instructors also like to hand out paper evaluations (but be sure to factor in the class time necessary for completing them). It is also possible to distribute midterm evaluations, especially if you feel in need of mid-course feedback from the students.If you have any further questions, please feel free to contact the Director of Undergraduate Studies (currently Professor Mu-Tao Wang).

Remote Learning

Delivery of mathematics courses vary greatly depending on the subject, level of instruction, class size, etc. Please visit the Remote Learning page for some general recommendations and guiding points you may want to consider while developing a teaching strategy that fits your course. You are welcome to contribute with questions, comments and suggestions by emailing to remote-learning@math.columbia.edu. Content based on these contributions will be added regularly.

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