Preceptor Handbook

the Preceptor Group

 Harvard University

This document collects some information for new preceptors at the Harvard Mathematics department. This document got started in 2000 and was updated until 2004 by members of the preceptor group. It is intended for internal use only.

Table of Contents
1. Preceptors
The transition from teacher to preceptor
Some ways to make a real difference.
Basic preceptor guidelines
Start of classes
Reading period and Exams
Professional Conduct
Dealing with troubled Students
Students charged with dishonesty in course work
2. Advising
General guidelines
Examples of Advising Questions:
Higher Level Course Descriptions:
3. Running a course
Coursehead Responsibilities
Advise to give for section leaders
Course meetings
4. Sectioning
Basic steps
Server information
5. Math club
Math Table
6. Apprenticeship
Guide sent to apprentices
Apprentice program welcome letter example
7. Tutorial Program
Organizing the Tutorial Line-up:
Selecting Tutorials
During the semester
Tutorial proposal letter example:
Tutorial Sign up sheet example
Tutorial feedback questionaire example
8. Course Assistants
CA Program
CA coordinator responsibilities
Semester Start
During the Semester
Math Course Assistants Job Description:
Lower level CA Application
CA Interviewing Guideline:
Role Playing during CA Interviews
Suggested Interview Guide:
CA Interview Record Sheet
Interview Comments and scoring
CA feedback:
Probably hire letter example
Possible hire letter
No hire letter
CA re-hire letter
No re-hire letter for old CA's
Example CA Introductory Meeting
Example Time/Course Preference sheet
Example: Sign-up sheet for Micro-teaching
General Issues for Math Course Assistants
Schedule and Course Preference update sheet
Professional Conduct Meeting
9. Evaluation
Online Evaluation Form
Midterm Evaluation Form Example
CUE Guide
10. Calendar
Preceptor Annual Calendar of Events
11. Placement test
Online Placement Test
Questions examples
Handout with written Placement test MOPE
12. Summer and Extension school
Summer school peculiarities
Extension school peculiarities
13. Computer stuff
Getting started
Course webpages
The Toolkit
Without Toolkit
Necessary ingredients of a course website
Basic formats of the web
Computer resources
For teaching
Useful Websites
List of Figures
1-1. Tree
1-2. Mindmap
8-1. Loker Commons
11-1. Online Placement Test
11-2. Questions Example
13-1. Toolkit
13-2. Projector in Hall 507
13-3. Public Computer Room with Scanner
13-4. Meccah


Welcome to the Preceptor Handbook! This document contains information on some of the responsibilities of the preceptor group. The goal is to provide a comprehensive guide for new preceptors covering as many different aspects of the job as possible. The idea is that by putting all of this information in one place, we'll be able to spend less time tracing down information, and more time creating an excellent calculus program. In addition to this guide, new preceptors should also read through the "guide for Teaching Fellows" produced by the Derek Bok Center as well as the Harvard Faculty Handbook.

Chapter 1. Preceptors

What is a "preceptor"? The term is not used in other universities or has an other meaning. Even at Harvard, preceptors at different departments have different jobs. Here is the official blurb from the application form: "The preceptor group works longside other faculty of the Mathematics department on teaching, developing and supporting sections of entry level courses through multivariable calculus and linear algebra."

Figure 1-1. Tree

The activities of the preceptor group include:

Besides teaching, preceptors do lots of administrative and organisatorial work as well as some research. They do in a professional way what in other places is done by "adjoint faculty".

Figure 1-2. Mindmap

The transition from teacher to preceptor

As a teacher you look after your charges - your students. Looking after means teaching, guiding, prodding, encouraging, ... learning about their strengths and weaknesses and doing what you can to help them both learn the material and develop intellectually. As a preceptor you look after your charges, who are now graduate student teachers, new teachers at all levels, undergraduate course assistants, and math concentrators. Looking after means teaching, guiding, prodding, encouraging, ... learning about their strengths and weaknesses and doing what you can to help them both develop as teachers and, for undergraduates, as students. While some of this teaching, guiding, prodding, encouraging happens formally, much of the most important interactions don't come under formal responsibilities. You can often have the most impact in informal interactions. I'd like to say that part of the job is to look for opportunities to do this. The impact that you might have on a "weaker" teacher can actually have the most far-reaching impact on students in general, since many of the students teaching here for the first time in their careers will make a career out of mathematics, and therefore a career out of teaching. Be sure to share teaching ideas and strategies. These may seem natural to you, but may not be something that other teachers are thinking about. Just as our weakest students are smart people who are not thinking when it comes to math, (they just don't believe their brains are supposed to be used when doing math), so too, our weakest teachers are very smart people who are not using their whole brain when it comes to teaching, (they just don't believe their brains are supposed to be used when teaching.) Some of this sharing and prodding people to think can happen at course meetings. Some of it will happen more informally.

Some ways to make a real difference.

Identify graduate students who are either having trouble with their teaching or are marginalized or disconnected in some way. Talk informally with them about their teaching, their classroom dynamics, their students. See what they are happy with and what is bothering them. Give a concrete suggestion or two. Illustrate how to diagnose the problem and demonstrate that looking for solutions is a doable and creative task. Check back with them about specifics. I've found graduate students universally grateful for the individual attention and specific suggestions. Have you discovered that a B.P. is having trouble in the classroom? Try to find an informal way to help him or her. Once you've established some sort of relationship with that person it will become easier for the BP to come talk with you when things are going astray or to bounce ideas off of you. All the most constructive "BP bailing outs" in the past have been very informal. But they can really make a difference; there have been people who have said as much when they move on to other jobs. Act as a mentor to CA's who have sharp corners or lack of confidence or other issues that are holding them back from reaching their potential. Again, this can make a world of difference for the person. Read the midterm questionnaires. It's really important and gives you an easy way to initiate and carry out difficult discussions. For instance, how in the world was I going to approach a haughty graduate student and say "you act like you think you're far better and more important than anyone else and that's getting in the way of your teaching"? Instead, we sat down with his midterm questionnaires. (We had to do this because we didn't want him to get a nasty letter from the Dean's Office - folks with low teaching scores get letters.) So we started out both on the same side. Protecting him from the big bad Dean. (And their are big bad Deans at many schools, so learning to protect oneself from the wrath of a Dean is a good career move.) Student after student described this fellow as arrogant. So I could ask for his comment - which was "most people think I'm arrogant". So I could ask "what does that image do for you that is good for you and what does that image do for you that is not useful for you?" Once he had established that the image of arrogance was more of a hindrance than a help I could ask him to analyze what he does in the classroom that promotes that image. (It's sometimes great to have never been to the class when doing the most difficult "advising" because you can say - 'look, I wasn't there - you're going to have to think about what you could be doing and tell me about it.') So midterm questionnaires let you have really hard conversations that end up with you and the teacher you're working with on the same side - feeling more like a team than adversaries.

Basic preceptor guidelines

Study carefully the entire "Information for Instructors" booklet issued by the Faculty of Arts and Sciences (see but for matters that involve people, rules, or money outside the Department, contact the Calculus Director or Senior Preceptor before proceeding. The Director of Undergraduate Studies or the Chair may also be consulted as appropriate. For all but the most routine e-mail or communications with people outside the Department about calculus courses or students, it is a good idea to send a copy to the Calculus Director.

Start of classes

Research and experience show that the first day of class is extremely important. Every calculus section leader should prepare, practice, and get feedback on their plans for that day. For those who have not taught before, it is especially important to do this in detail and well in advance. Some general advice about the first day:

  • Say a bit about who you are and why you are delighted to be teaching this course.

  • Present goals for the course as a whole and refer back to these throughout the semester

  • Get to work on some content. Minimize time spent on administrative details since these matters should all be covered in writing anyway.

  • Get to know the students and their names

  • Encourage participation and set a positive tone right from the start.

A good source concerning first days is the chapter by Jeff Wolcowitz in "The Art and Craft of Teaching" available at the Bok Center. To allow time for student to get from one room to another, classes start five minutes after the announced hour, but end precisely as announced. Thus, a section listed as meeting from 10:00 to 11:30 would usually begin at 10:05 and end at 11:30. Use those five minutes to get to know your students informally, but then start promptly, especially at the beginning of the semester. If you wait for everyone to arrive, they will just come later and later. Students sign up for classes with the Registrar after a week or so of "Shopping Period." They may not drop or add courses after the fifth Monday of term. Be sure to get to know your students and give them sufficient feedback well before the drop/add deadline so that you can counsel them into a more appropriate course if they are not well placed. FAS rules state that: "Instructors are expected to be in residence throughout the academic year, including the Reading Periods and Examination Periods. However, short absences may become necessary and are permissible, so long as academic responsibilities are met or adequately covered and [the prescribed] procedures have been observed." If you may be absent for two or more consecutive classes, speak with the Calculus Director or Chair in advance. Absences of a week or more during term require permission from the Dean.

Reading period and Exams

Humanities courses usually do not meet at all during Reading Period, but some upper level mathematics and science courses continue throughout. Calculus classes should, in any case, avoid introducing new material during reading Period. It is a good idea to hold review meetings during that time. You are not supposed to accept any coursework after the last day of reading period (other than the final examination, of course). Finals are scheduled and proctored by the registrar, but Course Heads need to be present for the start and end of the examination. It is the Course Head's responsibility to come early, bring enough copies of a carefully proofread test, answer questions, and sign for the completed papers at the end. However you arrange the grading, be very careful to make sure no examination papers ever get lost. Students may only take finals at the time and place determined by the Registrar. You cannot allow any exceptions. The Administrative board may grant students who miss an exam the right to take a make-up, usually near the beginning of the next semester. It is therefore a good idea to prepare a make-up examination, too, at the same time you prepare the regular final. Check with the Calculus director and other experienced course Heads about your grade distribution. Never post the final grades. Give a copy of all grade sheets to the department office. FAS rules state: "Most instructors return exam booklets, papers, and other academic work to the students enrolled in their courses. Work that is not returned to students must be kept in a safe, accessible location on campus for at least one year after the end of a course. By law, students have the right to review all materials submitted to a course, and for a reasonable charge, may have copies of any originals not returned to them. Course heads should be sure to collect from section leaders and tutors any course assignments that have not been returned to students for appropriate storage. Faculty who are leaving the FAS or who will be on leave and away from the University should make appropriate arrangements for maintaining the availability of students' work."

Professional Conduct

Excerpts from "Information for Instructors": Authority: By virtue of their authority within the academic community, teachers have the power to influence thought and behavior, and the concomitant responsibility to recognize the potential weight of their verbal and nonverbal expressions. As leaders in the classroom, teachers have the responsibility not only to impart the excitement of ideas and the challenge of academic debate, but also the importance of courtesy and respect in intellectual dialogue. Fair Treatment of All Students: Students should be treated even-handedly. Equity is not necessarily achieved, however, by treating all students in precisely the same way. For example, some students respond positively to hearty, well-intoned criticism while others are discouraged by it. Some students welcome public comments about their work, while others are embarrassed by them. Genuinely even-handed treatment of students depends upon making a conscientious attempt to recognize and appreciate such differences. Teachers (and students) should guard particularly against ethnic, religious, sexual, and other discriminatory stereotyping. Interpersonal Relations: The power teachers exercise over students to penalize or reward in the form of grades and recommendations requires caution in interpersonal interactions, and the need to avoid the kind of familiarity that compromises objective and fair evaluation of a student's work. In particular, sexual advances towards or liaisons with one's students are inappropriate, and violate University policy. Within these limits, however, intellectual mentoring and friendly interaction are important elements of the learning and teaching process. Clear Communication: Because the evaluation of students partly depends on their understanding of the requirements of a course, course heads should be clear in their articulation of expectations, assignments, and the rules of collaboration and citation. Providing written explanations of assignments and requirements reduces the risk of misunderstanding. Students have the right to expect prompt return of papers and exams and a clear justification of evaluation, just as instructors have the right to expect that assignments will be thoughtfully completed on time. Classroom Engagement: The classroom is frequently the site of intense intellectual debate-or, alternatively, unbearable silence. Maintaining an environment for a constructive contest between ideas and their supporting evidence is primarily the responsibility of the teacher. Teachers should be aware of any tendency to favor one mode of argument over another, in which only certain students thrive; of the importance of listening attentively and with respect; and of the significance of nonverbal clues (nods, frowns, gestures, etc.). Criticism of Work: Comments should be directed at the work, not the person; and they should contribute to the refinement of both thinking and presentation. Peremptory dismissiveness is not appropriate. Professors are responsible for the oversight of all grades given by teaching fellows. Letters of Recommendation: Students depend on instructors for letters of recommendation. Honesty and fairness in responding to requests for recommendations is essential. Advising: Access to advising should be offered and equally afforded to all. Confidentiality and Discretion: Teachers are privy to information (and opinions) about students that ought to remain confidential. Exceptions should be made only in cases of emergency, such as threat of suicide, or other harmful behavior, when confidentiality is secondary to a student's welfare. Talking with colleagues or other students about confidential student information is inappropriate, as is any form of public embarrassment or shaming of a student. Collegial Conduct: Status differences exist within the teaching staff of every university. Awareness of the relative positions of colleagues in the academic hierarchy may avoid placing them in awkward or compromising situations. The implications of making particular requests of one's junior ought to be considered before making them; the right to refuse, for reasonable cause, without consequence, ought to be guaranteed every member of the community. Professional and research opportunities should be awarded with equity and fairness. Sexual Harassment: The Faculty has devoted considerable attention to the topic of sexual harassment and has adopted guidelines describing harassment and procedures for resolving complaints. Both documents are available from the Office of Academic Affairs The first document, entitled Sexual Harassment: Guidelines in the Faculty of Arts and Sciences, is a policy statement describing what constitutes sexual harassment; it defines sexual harassment in the following way: "The determination of what constitutes sexual harassment will vary with the particular circumstances, but it may be described generally as unwanted sexual behavior, such as physical contact or verbal comments, jokes, questions, or suggestions. In the academic context, the fundamental element of sexual harassment is ordinarily the inappropriate personal attention by an instructor or other officer who is in a position to exercise professional power over another individual. [...]Such behavior is unacceptable in a university. It seriously undermines the atmosphere of trust essential to the academic enterprise." The statement also addresses the issue of amorous relationships between individuals of different university status: "Amorous relationships that might be appropriate in other circumstances always have inherent dangers when they occur between any teacher or officer of the University for whom he or she has a professional responsibility (i.e. as teacher, adviser, evaluator, supervisor). [...]Officers and other members of the teaching staff should be aware that any romantic involvement with their students makes them liable for formal action against them." The guidelines also indicate the manner in which sexual harassment may have an adverse impact in a scholarly community: "The Faculty of Arts and Sciences seeks to maintain a learning and work environment free from sexual harassment, including unprofessional conduct in faculty-student relationships and sexism in the classroom. These kinds of behavior are barriers to the educational, scholarly, and research purposes of the University." The second document, the Faculty of Arts and Sciences' Procedures for the Resolution of Sexual Harassment Problems, describes the options available to any member of the FAS community who believes that he or she has been sexually harassed.

Dealing with troubled Students

FAS rules state that "Instructors are not responsible for counseling students on personal or emotional difficulties, even when those problems affect academic work. Undergraduate students who seem to be unusually upset or who are in need of special help should be referred to their resident dean (Allston Burr Senior Tutor or Assistant Dean of Freshmen)." In practice, contact the Calculus Director or Senior Preceptor immediately if you even begin to suspect that a student or colleague is having personal, emotional, or academic difficulties.

Students charged with dishonesty in course work

FAS rules state that: "Although instructors have the responsibility for evaluating students academic performance, the Faculty has granted jurisdiction over matters of student dishonesty to the Administrative Boards. Therefore, any incidence of possible student dishonesty in course work should be reported at once to the Dean of Harvard College if an undergraduate is involved or to the Dean of the Graduate School of Arts and Sciences in the case of a graduate student. After a preliminary investigation, the Dean will decide whether to refer the matter to the appropriate Administrative Board." If you do suspect academic dishonesty, try to document or preserve evidence to the extent possible, then contact the senior preceptor or Calculus Director immediately before taking further steps. The administrative board takes very seriously allegations such as plagiarism, collaboration, or dual submission (handing in the same work in two classes without prior written permission). It is important to make explicit in writing your course policies and expectations about what constitutes proper and improper group work, for example. One approach is to tell students that, as with any other form of scholarship, they must always document their sources. There is no explicit honor code enforced by the students.

Chapter 2. Advising

General guidelines

When a student comes to you for placement advice, try to find out the following:

  • Where they are mathematically?

  • What are their goals?

  • What else are they doing academically and otherwise?

1. Where is the student mathematically? Don't just have the student tell you what they studied. Ask questions. For example, did they study Taylor series? If yes, can they tell you what one is? If they can't at all, then it's not quite clear that studying it made an impact. Advising the less well-prepared student: Ask questions and then see how the student constructs his or her knowledge. For instance, to determine whether or not a student should take first semester calculus, among other questions I'll ask the following type to poke around. Solve for x: (2x+1)/(x+1) + 1 = pi Yes, fractions can be a problem. pi 3^{2x} + pi = 10 x ln 2 + (2x-3) ln 3 = ln x + 4 About how big is log117? (Give consecutive integers smaller and bigger) Do they know what skills to use when? The second questions asks about log manipulations, the fourth about whether logs have any meaning to them. (Some students can do manipulations but attach no meaning. Others have trouble with manipulations. Inquire about both. When students make mistakes, don't assume they are careless. Ask them to find the errors. It's very enlightening to ask a student to graph ln x or log x. If the student can't, can he figure out how to reconstruct it when prodded? If he can't, can he graph 10^x? Watch how he does this. Once that is done, can the student now graph log x? In other words, does the student see connections or does he have things poorly memorized but floating around anchorless? 2. What goals does the student have? Suppose you're advising a student who is between two courses and doesn't seem to be very good at making connections - the knowledge they have is not extraordinarily solid. If this student wants to be a novelist, you might advise the student to get exposure to new material, whereas if the student plans to be an engineer, then jumping ahead with a weak background will be fatal to his career plans. Prospective engineers tend to place themselves too high and it haunts them throughout their coursework because they never have time to go back. It the prospective engineer is missing a tad of material but is very solid on what she knows and is able to be led through things easily, then going ahead is beneficial, but if that solidity is missing it is disastrous. 3. What else is the student doing? Is the student taking Chem 10? CS 50? Beginning Chinese? Is the student also planning to row varsity crew and work 20 hours per week? Perform in a couple of plays? If a student is between two courses the student must consider how much time he has to play catch-up. Does the complete package of activities make sense or is the student playing Superman to later find out he can't really fly? Students ought to be academically challenged by not completely overwhelmed. 4> Cautions: You've got to use judgement in advising. Some students think they are much stronger and much better prepared than they are. These students were the best in high school and are certain they are the best and the brightest. Other students are certain that they were the admissions error. They are very smart but they are absolutely terrified by Harvard. Try to make sure that students don't undermine themselves before they even begin. Be on the lookout for women in particular who are doubting their abilities. But this applies to everyone. Never stereotype. All students here really are exceptional in some way - and in a short interview you'll be challenged to get a clue as to what that is. 5) Example notes on Math X helpful for in advising.

  • Taking Math X is not an academic disaster.

  • One of our students graduated in applied mathematics. (Christian Castillas)

  • One student is a pure math concentrator - entering his senior year. (Ian Goldstone)

  • One is graduating from Harvard law school. (Joi Pierce)

  • Several are working for investment banking firms on Wall Street. (Carina Williams, Ashley)

  • One concentrated in History of Science, is going to medical school, and actually graduated in three years! (Edidiong Ikpe)

  • There are students who took Ar/1a who went to Harvard Medical School (Rey Ramos)

  • One student even failed Ar at least once and still ended up going to graduate school at Princeton.

Math X is a first semester calculus course that moves at a speed that allows to cover precalculus material as well. In fact - students who come to Harvard placing into math 1b took the advanced placement AB calculus in one year of high school. Math 1a crams that all into 1 semester; Math X leaves it as one year. So, in effect, students in Math X are given the same amount of time to learn calculus as their counterparts in high school.

Examples of Advising Questions:

Math X to Math 1A: (If you can answer all of these thoroughly then it is unlikely that you need to take math X)

  • Solving equations: Can you solve for t in the equation ...

  • Logs: Do you know what a log is - give a number higher/lower than Log of 135 to the base 10.

  • Graphing: graph log x, (x-2)2, 3 Sin (2x)

  • Trigonometry: What is Tan(2), Sin(3), Cos 3 Arctan (-1)

  • Algebra: Question: If one person can do a task in 3 hours and another person can do it in 5 hours, how long might it take them to do it if they worked together? (Have the student set it up and carry it to completion.)

  • Derivatives: Need to be able to give a definition of a derivative. To go into Math 1 instead of Math X, need to show some math sophistication, i.e. can learn math on own.

Note - Math X is a year long class. We'd like to avoid the students who take math 1A in the fall, then want to go to math Xb in the spring. Math X is for people who have a little more trouble learning on their own - if you can learn quickly, then it might make sense to take a higher level course and do some catching up on their own time. It may be helpful to know that some students do successfully take Math Xa in the fall and go directly to Math 1b in the spring. Certain topics might be skipped under this option, but it may be appropriate for students who have done calculus already (as evidenced by an 8 on Part II of Placement Exam) but whose precalculus scores are clearly inadequate (not just borderline). Time commitments - what is the rest of their schedule like Tougher (higher time requirement) classes: Chem 5, CS 50, Students' goals: What are their general plans - pre-med? Concentration possibilities, etc. For example, an Economics concentrator could take Math Xa-Xb during his freshman year and be able to go into Math 20 during the first semester of their sophomore year. For other concentrations, the pressure to complete Math 1 during the freshman year in order to enter Math 21 in the sophomore year may be greater. From 1A to 1B: Need to know basic integration - but not just basic examples, also need to show understanding, what does it represent. Given a function with pos and neg, over a pos /neg interval, velocity curve, get an expression for the total distance traveled, net distance traveled, what it corresponds to on graph. Concrete example, Sin (2x) for instance - can they reconstruct this. What does a definite integral have to do with area? The student should have some idea about how the Riemann Sum construction relates to integrals. Being able to do an integral like without knowing what it represents indicates insufficient background. To go from Math 1B to Math 21: Need to know some ODE's - not necessarily for 21A, but helps for 21B and for the applied sciences, you're expected to know some ODE material, and you should have picked this up in 1B. Should have a really good understanding of taking derivatives and integrating - this will be used immediately in the course, and it needs to be second-nature.

Higher Level Course Descriptions:

Math 19: designed for life-science, bio, pre-med majors, don't need to know a lot of techniques. Having a math 1B background is what we ask, but you don't need to know the series material, actually, it's more of a 1A pre-requisite, and a good feeling for integration/differentiation (could take it after a good result in math X). Helps to remember the chain rule, but you don't need to remember all the integration techniques. Good course for Bio majors, nervous about their background, questioning whether they should be in 21A Math 20: if someone's interested in social sciences, econ, poli-sci, (Rob Winters designed the class by looking in macro-econ texts). Similar background requisites as for math 19 (roughly a math 1A bacground). Need to understand the diffentiation well, not necessarily the integration. Adds in some linear algebra - at the level an economist would need. Math 101: probably covering the material from math 1A would be enough as a background, making sure to include some trigonometry. Have to be interested in doing serious proofs. Can do it concurrently with 1B or 21. If you take enough calculus and 101 you should be all set for the other 100 level classes, or for someone who's interested in proofs in general. Time commitment it's about the same as taking math 23, but not the amount of time as for math 25. Math 23 and Math 25: For people with interest in theoretical math, want proofs, modern sophisticated approach. Math 23 is supposed to be more of a normal course load than math 25. So there is a difference in the level of intensity from math 25. General question - do you want to have a life outside of math (if so take 23 instead of 25). Would you rather spend your time doing math problem sets instead of going to a movie on Saturday night (then take 25). Message is you don't have to take 25 to be a successful mathematician. Of course, the intensity of math 25 means that your understanding and general math sophistication should be greater at the end of taking math 25, should you choose to take that class. Math 55: Hard core, for seriously intense math lovers only. This course is designed to keep extremely advanced undergraduates thinking and doing math for a good amount of the semester. The course varies from year to year depending on the interests of the professor, but it is always a major time commitment. The document gives the current view of the department.

Chapter 3. Running a course

Coursehead Responsibilities

  • Pick a textbook in consultation with others.

  • Write a syllabus

  • Schedule examinations well before the semester begins

  • Book rooms for the examinations.

  • Make course policy.

  • Orient teaching team: the teachers at least a week before the term begins.

  • Orient the course assistants after they are assigned.

  • Watch practice first lectures for all new teachers well before the first day of class.

  • Oversee the course - the content, teaching, etc.

  • Deal with all organisatorial problems that arise like sectioning problems

  • Run plenary orientation session for all students at the beginning of the term.

  • Schedule and run weekly course meetings. If you have new and or weak teachers. These meetings ought to have pedagogy content and are part of the training process.

  • Organize the writing and grading of examinations.

  • Read all midterm evaluations to keep up with how section leaders and CA's are doing. This will help guide your meetings. Do this in a timely fashion.

  • Talk with people when necessary. If there are problems with CAs, report them to the appropriate people.

Advise to give for section leaders

  • Come early to class. Bring chalk. Talk with the first few people who arrive.

  • Write down the name of the course, your name, contact info, office hours.

  • You are encouraged to hold office hours at the Math Question Center (8-10pm at Loker).

  • Always start on time (6 or 7 minutes after announced time).

  • Say something about yourself, where you are from, what you are doing and how it might connect with the course, why you are delighted to be teaching this course in particular.

  • Find out something about them, preferably by distributing a questionnaire that asks about their background, plans, interests, etc.

  • Begin learning their names. Use their names in class. Make eye contact.

  • Get to some new or unusual mathematical material quickly on the first day.

  • Look for a topic you find interesting to bring up. Your enthusiasm will be infectious.

  • Discuss a brief overview of the course and what they will be able to do by the end.

  • Get them talking early. As you go through the overview, you can ask them about what they remember, what this reminds them of, etc. Always be encouraging, positive, and upbeat. Never let the class feel discouraged, dumb, or ill prepared. It gets in the way of learning.

  • Make good on the fact that this is a small and potentially interactive section rather than a big lecture. Use activities, group work, polling, debates, in class exercises, demos, etc.

  • Pay attention to the fact that there are many implicit and explicit contracts set up between you and the students on the first day. Try to make your expectations clear.

  • Keep administrative discussions to a minimum. Refer to handouts and the web.

  • When asked for clarification of policies, stress the sound pedagogical reasons for them.

  • Be very careful about abbreviations, technical terms, or notation that you take for granted but they may never have seen before. Check in with them constantly to make sure.

  • Introduce your Course Assistant and have them say a few words.

  • Encourage students to check the course web site regularly.

  • The CA should count the number of people in the room and tell Susan how many were there.

First Week or so

  • Have your CA arrange a recitation time and room. Not everyone will be able to make it, but they can go to the recitation for another section since all will be posted on the web.

  • Give a 5 or 10 minute diagnostic quiz on prerequisites that does not count, but that they should pick up graded from you in your office by appointment or during office hours. It makes a huge difference once you have exchanged a few sentences with each of your students one-on-one.

  • Try to start each class with an overview of your goals for that day with lots of motivation. Writing down the main topic together with an agenda on the board is always a good idea.

  • See if you can pose a compelling problem for them to think about at the beginning of class that they can see how to do by the end.

  • Make good on the fact that this is a small and potentially interactive section rather than a big lecture. Use activities, group work, polling, debates, in class exercises, demos, etc.

  • Pay attention to the assignments and let them know that you do. That does not mean that you have to do a problem just like the ones assigned, but you should make sure they are adequately prepared to tackle the homework. Refer to and jump off from problems.

  • Don't hesitate to give them advice about how to study and what it takes to learn mathematics. Some students think it is all a matter of cranking formulas and do not realize that you have to think about what you are doing, sometimes even for more than a few minutes. Encourage them to work with others and seek help, but to write up answers in their own words.

Be on the Look Out

  • Your CA can be an extremely valuable set of eyes and ears. The CA should write a very short homework score report each week indicating problem students and problem topics, as well as good students and trends, and send it to you with a copy to the course head.

  • The CA should also attend your class regularly so they can talk about and answer questions about what has been going on.

  • Be on the look out for students who are improperly placed and flag them for the course head. Getting them into the right course quickly will avoid lots of problems later.

  • If there are students who hand in no or totally unsatisfactory homework for the first two weeks, the CA should contact them, ask what is going on, offer help and encouragement. The CA should flag such students after the third assignment and you should contact them with the same message. The CA and you should flag any such students after the fourth assignment so the course head can contact them. After the fifth week, it becomes very hard or impossible for them to drop the course.

  • While most of your students probably do not think they want to concentrate in mathematics, a few might, and a few more might be inspired by your class to do so. Look out for them and encourage everyone to take more math courses.

  • Injecting a little history of math can add color. Many students do not have any idea what mathematicians do or why. Your course may leave a lasting impression on them about all this. Remember that any one of your students could end up in Congress, for example.


  • Prepare. Even simple examples should be worked out in advance rather than on the fly.

  • Plan your board. Use headings and labels. Practice sketches or make a handout.

  • Write down on your notes about how much time you want to spend on each big topic.

  • Have some extra examples ready. Try to anticipate what questions they may ask.

  • After you prepare the subject matter, make sure your notes also contain guidelines and reminders to yourself about choreography and management: What questions do you want to ask when? Where and how do you want to summarize, pause for questions, invite participation, or check in with them to probe what they are and are not understanding? Who do you need to encourage or discourage about speaking up in class?

Every So Often

  • Make good on the fact that this is a small and potentially interactive section rather than a big lecture. Use activities, group work, polling, debates, in class exercises, etc.

  • Do a minute paper. At the end of class ask them to write down on paper, without their names, their answers to: What was the most important thing you learned today? And what are the most important questions you still have? Reading these is a tremendously eye-opening experience. Make sure to respond (broadly) on the web or during the next class.

  • Have the Bok Center videotape one of your classes and view the tape with a consultant.


  • Running a multisection course is hard, so be a good team player.

  • Try to keep up with the syllabus. Let the course head know if you are falling behind.

  • Do not miss class. Get a substitute if you really have to be away once or at most twice.

  • Come to weekly meetings with ideas and suggestions.

  • Share your handouts, examples, and what not with all the other section leaders.

  • Contribute potential examination questions. Help proofread carefully.

  • Show up on time for proctoring and grading exams.

  • Let the course head know right away about any unusual incidents or students, even if it is just something wonderful or something that you feel funny about. Our job is to teach mathematics, and to alert others to anything that may get in the way of that. You should not have to be a psychotherapist or a disciplinarian, but it is your responsibility to let the course head know if there are signs of anything strange.

  • Maintain professional conduct. No favoritism or fraternizing with individual students!

  • Keep records of what you have done for your teaching portfolio, since this may be useful for you when applying for jobs.

  • Keep records of what students do, too, since they are likely to ask you for letters of recommendation at some point in the future. The students are almost all very interesting, responsible, busy, and accomplished in something (not necessarily math), so enjoy getting to know them and helping them learn some mathematics.

Course meetings

Share teaching ideas and strategies. These may seem natural to you, but may not be something that other teachers are thinking about. Just as our weakest students are smart people who are not thinking when it comes to math, (they just don't believe their brains are supposed to be used when doing math), so too, our weakest teachers are very smart people who are not using their whole brain when it comes to teaching, (they just don't believe their brains are supposed to be used when teaching.) Some of this sharing and prodding people to think can happen at course meetings.

  • Ask questions!

  • How are you planning to motivate this topic?

  • What will be the stumbling blocks for students?

  • How will you structure your class to help them around these stumbling blocks?

  • What are students having most difficulty with?

  • What examples with drive home the main points?

  • Share your own ideas and techniques.

There is a fund available to have course meetings in the faculty club. Some course heads chose to do that and meet with their TFs during a business lunch. See the main office for details on how to get funded.

Chapter 4. Sectioning

Unlike at institutions like MIT or Berkeley, the service calculus courses at the mathematics department are organized in sections. Instead of one big lecture for hundreds of students, students learn in smaller sections of 10-30 students. The advantage is that students get more individual attention and that the lectures can be organized more interactively. An other benefit is the training of teachers and graduate students. Sectioning is the process to assign students to individual sections in the service courses Math21a, Math21b, Math1a, Math1b, MathXa, MathXb at the Mathematics department. We must section from 850-1000 students in the fall and 600-700 students in the spring. In the fall, we end up with about 30-40 sections with approximately 25-30 students in each and about 25 sections in the spring. A computer program developed by the Instructional Computing Group (ICG) is used to section students. Since the registrars solution could not deliver what we needed, it is an emergence solution but it works.


In 2001, ICG discontinued to run the sectioning program. It got ported from the Solaris operating system to our own Linux server with the help of one of the authors of the program. Until the registrars web-based program will work (there were too many performace problems), this ICG sectioning program is used at the Mathematics Department. Porting the sectioning program (a C++ application) from Solaris to Linux was not so easy, partly due to the lack of documentation and because the code is sensitive to compiler and library issues: (it requireed suitable ncurses libraries and a suitable version of the gcc compiler).

Basic steps

  • Before sectioning starts, links on the invidual course pages and on the Department page should point to the sectioning page

  • The calculus office requests rooms in the Science Center. Rooms can be scheduled also online. It is often faster to get the rooms by talking to Chris directly. The main office SC 325 controls SC 310, 411, 507 and 530 outside of prime time class hours Mon-Fri 10am-1pm when courses are booked in these rooms. If there is nothing available in the science center, contact the classrooms people in the Registrar's office at 5-1541.

  • The server with the sectioning program has to be preparied prior to the beginning of the semester. The student data and the appropriate time slots have to be feeded in the program. This happens in August.

  • Coordinate the teaching assignments between approximately 40 instructors, taking into account the instructors individual schedules and conflicts as well as student enrollment and time preferences.

  • Coordinate the room assignments for 40 sections taking into account class size, room availability, student time preferences, and particular teaching characteristics and needs for faculty, graduate student fellows and teaching assistants.

  • After all students have given their preferences, the sectioning program "sectioner" distributes the students into individual sections in such a way that most students have their first choice. The person who sections can move around individual students. After students have been assigned, the seconed data are filled into the ICG toolkit so that section leaders can see the face books of their sections.

  • Manage enrollments and resection. Once students have been assigned sections (usually between 85-95% get their first choice for a time slot), a large number of them then want to switch their section. For example, it's not unusual in the fall to have from 250-300 students ask to change their section. After discussing the request with each student, we must decide which students we can redistribute into the existing 40 sections which already have specified time and room assignments, while maintaining small section sizes of approximately 25-30 students.

  • After students are assigned the list of students is sent electronically to each section leader.

Server information

  • Support Evenso the terminal based sectioning program is as simple as it can be, a small fraction of students have problems with that process. The preceptor group can assist in case of problems. The type of students having problems are students who in general have problems with computers, people who do not realize when their caps lock is on or hit the return button several times for no reason.

  • Hardware In the fall 2001, the mathematics department used the sectioning program on a PC running Linux. Since the spring of 2002, the program is at home on a dual processor Dell PowerEdge Server ( There is a backup PC in place, in case the server would fail.

  • Backup A second computer which carries an identical configuration is in place as a backup. During sectioning time, cron triggered scripts sync the data. Every 2 minutes a backup of crucial data is done on a different medium and every 10 minutes a mirror backup from one machine to the backup machine. Every day, a CD is burned which contains the sectioning information of the day. Backup is crucial. It would be a disaster if during the sectioning process, data would get lost and 1200 students would have to be asked to section again. Technology can fail. It is good to be prepaired for that case and have to deal with minimal damage. Besides failure of hardware, it can also happen that the server gets hacked. This is a possibility for any computer which is online.

  • Installation Installation and configuration of the sectioning program is not straight forward: here are the main things which need to be configured:

    • Compiler: A gcc 2.95.3 compiler is needed. (Other gcc compilers do not necessarily compile the "section" program and the "sectioner" program)

    • Sendmail (don't use postfix), replace mailx (Solaris) by mail (Linux)

    • A Pico or Nano editor is needed and needs to be installed seperately.

    • A recent ncurses library (ncurses-5.2 works).

    • accounts: s_math21a etc., section (permissions are crucial)

    • put cron scripts in place

    • put monitoring scripts in place to watch the sectioning progress at

    • the result of the translation script which produces the input for the sectioning program must be checked and tested. In the fall 2001, we had problems with student names which are longer than 30 characters.

    • in general, there are many things which can go wrong. Most problems are wrong permissions.

  • Maintainance: It should be noted that maintaining and running the sectioning program requires quite a solid understanding of Unix, Perl, C and also a basic understanding of what the 13'000 lines of C++ code do. The authors of the program or the ICG professionals did a great job in writing the program, but due to the lack of documentation, one should not underestimate the task to run and maintain it. We obtained the program in February 2001 from ICG. It was used in September 2001.

  • Glitches: It can happen that the sectioning process gets stuck. This is possible mainly when sectioning information is requested at the wrong time using the sectioner program. It is advisable to minimize interaction with "sectioner" when lots of students use the service.

Chapter 5. Math club

Math Table

The undergraduate Math Club has dinner called "Mathematics Colloquium" together once a week during the semester, at which a short talk of thirty minutes is presented by anyone ranging from a Harvard undergraduate to a graduate student, a faculty member, or a specially invited guest speaker. Ideally, the talks should begin at a level accessible even to first-year undergraduates who are considering the mathematics concentration, but speakers should also be strongly encouraged to present material which would not be part of a normal course offering, or if so, to draw several topics together or to present something from a different or unusual point of view. These dinners have traditionally been held each Tuesday from 5:30-6:30 P.M. in the Mather House Dining Halls A & B. The talks begin at 6. The faculty advisor has several responsibilities associated with Math Table, the first and foremost of which is arranging to have speakers. The best option is to have as many undergraduates speak as possible, and seniors, writing a theses should be particularly encouraged to speak on their areas of research. Most undergraduates are more willing to speak in the spring, however, as they then have time to attend others talks first and time to have learned enough about their topics. Other good candidates for speakers are new junior faculty, especially for autumn talks. Arranging talks, especially early in the year, can require a lot of cajolery. The advisor should be aggressive in trying to fill slots as far in advance as possible. Some talks are traditional and pre-arranged. The first talk in the autumn is often given by the department chair. Early in November, for seniors applying to graduate school, there is a panel discussion by young faculty representing the various upper-echelon graduate schools. Shortly after senior theses are due in the spring, there is another discussion by the seniors and for the benefit of the juniors who should begin thinking about their theses for the coming year. Noam Elkies has also given a Putnam Exam talk in the last couple of years. The other principal responsibility of the faculty adviser is the judging of the Rogers Prize. Each year, the Rogers Prize is given for the best undergraduate talk of that year. It is best if there are two or more faculty judges who have attended at least all of the undergraduate talks. The criteria for the prize are not spelled out more explicitly, but a good talk should have significant mathematical content, should be aimed at the appropriate audience, and satisfy all the usual standards for a good talk (clarity, liveliness, relevance, humor, etc.). Finally, the Undergraduate Math Club officers can help with some details like putting up posters to advertize the upcoming talks.

Chapter 6. Apprenticeship

Guide sent to apprentices

This is a guide to what happens at each stage of the Apprentice Program. The goal throughout is to help you get off to a strong start with your own section. Please note that it is your responsibility to schedule your visits, practice sessions, lectures, taping, and viewing. At the beginning of apprenticeship, you must work for one hour at the Math Question Center which is open from Sunday through Thursday evenings from 8-10 pm in Loker Commons. Please let the apprentice coordinator know what date you re planning on attending. The Question center is staffed by Course Assistants and Graduate students and will provide you with one on one experience working with students while also letting you get a feel for what level the students are at. Visit your Coaches Classes: while you are in class:

  • Notice the level at which the course is taught. How rigorous is the presentation? What can you assume about the students' backgrounds?

  • Pay attention to the number and type of examples done. How difficult are they compared to homework and exam problems? Pay attention to the transitions from one topic to the next.

  • Notice the pace at which topics are covered. How does the coach keep moving without leaving the class behind?

  • Think about motivation. Does the presentation make the material seem interesting and purposeful? How does the coach connect new ideas to previously learned material?

  • Observe the blackboard work. Is it well organized and easy to follow? What do you think the student's notes look like?

  • How does your coach promote interaction? Does he/she make eye contact with the students? What kind of and how many questions does the coach ask?

  • Listen carefully to the students' questions. What do they tell you about the students' perspective? Do the students look like they feel free to speak up?

After class:

  • Discuss your observations with your coach and with other apprentices.

  • Ask your coach about why specific things were done as they were.

  • Although you may or may not want to conduct your class in the same way your coach does, you should use him or her as a sounding board for your own ideas.

Conduct a Problem Session [Optional] Before the problem session:

  • Discuss with your coach and/or his course assistant what kinds of problems to do.

  • Look over the recent homework assignments.

  • Plan a very short review lecture on a specific topic.

  • You may present this for the first 5 or 10 minutes.

  • Choose and prepare problems which illustrate important techniques.

During the problem session:

  • Do everything you can to involve the students.

  • One strategy: put a problem on the board; ask for ideas; write down only what they say; try not to make suggestions yourself until the class is completely stumped.

  • Another strategy: put problems on the board; have them work out solutions on paper; walk around; offer encouragement and suggestions; ask students to help one another.

  • Remember that the point is for them to do the problems, not you.

Give a Practice Version of your Lecture to your Coach and Student Volunteers. Before the lecture:

  • Attend the class meeting before your lecture.

  • Begin with a transition from where your coach left off.

  • Prepare detailed lecture notes.

  • Go over them with your coach in advance checking the level, pace, motivation, etc.

  • Be sure to choose lots of examples the students will find helpful and interesting. These may not be the same ones you find interesting.

  • Have a few extra examples ready in case they are needed. Plan your blackboard layout.

  • Think about how to get the students involved.

  • How and where will you ask questions?

Give Three Lectures, the Second of Which is Videotaped. During each lecture:

  • Try to relax; a deep breath on occasion can help.

  • Ignore the video camera as much as possible while taping.

  • Turn to face the class whenever you can.

  • Make eye contact with students, including the front, back, and in-between rows.

  • Are you speaking loudly enough so that everyone can hear?

  • Project your voice without shouting.

  • Can everyone see? Is your writing big enough?

  • Don't erase or stand in front of what you just wrote.

  • Take all questions seriously.

  • Be careful not to talk down to or belittle the class.

  • Are you checking in with your audience?

  • Are you really being understood?

  • Keep your mind on the students.

  • Concentrate on communicating with them.

  • Try to look at the mathematics from their point of view.

Note: At the end of your lectures, it can be helpful to hand out and collect brief student questionnaires. You must do this after your second lecture. You can either use the attached form, or create your own asking for student feedback. Whichever you choose, it is your responsibility to make copies and administer the process. After each lecture:

  • Talk with your coach and, if possible, some students.

  • Review the student questionnaires.

  • Decide what needs improvement and how to do it.

View the Videotape. Between your second and third lectures:

  • Watch and discuss your tape with someone from the attached list.

  • It is usually a good idea to invite your coach as well.

  • Have the completed student feedback forms with you to go over at the tape viewing.

  • Copies of these forms should be kept to help with placement, etc.

  • Based on the tape, figure out what your strengths and weaknesses are (everyone has both).

  • Develop a strategy for improving your third lecture.

Apprentice Review Before the end of the semester, coaches and apprentices should discuss the next steps with one another and with the Committee on Instructional Quality. In consultation with the Committee, the Department Chairman and the Director of Graduate Studies ultimately determine teaching assignments. Apprentices who receive teaching fellowships are expected to have:

  • shown responsibility,

  • prepared their classes carefully,

  • demonstrated an ability to interact appropriately with students.

Only the best teachers will be offered sections to teach. People whose support includes a teaching fellowship but who have not demonstrated readiness to teach a section of their own are typically assigned course assistantships, grading jobs, and other training activities to help them prepare to reapprentice during a subsequent semester.

Apprentice program welcome letter example

On behalf of the Committee on Instructional Quality, we are pleased to welcome you to participate in the Mathematics Department's Apprenticeship Program. All graduate students must participate in the Program before they can be considered for a teaching assignment. The Apprentice Program is one way in which the Mathematics Department does its best to ensure a very high standard of instruction in its courses. Moreover, learning to teach well is an important part of your training or a career in Mathematics. Apprenticeships are therefore designed to give graduate students who may not have taught very much before a chance to gain some experience and training before starting to teach on their own. Each participant is paired with a coach who is presently leading a section of Math X, 1 or Math 21. The apprentice first attends a few of the coach's classes, then conducts a practice lecture, and finally plans, delivers, and reviews three lectures of his or her own. The attached training roster has been prepared based on the information you have already submitted. Please meet with your coach as soon as possible to determine a schedule for the apprentice program. There is a letter from the Chairman explaining the program to the students in your coach's class. If you or the coach wishes, the letter can be handed out or just read when you are introduced on the first day you start attending lectures. Please note that before delivering your first lecture to your coach's entire class, you must satisfactorily present a practice version of that lecture to your coach and to at least three student volunteers from the class. It is your responsibility to arrange a time and place for this practice session. Make sure to leave enough time for this since the student volunteers may have hectic schedules. Count on spending up to two hours to go over an hour long lecture. If your coach then feels you are ready, you will give a total of three lectures to his or her class. The second of these should be videotaped and viewed before giving the third. The tape should be viewed by one of the persons listed at the end of your outline as well as by your coach. Again, it is up to you to schedule the taping and viewing with the Derek Bok Center, whose number is 495-4869. Due to increasing demand for their services, it is best to try to make arrangements a week or so in advance. Tapes will not be seen by anyone without your permission. With the attached outline as a guide, please confer with your coach about appropriate dates for each stage of your apprenticeship. Please do not hesitate to contact the calculus coordinator. if you have any questions. Good luck!

Chapter 7. Tutorial Program

The tutorial program forms a very special part of the undergraduate math concentrator program. Its strength relies on a couple of key factors. First, tutorials give upperclass math concentrators the opportunity to take smaller seminar-styled math classes covering topics not likely to be offered as part of the regular undergraduate curriculum. Second, tutorials give graduate students the opportunity to gain teaching experience apart from the normal calculus sequence classes. Tutorial projects typically end up turning into senior theses for math concentrators. With this in mind the general model for tutorials is that they are generally filled with mainly juniors, some seniors, and some sophomores, and are generally taught by experienced grad student teachers who have already taught calculus for several semesters. However, there have often been exceptions to these guidelines.

Organizing the Tutorial Line-up:

In the spring, prior to spring break, notices are sent out to grad students soliciting tutorial proposals. The tutorial organizer should also speak to grad students directly about possibly running a tutorial (depending on how much interest there is - if you've already gotten 7 or 8 proposals, then it probably doesn't make sense to talk to more grad students). Usually you'll need to send out one or two reminder notices. The deadlines aren't as important as making sure that people get going with their planning. A critical issue to keep in mind while planning for the tutorial line-up is to make sure that the people who will be teaching tutorials aren't needed elsewhere in the teaching line-up. Also, if there is going to be a shortage of teaching jobs, then the tutorials should go to those grad students who need to teach, up to a point. Tutorial proposals should be collected and perused both by the tutorial coordinator and by the Director of Undergraduate Studies, Cliff Taubes, who is officially in charge of all undergraduate classes, including tutorials. Decisions should be made and coordinated along with the regular teaching lineup, so that teaching assignments are all made at the same time. Be sure to notify everyone who applied at the same time via e-mail, so that people don't find out second-hand that they weren't chosen. Remember to remind those people who didn't get a tutorial spot that they can reapply for the next year.

Selecting Tutorials

There are two main issues to consider - the choice of teachers, and the choice of topics. Regarding teacher selection, you need to balance several factors: who needs to teach, their teaching ability, whether a grad student has already had an opportunity to teach a tutorial, as well as how good a teaching proposal submitted has been submitted. As for topic selection, typically you should try to have one lower (few prerequisites) and one higher level tutorial each semester. Also, you should take into account whether there is likely there will be a significant interest in the tutorial topics. For instance, if there are going to be two number theory related topics, then they should be split up among fall and spring, so that there are alternative topics offered at the same time. To get a sense of student interest, you can ask around at the Math Table, or at one of the math concentrator gatherings in the math department. We've never done it, but you might also consider sending around a request for topics of interest, well before asking for tutorial proposals, and then letting graduate students know that there is a particular interest, if one comes up often.

During the semester

Just prior to the semester starting, you should make sure that the two tutorials are promoted at one of the first Math Table meetings for the semester. This can happen a day or two before the tutorial sign-up meeting. Each person running a tutorial should give a short presentation on a highlight from the course, or give an indication of an interesting main theme for the tutorial. Next, you should have organized a meeting in the afternoon on of the days of the first week of classes to have a tutorial organization meeting. This should have been promoted to math concentrators well ahead of time. At this meeting the two tutorial leaders again give a short presentation on their tutorials, but this time the emphasis should be more on describing exactly what will be covered in the tutorial, prerequisites, possible topics for the projects, and any other expectations. At this meeting students should fill out tutorial application forms, although we typically give everyone until a time on the next day, as there are often people who can't make the introductory meeting. The next step is choosing who will be in each tutorial. Exactly how this is done varies somewhat from year to year, but as a general guideline, juniors who haven't taken a tutorial yet should be at the top of the list, followed by seniors who haven't taken a tutorial yet, then sophomores. If someone has already taken a tutorial, then it's possible to take another one, but usually the spots are filled by those who haven't already taken one. Students must also meet tutorial prerequisites, of course, and should show an interest in the subject, and be able to meet all together at least one evening during the week (this can cause problems!). There can be a tension between the tutorial teachers and the coordinator in that the teachers want to put together a list of the best students, perhaps choosing the ones they already know and like, whereas the coordinator's job is to make sure that everyone is given a fair chance to take a tutorial as part of their undergraduate career, and that they can be used to launch senior theses. There is also something to be said for letting a student who perhaps hasn't stood out among their group of Math 55 classmates, be given a chance to shine in a smaller setting. Make sure that everyone is told about who's gotten into a tutorial and who hasn't at the same time to minimize the hassle for the students (they need to figure out the rest of their schedule too). Pass the list on to Cliff Taubes, and make sure that the tutorial teachers set up a meeting for the next week. During the semester you should keep in regular contact with the teachers to make sure that everything is going smoothly. If they are having trouble getting a student to turn in work, be sure that they give the student plenty of warnings, both verbal and written, and set deadlines that are agreed to in advance. Students will sometimes try to turn everything in, both homework and papers, at the last minute, which can cause problems for grading. Teachers should always request that students turn in drafts ahead of time. This can prevent a completely inadequate paper being turned in later. Also be sure that the teachers let everyone know what the expectations are for grading - if they want to assign half of the grade based on homework and class participation, then that's fine, as long as they've specified that to their students. Towards the end of the semester you should pass out tutorial evaluation forms for the teachers to use at one of their last meetings. Make sure that they let students know that they won't see any of the evaluations until after all of the grading is done for the semester (and make sure that this is adhered to). At the end of the semester, you'll need to set up a time to go over the grades with each of the teachers. Be sure to check the academic calendar at the beginning of the semester to check when grades are due. This impacts when the tutorial papers should be turned in, so make sure you've gotten all that straightened out early in the semester! For grades, your job is to ensure that the tutorial grades are roughly consistent from teacher to teacher, semester to semester. The two teachers should come to you with their ideas for grades, and bring the tutorial papers with them. They then should explain what they have in mind, and you should query anything that seems odd. Make sure that the teachers realize that with such small classes, it can often be the case that everyone really is doing extremely well, and so there is a fair likelihood that the grades will all be in the B+ range or higher. Occasionally everyone merits an A or A-. If anyone is in danger of failing, then you and they should have had some warning of this when they turned in their first drafts of their papers. Finally, the grades need to be approved by Cliff, so have the tutorial teachers write down a short explanation for each of the students' grades, and run that by Cliff.

Tutorial proposal letter example:

To: Cc: Hi, all, hope everyone's doing well. For those of you who aren't graduating this year, and who would like to teach next year, I want to let you know that we are in the midst of putting together the list of tutorials to be taught during next year. I'm writing you right now to ask those of you who are interested in possibly teaching a tutorial, to put together a proposal for a course, and submit it to me by Friday, April 7th, the first Friday after the Spring Recess. I'm sure that many of you already know how the tutorial program is run, but for those of you don't know, a tutorial is a math seminar, for 6 to 10 students, usually at the junior undergraduate level, covering a topic of interest (of interest to both you and at least 6 to 10 undergraduates!) Classes being offered this spring include Spiro's Geometry and Gauge Theory, and Tomas' Arithmetic of Elliptic Curves. Tutorials meet once per week for several hours, usually in the evening. During the first part of the semester, the tutorial meetings typically follow a lecture format, and often include weekly problem sets. After the semester has gotten underway, you should start meeting with students to set up projects for them to work on, on problems related to the course material. The main bulk of the tutorial program then revolves around students putting together papers and presentations on the projects that they're working on. Typically the last one-third to one-half of the course consists of students presenting their work. As the person running the tutorial, it is expected that you will meet with each of the students on a regular basis to get them going on their projects. You should also help them practice their presentations, so that these will be of a high enough caliber to be presented to the other students in class during the regular tutorial meetings. Teaching a tutorial is considered a regular teaching appointment, and is equivalent to teaching a section of calculus. For those of you who have been teaching calculus sections for a number of years, I would highly recommend your considering teaching a tutorial before you graduate. It's a nice change of pace from calculus, in that you get to teach about a subject that can be closer to your research interests. It also looks good on your c.v. as an example of curriculum development and teaching ability. If you're interested in the program, you might want to speak to either Tomas or Spiro, who are teaching tutorials this semester, or to Henry or Tom Brennan who taught in the fall, and ask them what the experience has been like. In your tutorial proposals you should include the following:

  • An overall tutorial objective, (an abstract for the course)

  • A brief but descriptive syllabus for the semester

  • A list of possible projects students could work on

  • A list of reference materials, textbooks, that students could use

  • A description of prerequisites that you would want for the students in the tutorial.

If you have any questions about the tutorial program then please get in touch with me. In terms of number of tutorials available, we still have several openings for next year. We'll give preference to more senior graduate students who haven't had a chance to teach a tutorial, so that they get a shot at it before they graduate. Otherwise, we're looking for the best, most thoroughly planned-out, tutorials. Looking forward to your proposals! Tutorial coordinator.

Tutorial Sign up sheet example

Math Tutorial Sign-up Sheet Spring, 2000 Due Thursday, Feb. 3rd by 2pm. (please return this form to the Tutorial coordinator)

  • Name:

  • Campus Address:

  • Phone:

  • E-mail:

  • Most likely graduation date:

  • Concentration:

  • Math course and other related courses taken:

  • Course Year:

  • Professor:

  • Grade:

Which tutorial are you interested in taking? (circle one or both - if interested in both, then please indicate which one you are more likely to take).

  • Tutorial 1:

  • Tutorial 2:

Why do you want to take this tutorial? (if interested in both, then please write down reasons for wanting to take each tutorial) Is there anything else that we should know about you? (i.e. relevant to taking one of the tutorials!) Tutorials typically meet one evening a week for two hours. To the best of your knowledge at this point, please X out those times which would definitely not work for you this term. The more flexible you are with your schedule, the better in terms of establishing a meeting time for the tutorial.

Tutorial feedback questionaire example

Please take the time to answer these questions carefully. Your feedback will help ensure that the tutorial program continues to be successful. Thanks!

  • Tutorial Leader's Name:

  • Tutorial Title:

  • Semester:

  • How valuable has this tutorial been for you?

  • Were the classes well prepared?

  • Were the classes as interactive as you had hoped?

  • Did your teacher encourage student participation?

  • Did your teacher answer students' questions well in class?

  • How available has your teacher been to help you during the semester?

  • Have you received as much help as you've needed with your tutorial project?

  • What did you like most/least about this tutorial?

  • What changes do you think would have made this tutorial more effective?

Chapter 8. Course Assistants

CA Program

Overview: the math Course Assistants are comprised mostly of junior and senior undergraduates, many of whom are math concentrators, who form an integral part of the calculus program. Their main duties include grading homework, teaching weekly problem/review sessions, and helping out one evening a week with the Math Question Center. They're also asked to help prepare homework solution sets, occasionally host review sessions for exams, and take care of other minor tasks during the semester as needs be. The ideal math CA is someone who is excited about teaching others, excited and competent at mathematics, and who is extremely capable, organized and professional. There are plenty of students who excel at the job, but there have also been a number of students for whom math CAing is simply not appropriate. As the math CA coordinator, you have a major responsibility to ensure that the caliber of math CAs is kept high, and that the program runs smoothly during the year. In this guide we attempt to highlight the key parts of the math CA program, however it is not possible to cover every last detail of the program. It is advised that anyone who will be working with the program in the future spend time helping out with the current CA coordinator during the course of the year in order to make the transition from one year to the next as smooth as possible. Also they should spend some time the year before getting to know the students who are currently CAs in order to be familiar with as many of them as possible. Next year's coordinator should also be in charge of the recruiting that's done at the end of the previous year, as recruiting has such a large impact on the overall success of the program.

CA coordinator responsibilities

There are three main duties for the CA coordinator: recruiting, training and overseeing the program during the semester. We visit each of these component parts in turn, beginning with recruiting. In this guide, everything is written from the perspective of the lower level Math CA program (Math X through Math 21b). For the upper level Math CA program, the basic approach is the same, but there are a number of differences to be aware of.


Without question recruiting can make or break the semester, and it takes far and away the most time. Ending up with the right people for the job is crucial to maintaining a successful CA program. The recruiting season usually takes place during the last five or six weeks of the spring semester, after Spring Break. It's good to start the interviewing at least 3 or 4 weeks before reading period starts, so that you'll have time look for more students to recruit if you need to, and so that you have enough time to make your selections, and let people know about the outcomes before they start leaving campus for the summer. To make sure that you have the forty or so CAs for the fall semester, you will need to recruit more like 55 to 60 students, as there will be scheduling conflicts, changes of heart at the last minute, and other reasons why not everyone you recruit will be able to become a CA. Although it can vary quite a lot, there are usually between 15 and 25 returning CAs from the previous year. To get 55 to 60 students that you would be willing to offer jobs to, you will thus need to find somewhere between 30 to 45 new candidates. Given an approximately 50% hiring rate (i.e. that you would not want to offer jobs to about half of the students you interview), this means interviewing anywhere from 60 to 90 candidates. It's much better to err on the high side. This gives you more selection, and keeps the job competitive. We'd like everyone in the program to feel that they worked to get there, and that we didn't offer them a job just because we couldn't find anyone else to do it! Typically for the recruiting season, we put up posters in many places around the Science Center, and around campus, announcing that interviewing is taking place. We usually place one large poster in the main hall of the Science Center, on the first floor, and then put smaller ones around campus. It's good to give some sort of deadline for signing up for the interviews, or too many people wait until the last minute, and it's impossible to interview them all at once. The posters, although you should try to add colors and pictures as much as possible to be more eye-catching) should direct students upstairs to the Math Department, to your office, where you leave out a job description, application forms, and a sign-up sheet for interviews. In order to go through 80 to 90 interviews in a several week period, we suggest breaking up the interview process into 2 to 3 hour chunks, split up among several people. We have typically signed students up for 20 minute interviews, with 5 minute breaks after every second interview, to catch up and record notes from the interview. As one addendum to this recruiting advice, be aware that the CA program also includes a provision to hire "Head CAs" for the larger multi-section courses. There aren't as yet any hard and fast guidelines to whom should be offered these jobs, but the criteria for the Head CA positions should be a little different. What we really want for these 3 or 4 positions, is to find students who are extremely organized, punctual, and web-savvy. As you're interviewing people, if you meet someone who might not have the best teaching background or ability, consider thinking about how they would do as a Head CA. Also, consider offering Head CA positions for students who might not have quite enough time to do a regular CA position during the semester, but who otherwise would make good CA candidates (the time requirement for the Head CA position is considerably less than that of a normal CA position because of the lack of grading responsibility). For more detailed guidelines to the interviewing process, see the CA Interviewing Guide below, and interview scoring sheet. At the same time you're interviewing students, you should send out notes to the current TFs to find out how they feel their current CAs have done during the semester. If possible you should also send out emails to each of the applicants' math teachers to get their read on how they would be as CAs. With all of this information, the most important piece of which is the interview itself, you're ready to figure out whom to offer jobs to. At this stage, all you can tell students is how likely they are to have positions in the fall. We usually split it up into three groups - those who will almost surely have positions (about 30 or so), those who might get a job (the rest of the applicants), and those who will definitely not be offered jobs.

Semester Start

The main training time for the fall semester occurs right before classes begin. As part of the offer letter you send out, you should include the time for the before-class training session. Currently this consists of a roughly four hour session, although you can break it up over two days if you wish. We split the group into returning CAs and new hires. The new hires stay the whole time, and the returning CAs join in about halfway into the session. There is ample documentation for running the training session. We usually begin with a couple of videos from the Bok Center - A Private Universe, and Learning Together to start the process of thinking about what it takes to teach effectively. If possible, the day should be split between providing information and group discussions or exercises, in order to keep everyone's attention for the whole time. At the end of the training session the two critical tasks are to have all the new recruits sign up for microteaching sessions, and to have everyone take a Course and Time Preferences sign-up sheet. The Course/Time Preferences sheets are what you'll need to use to coordinate everyone's schedules and course choice - they're absolutely critical. Make sure you emphasize when the drop deadline is for those sheets. Usually we have them turn them in at the same time the sectioning program is closed. Next you'll begin the fabulous task of matching up teachers and CAs with courses and times. In fact, before you even get started, at the training session, you'll need to assign CAs for the classes that don't section, for instance Math 19 and Math 20, as their classes start right at the beginning of the semester. Also you'll want to do some special recruiting for Math X if you haven't already set people up for that. There is a whole art to matching skills and personalities that simply has to be experienced to appreciate. Needless to say, one shouldn't simply match randomly. Think hard about how well the pair of people you're matching will work together. Also consider how well a group of CAs for a particular class will work as a team. Try to pick Head CAs for each course who will complement the coursehead's strengths. Think also about possible back-up strategies - are there some extra people you can have come in in a pinch? Start with conservative numbers for CAs - it's far better to add a CA then to withdraw a job offer, so if you anticipate that there will be some larger classes, start with fewer CAs then add more if necessary. Make sure you have a way to get in touch with CAs over the weekend to check on assignments, and require everyone to get back in touch with you to acknowledge that they've gotten their assignment and that they're ready to go. During the first week of classes, you'll want to set up a meeting time for all the CA s to go over professional conduct (including sexual harassment issues). If you can get an assistant dean to help out with this so much the better - we want to impress upon the group of CAs the importance of getting help when they need it in regards to any potentially difficult situations (grading roommates or boyfriend/girlfriends, etc.). At the end of this short meeting, you should have the CAs break into smaller groups to meet with their individual courseheads, who should introduce the semester, and talk about the course and about grading policies. As the CA coordinator, you should make sure that the CAs have a good experience interacting with the rest of the teaching staff, so you should ask the courseheads to make sure and meet several times each semester with their CAs just to check in and see how everything is going.

During the Semester

During the semester, you should make sure that you keep in close contact with all of the courseheads to keep up with any CA situations that occur. Check with the T.F.s on a frequent basis to make sure that you know what's going on and how people are doing. If an issue does arise, be sure and hear out all sides of the issue before jumping into the fray. Try to have CAs and TFs work out problems as best they can before intervening. In general, if you've recruited well, you can expect fewer problems, but there will always be times during the semester when several CAs can't keep up with the grading schedule, or miss class, so be prepared to figure out solutions. Also, try to remain on the CAs side - they don't have anyone else to turn to necessarily within the department, so to a certain extent, you're their confidant. It's far better to have CAs trust that they can talk to you confidentially, then to end up in a situation where you're left in the dark as to what's going on. There are several tasks during the semester that you need to take care of. One of which is to request midsemester feedback about the CAs from their TFs and courseheads. The other is to get feedback from the CAs themselves at midsemester dinners. For the dinners, you should simply set up a time during the week to go to a house for dinner with all the CAs from one of the courses. This is a good time to get the CAs to build some camaraderie, and for you to continue to build your relationship with individual CAs. Consider asking them to write down helpful tips for future CAs as a simple exercise during the meal. Also, you might consider having a fall and/or spring field-day with all of the CAs (and perhaps TFs). There aren't too many occasions for all of the CAs to come together and feel appreciated by the department, so if you can provide them with something special during the semester, then do it. At the end of the semester, your main tasks will be to make sure that CAs are all sending their grades to the courseheads on time, and that you collect end of semester feedback from TFs about their CAs to help with the hiring process for the next semester .

  • "Best job I've ever had!" - B.T.

  • Got Math? Want to help teach calculus?

  • Want to get paid to do it?

  • "Loved every minute of it!" - S.L.

Math Course Assistants Job Description:

All of Harvard's calculus classes are taught in small sections of around 25 students. Each section meets 2 or 3 times per week, taught by an instructor called a Teaching Fellow (TF), who is either a faculty or graduate student in the math department. Each Course Assistant (CA) is associated with one calculus section and is responsible for working with the TF to ensure the success of the section. CAs attend each of their section's classes, in order to see what is being taught, and note any topics that the students are having difficulty with. CAs do all of the homework grading for their section during the semester - students typically turn in a problem set each class period, and CAs are normally expected to grade the work and get it back to the students at the next class meeting. CAs get to run a weekly problem session (1.5 hours long) to go over homework problems and other topics which might have come up during the week. In addition we ask that CAs help out with the Math Question Center by stopping by for one evening per week. The Question Center is a general math help center that meets from 8 to 10pm each evening in Loker cafeteria. The Question Center responsibility replaces CAs having to offer any extra office hours at any other time during the week. CAs are also expected to be available to help their Course Head during the semester by doing several other small tasks, such as occasionally writing up homework solution sets, or helping with review sessions before exams. The CA position is a great job for those people who want to get involved in teaching math, and in interacting with students to help them learn. It's also a real responsibility - this is a professional job, and we expect that CAs will meet all of the requirements during the semester and not let down either their TFs or the students in their sections. Students in calculus classes really count on the CAs to help them out - quite a number of students find it easier to relate to the CAs in their courses, as they're closer in age.

  • Pay Scale for CA's: The job usually takes between 15 to 20 hours per week for the semester. The compensation is quite good - the salary averages around $2,350 for the semester per CA (at 1999-2000 Junior pay rates), depending on how many students are in your section. The pay scale consists of a base salary of about $1370 plus about $40 times the number of students in your section. The reason for the fluctuating scale is that a significant proportion of a CA's time consists of grading homework, and the amount of time required depends directly on the number of students turning in homework. Thus if there are more students in your section, then you'll be paid more for the increased grading that's required. If you're a CA for two semesters, then starting with the third semester you'll earn a Senior CA rate, which pays several hundred dollars more per semester.

  • Prerequisites for CA's For a position in Math X, 1a or 1b, you'll need to have satisfactorily completed classes through at least Math 21a and b, or taken a higher numbered class such as Math 25, or 55. For a position in either Math 21 course, you should have satisfactorily completed at least one semester of math or applied math beyond Math 21 (for instance any 100 level Math course, or Math 23, 25 or 55).

  • How to Apply for the CA job Fill out an application form available in an envelope on the door of the CA coordinator. Make sure you bring the application form with you to your interview. Sign up on the interview schedule posted on the door of the CA coordinator. Make sure you check the location of the interview, and show up promptly at the time you signed up for. Note: At the interview you may be asked to explain a problem dealing with the basic notions of integration or differentiation. You should also have thought about how you would run your weekly problem session. Candidates will be notified by e-mail of their chances of getting a CA job. We'll send out the notification by mid to late May, but final decisions cannot be made until after sectioning is done for the calculus classes in the fall (as the number of jobs depends on how many sections are signed up for). Those people who are told that it is likely or possible that they have a job must attend a half-day training session that will take place several days before the academic year begins in the fall. If you have any questions about the job, please contact the CA coordinator. We look forward to the possibility of working with you next fall!

  • Head CA The primary goal of the Head CA is to assist the course head to make their math course run as smoothly as possible. Specific tasks will vary course by course, and should be worked out with course head at the beginning of the term. Head CAs are selected based on their proven professional maturity, their ability to oversee and aid in course-related tasks, as well as their ability to teach and communicate math effectively. Although it is expected that all math CAs are responsible and committed, the Head CA position entails even more professional responsibility and decision making expertise. The Head CA position is typically only offered to someone who has already demonstrated success in a regular math CA position.

  • General Head CA Job Description: The following is a list of responsibilities that should be assumed by all Head CAs. If there are specific tasks that the Head CA does not know how to do (for instance, working with the course website), then it is up to the Head CA to work with the course head to figure out how they will become proficient in that task, or to coordinate some other way to take care of the task.

  • Head CA Responsibilities:

    • Section Attendance Attend sections regularly to keep up with course, understand student issues When possible, attend different sections, report on student interaction, general issues to course head (up to course head to decide)

    • Homework Solutions Coordinate and collect homework solutions from other CAs or write up solutions Provide early copies of solutions for other CAs to help them with their grading Post solutions on website at the appropriate time (to be coordinated with the course head)

    • Website Management Update website on a regular basis (to be coordinated with course head) Post notes on upcoming exams, reviews, etc. Update section times Post homework solutions at appropriate times Oversee discussion website on a regular basis (if course head has set up)

    • Math Question Center Attend regularly (at least once per week, to be coordinated with MQC director. Oversee other CAs: make sure that they are showing up at their appointed times, monitor student attendance, pass out nametags, etc.

    • Exam Review Organize CAs to provide exam reviews Collect, post old exams and extra review problems (with oversight of course head).

    • Administrative Duties Provide help with administrative tasks determined by the course head to help the course run smoothly

    • Report to Course Head Meet at least once per week to report status of all of the above (set a time to do this with course head) Report on any issues that would be helpful for the course head to know to run the course effectively. This would include such matters as issues about grading, about section attendance, etc. It is up to the Head CA to take the initiative in keeping up with and reporting on such matters.

  • Head CA Compensation In terms of compensation, the Head CA position is the same as a regular CA position except that it is without a weekly section. As a result of the fact that there is no grading involved, or preparation for a weekly section, the compensation is equivalent to the base pay amount for a CA. This is currently set at 0.14 FTE (in 1999/2000 this is equal to $1540 for senior rates, and $1372 for junior rates for the semester). The Head CA position should be understood to require an average of 8 to 10 hours of work per week, with some variation during the semester. If the tasks are proving to be more time consuming than this, then please discuss this with the course head, and with the Math CA coordinator. If there are any questions about the Head CA position, then they should be directed to the Math CA coordinator.

Lower level CA Application

The application asks for

  • Name

  • Class

  • School Address

  • Phone

  • E-mail Address

  • House for next year?

  • Permanent Address.

  • Phone

  • Field of Concentration

Please list all of the (college-level) Math and Science courses you've taken, with instructors' names and grades: Please list any previous teaching or tutoring experience, as well as any other extracurricular activities that you think are relevant. Feel free to continue on the back of this page if you need more room. Important! University rules state that in order to hire an undergraduate course assistant, employers need to, with the student's written permission, confirm with their Senior Tutor that the proposed candidate has attained sophomore standing and is at least in the third term of residency upon accepting the job. Is not on probation. Has an academic record equivalent to Rank List Group II or better in the two previous semesters. Therefore as part of this job application, please sign this form giving the required written permission:

CA Interviewing Guideline:

There are a wide variety of different ways to conduct successful interviews. The bottom line is that we're looking for students who would make good CAs, and you should run your interview in whatever way you want as long as you are able to ascertain whether or not the candidate would likely be a successful CA. Our goal is to find people who are responsible, professional, mature, mathematically savvy, communicative, energetic, etc., and who are capable of communicating mathematics well. You should ask all the questions you need to be able to make judgment calls on all of these basic attributes. At the end of this document is a suggested interview guideline. Don't feel that you have to follow this exactly - you should vary things to suit your particular style. The interviews are scheduled every 20 minutes, with a 5 minute catch up time at the end of each hour. If possible, you should take enough notes during each interview so that at the end of a day's round of interviews you are then able to write up a thorough interview summary for each candidate. It is extremely easy to get candidates mixed up after you've spoken to 8 or 9 people, so be careful!

Role Playing during CA Interviews

One interview technique I've used to distinguish good potential CAs from dubious ones is by including a mock teaching role playing session, as part of the interview. I have been in numerous interviews where I thought that the interviewee was giving me great answers during the regular interview questions, had a solid background, and looked promising. Then, when I got to the teaching role playing, I found out that the candidate couldn't explain math to save themselves. Other times, I've discovered that someone tended to babble incoherently, or said things that were just plain wrong. This part of the interview really tends to nail down whether or not the candidate would be good as a CA. If they botch the role play the first time round, see whether they're able to patch it up if you give them some guidance, you don't want to discount someone simply because they're too nervous at first (but make a note of this in the interview summary). In my interviews, I've asked candidates to describe how you can set up a volume of rotation integral for the sine curve around the x-axis, using the idea of a Riemann Sum. Sometimes I've had to remind them of a little bit of the math to get them going, but usually candidates can do the whole thing pretty easily. I've pretended that I'm a student who is lost on the whole concept, and that I need them to explain it to me from scratch. You might want to develop your own role play situation. Try to set it up so that the first thing they need to do is ask you, as the confused student, for help figuring out where you're confused. Also, be sure to ask several questions during the role play, to force the candidate to respond to your confusion. Things to test with the role play: Does the candidate try to figure out where you're confused, to set up the explanation at the correct level? Can the candidate communicate clearly? Can the candidate use a chalk board effectively? Does the candidate ask questions, or simply lecture? Does the candidate answer your questions well? Does the candidate know the basic math involved? It probably makes sense to choose one role play question and stick with it. Even if it doesn't turn out to be the best possible topic, it's a lot easier to compare candidates if they're all being asked to do the same thing. Make sure that you take time to explain the set-up carefully for them, so that they completely understand the context, that you're a pretend student, and that they need to figure out why you're confused, and help you out. As I already wrote, but will mention again, be sure to take notes during the interview, so that you can keep track of how each candidate is doing!

Suggested Interview Guide:

Scan through the application form as the applicant comes in. Note in particular the candidate's teaching background, and math level. Ask how they learned of the job What do they know about being a CA Fill in a few details about the position if necessary Ask why they want the job What about them makes them a good candidate (i.e. why should we hire you?) Note basic communication skills - eye-contact, coherence, enthusiasm, etc. Ask them to talk about any teaching or tutoring experiences they might have had (If they haven't taught or tutored math, ask about other tutoring experience) What did they learn from the experiences? What were the best and worst experiences they had teaching? Do they consider themselves to be good teachers - if so, why Ask them how they would run a weekly problem session What would they do to prepare How would they structure the time with students What type of problems do they think they might run into How would they deal with the issue of students with widely varying backgrounds Ask them to role play a situation from a weekly problem session Set up the situation carefully Explain that you're a confused student with a simple math problem Provide enough detail about the math question so that they can get started While they're doing their explanations, ask several off-the-wall questions to see how they react Take careful notes during the role play describing their performance Thank them for their time Explain that the next interaction will be our sending them an e-mail with the likelihood of their getting a job. Apologize that there aren't enough jobs for everyone We won't know exactly how many positions there are until the fall semester starts If we're unable to provide a job, we'll be sure to keep their name on file, etc. but that they should reapply if it doesn't work out the first time - we give preference to experienced CAs, but there is a fair amount of turnover as students graduate. Ask if they have any other questions about the job Tell them to feel free to e-mail you with more questions in the future.

CA Interview Record Sheet

  • Date:

  • Candidate:

  • Interviewer:

  • How did the candidate find out about the CA position? (current CA, in class, posters)

Interview Comments and scoring

  • Fit with CA position

  • General communication ability

  • Energy level

  • Ability to teach math

  • Mathematical knowledge

  • Overall Interview

CA feedback:

Now that the semester is almost over, we would like to get some feedback on your course assistant(s). If you could please take a few moments to answer the following questions and send your responses back to me by the end of next week (by Friday, Jan. 28th), then we will use your information to help make CA hiring decisions this spring. Please rate your CA's level of responsibility on a 1 - 5 scale:

  • 1 = Extremely irresponsible, missed many classes, homework returned late

  • 2 = Pretty poor

  • 3 = Just okay

  • 4 = Very responsible

  • 5 = Excellent

Please rate any feedback you might have gotten about your CA from your students: I didn't hear anything at all about my CA this semester either positive or negative

  • Students complained all the time about the CA

  • I heard a small number of complaints

  • Neutral feedback - some positive, some negative, but nothing major

  • I heard very positive comments

  • Extremely positive comments all semester - students were thrilled!

  • Terrible, please do not rehire this person!

  • Did a minimally passable job, rehire only if necessary

  • Did an okay job

  • Very good

  • Excellent, was a pleasure to work with

Please provide any extra comments to help us on our rehiring decisions: Please just duplicate these questions for each CA, if you worked with more than one CA this term.

Probably hire letter example

Dear CA Applicant, We are happy to let you know that it is very likely you will be able to be a Course Assistant in calculus next fall. Absolute and final decisions cannot be made until after sectioning in the fall when we know enrollments and your schedule, but we are expecting to hire you if you accept the job. There will be a Training and Orientation Session for Course Assistants and potential Course Assistants at the beginning of the semester that you need to attend if you want to work in the fall. This session will be on: Friday, September 15th, from 1 to 5 pm in Science Center A. (This is the Friday before the first day of classes in the fall) At the training session we will prepare for the upcoming term and discuss ways to make sure that problem sessions (and Course Assistants) are a valuable part of the course. Please give this some thought in advance. This is likely to be the only notice of the meeting you will receive, so please mark this on your calendar. It is very important that everyone who would like to be a Course Assistant shows up at this meeting. It is necessary to attend it in order to keep your application active. On the other hand, attending does not absolutely commit you to taking a job - we will give you a deadline (after the Sept. 15th meeting) for making that commitment. Be sure to bring along your tentative class schedule to the meeting. If you are absolutely unable to attend, contact us as soon as you can. Congratulations on such a strong application. We hope you accept the job and look forward to working with you!

Possible hire letter

Dear Applicant, This is to let you know that it is possible that you could get a Course Assistant job for next year. This means that we do not have a job earmarked for you, but it is very possible that a job may open up. Often a large percentage (50% or more) of the people receiving this 'possible' letter end up actually with jobs. There will be a Training and Orientation Session for Course Assistants and potential Course Assistants at the beginning of the semester that you need to attend if you want to work in the fall. This session will be on: Friday, September xxx from xx to xx in Science Center A. (This is the Friday before the first day of classes.) At the training session we will prepare for the upcoming term and discuss ways to make sure that problem sessions (and Course Assistants) are a valuable part of the course. Please give this some thought in advance. This is likely to be the only notice of the meeting you will receive, so please mark this on your calendar. It is very important that everyone who would like to be a Course Assistant shows up at this meeting. It is necessary to attend it in order to keep your application active. On the other hand, attending does not absolutely commit you to taking a job - we will give you a deadline (after the Sept. 15th meeting) for making that commitment. Be sure to bring along your tentative class schedule to the meeting. If you are absolutely unable to attend, contact us as soon as you can. Congratulations for doing well on your application. We look forward to the possibility of working with you in the fall. Sincerely, CA Coordinator

No hire letter

Dear Applicant, We are sorry to tell you that we do not expect to be able to offer you a Course Assistant position in the Mathematics Department next fall. We hope you understand that with many strong applicants, we simply could not fit everyone in. Thank you for your interest and for the time you gave to the application process. If you are interested in tutoring in mathematics, please contact the Bureau of Study Council at 5 Linden Street, Cambridge (495-2581) in the fall. If you are interested in volunteer work in math in the local high schools or middle schools, you can contact Cambridge School Volunteers at 349-6794. In the meantime, we hope you have a good summer! Sincerely, CA Coordinator

CA re-hire letter

Dear CA, Thanks so much for the work you've done as a Course Assistant this semester! We know that you have put a great deal of energy into your work, and this is appreciated! We'd be happy to rehire you if you want to work again as a CA next fall. There will be a Training and Orientation Session for Course Assistants and potential Course Assistants at the beginning of the semester. The meeting you need to attend will be on Friday, September 15th, from 3:30 to 5 pm in Science Center A. (This is the Friday before the first day of classes in the fall) At the training session we will prepare for the upcoming term and discuss ways to make sure that problem sessions (and Course Assistants) are a valuable part of the course. As an experienced Course Assistant, you will play a big role. Please give this some thought in advance. This is likely to be the only notice of the meeting you will receive, so PLEASE MARK THIS ON YOUR CALENDAR!! It is very important that everyone who would like to be a Course Assistant shows up at this meeting. Be sure to bring along your tentative class schedule. If you are unable to attend, please contact us as soon as possible. Finally, we are looking for new Head CAs for Math 1a, 1b and 21a for next fall. The requirements for the job are to be in charge of updating the course website, providing solution sets for homework, as well as helping the course head insure smooth running of the course. Head CAs are not assigned any grading, so the job requires about half as much time as being a regular CA. The pay consists of the base salary for a regular CA, and so is also about half as much, but for those people who would like a less demanding job, but still want to help out with the calculus program, this can be a good job to have. Please get in touch with me about this possibility if you are interested. Thanks again for the work you have done. Have a great summer! Sincerely, CA Coordinator

No re-hire letter for old CA's

Dear CA, We are sorry to tell you that we do not expect to be able to offer you a Course Assistant position in the Mathematics Department next fall. Unfortunately we received some negative feedback from either students and/or Teaching Fellows about your performance so that it doesn't make sense for you to continue working next fall. We would be happy to sit down and talk to you about the feedback if you would like. The CA job is quite competitive, and we felt that it would be better to offer a slot to some other person who hasn't yet had the opportunity to teach instead. In the meantime if you are interested in tutoring in mathematics, please contact the Bureau of Study Council at 5 Linden Street, Cambridge (495-2581) in the fall. If you are interested in volunteer work in math in the local high schools or middle schools, you can contact Cambridge School Volunteers at 349-6794. Sincerely, CA Coordinator

Example CA Introductory Meeting

  • Welcome and introduction

  • What is expected of CAs?

  • Interaction with TFs

  • Textbooks, where to get them.

  • Signing up for rooms

  • Video and discussion

  • What does it mean to teach?

  • Microteaching explanation and sign-up

  • People to get to know

  • Weekly grade reports

  • Final homework grade report

  • Getting paid

  • Whom to contact with questions/concerns.

  • Signing up for classes

  • Filling out time and level preference sheet.

  • Reminder: when changing mind, let us know.

  • Wat's the goal of grading.

  • Returning homework promptly

  • Posting solutions

  • Consistency and fairness

  • Calculus Help Center promo

  • Professional conduct for CAs

  • Calendar: what is next

  • CAs meet with respective Course Heads

Example Time/Course Preference sheet

  • Name:

  • E-mail:

  • Phone:

  • Campus Address:

As best as you can tell at this point what are the times that you could attend a math section? Please assign a ranking for the following - put a 1 next to your first preference, 2 next to the next best, etc., and put an X next to any class time which completely conflicts with your schedule. You can have ties, so, for instance two 1's means both times would be equally excellent, and also use much higher numbers to indicate possibly could do, but would much rather not meet at that time

  • MWF 9am-10am

  • MWF 12pm-1pm

  • MWF 10am-11am

  • MWF 11am-12am

  • T/Th 10am-11:30am

  • T/Th 11:30am-1pm

Next, please do the same type of ranking for each of the possible math courses offered this spring - again rank with a 1 next to your favorite option, 2 next to the next best, etc.

  • Math X

  • Math 1a

  • Math 1b

  • Math 21a (Regular section)

  • Math 21a (Physics section)

  • Math 21a (Biochem section)

  • Math 20

  • Math 21b

What is your level of Web savviness? Please check off one of the following:

  • Able to get around Internet sites without getting lost.

  • Able to modify sites, i.e. scan in images, make minor changes

  • Know how to upload files

  • Totally savvy, can do really cool things with web sites.

Are you proficient in TeX, or some other math symbol word processing software?

  • No, I don't have experience with these and/or am not interested in this.

  • I've worked with some occasionally and would be willing to do more.

  • Yes, I am quite proficient, and would be willing to put my skill to use.

Are you proficient in Mathematica, Maple, Matlab, or some other computer algebra software?

  • No, I don't have experience with these and/or am not interested in this.

  • I've worked with some occasionally and would be willing to do more.

  • Yes, I am quite proficient, and would be willing to put my skill to use.

Would you be willing to work as a Head CA for your course, involving extra administrative and web site maintenance tasks? (this would require approximately 4 to 6 hours more hours per week than ordinary CAing, with additional compensation). Do you have other requests, or skills that you think we should know about?

Example: Sign-up sheet for Micro-teaching

Microteaching sessions are required for all new CAs. All meet in Science Center, room 116 - Make a note of the time you've signed up for! When you sign up for a slot, note the two problems listed, and prepare one of them for the microteaching session. Please try to limit each session to a maximum of 6 participants (only sign up as a seventh participant if you absolutely cannot make any of the other meeting times). Homework Grading Discussion:

  • Problem 1) Find the interval and radius of convergence for the following infinite series.

  • Problem 2) Let R be the region bounded by the graph of y = ln x and the lines y = 0, y = 1, and x = 0. Find the volume of the solid obtained by revolving R about the y-axis.

General Issues for Math Course Assistants

We will use the information you've given us on time and course preference to put together a tentative Course Assistant assignment. On Thursday afternoon, after all of the undergraduates have done their sectioning by computer for math classes, we will make the final assignment list. It is critical that any changes that you need to make to the information you hand in at the orientation meeting get passed on to us as soon as possible, and absolutely by Thursday afternoon, by 4pm. When you need to make a change, come in to room .... fill out a change of information form, and date it before you leave it in the "CA Scheduling" envelope. It is also critical to let us know if you change your mind about being a CA for this fall. We're counting on you all to keep us informed as we sort through the giant sectioning jigsaw puzzle! We will post the assignment list as soon as we can, probably by late Friday or on Saturday, and we'll let you know by e-mail as soon as this is done and what your assignments are. Some organisatorial issues:

  • Meeting with TF Arrange to meet with your TF before class, at least to get to know one another briefly, so that you can appear as a team at the first class. During the second class, collect information from the students in the class about what times will work for them and for you for the weekly problem session time. Be aware that it is absolutely impossible to please everyone, so make as reasonable a compromise as possible. Also let students know that they can attend another CA's session if they can't make yours. Make a weekly section Scheduling sheet.

  • Room You can get a room for your weekly problem session by either stopping up for a slot posted on the bulletin board outside of Susan Milano's office (room 308), or by scheduling one yourself down in the Science Center room schedule office. After you've chosen a time and place, let it posted on the course website.

  • Mailboxes: Mailboxes are outside of room 308. These mailboxes can be used for students to drop off homework ahead of the classtime if they can't make it to class. Check it periodically.

  • Books: Nancy Miller in the Birkhoff Math library on the third floor will sign you out a book for use during the semester. Nancy is usually there in the morning until noon. Do not ask for books in the main office. Thanks!

  • Getting Paid: Make sure that you stop by the math department office 325 during the first week of classes to fill out the necessary payroll forms. The pay schedule has not been set for the semester yet, but you will be paid three times during the semester, in three roughly equal parts.

  • Microteaching: All new CAs sign up and participate in a microteaching session before they can teach their own sections. Sign-up lists will be passed around at the orientation meeting. Make sure you note which session you signed up for, and note which problems you will need to prepare for your session. Microteaching is organized practice teaching. The goal is to give section leaders confidence, support and feedback by letting them try out among friends and colleagues a short slice of what they plan to do with their students. Microteaching is a quick, efficient, proven and fun way to help teachers get off to a strong start! When you prepare for your microteaching session, make sure to plan out not only how you will communicate the subject matter, but also give some thought as to how you are going to present yourself, manage the class, and involve the students. There are, of course, many different ways of teaching a given lesson very well. This is why participants find that in addition to learning from their own practice teaching, they can also pick up many helpful ideas from observing fellow microteachers.

  • Calculus Question Center: MQC

    Figure 8-1. Loker Commons

    The MQC is located in a corner of Loker and operated 5 days a week. It will be part of your responsibilities as a CA this semester to help out with the center by signing up for a weekly time slot. You should just think of this time as being the same as any "office hours" which you might have offered to your class. Feel free to bring homework you might be grading to the question center and work on it there if there aren't any students waiting. The MQC coordinator will be sending out more information about the center soon via e-mail, on how to sign up for a time slot.

  • Keeping in touch with your fellow CAs: It is important to consider yourself as a member of a whole team of CAs. Your course head should meet with you all several times each semester. In addition, however, you might also want to schedule some times to get together informally with your fellow course CAs for a meal to find out how you are all doing, and to trade tips and concerns which might come up as you teach. If you are feeling frustrated or anxious about your CAing, don't stay isolated - make sure you get in touch with other CAs, especially those who have CAed already. Often they will be able to help you work out any issues that might come up during the semester.

Schedule and Course Preference update sheet

Just fill out the schedule info that has changed If you leave a section blank, we'll use the info you've already submitted.

  • Date and time submitted:

  • Name:

  • Phone:

  • E-mail:

  • Campus Address:

1) As best as you can tell at this point what are the possible times at which you could attend a math section? Please assign a ranking for the following - put a 1 next to your first preference, 2 next to the next best, etc., and put an X next to any class time which conflicts with your schedule Feel free to have ties, so, for instance two 1's means both times would be equally excellent, and also use much higher numbers to indicate possibly could do, but would much rather not meet at that time (so a 99 means "bleah, yes I could wake up by 9:30am, but I really don't want to")

  • MWF 10am-11am

  • MWF 11am-12am

  • MWF 12pm-1pm

  • T/Th 10am-11:30am

  • T/Th 11:30am-1pm

2) Next, please do the same type of ranking for each of the possible math courses offered this fall - again rank with a 1 next to your favorite option, 2 next to the next best, etc.

  • Math X

  • Math 1a

  • Math 1b

  • Math 21a (Regular section)

  • Math 21a (Physics section)

  • Math 21a (Biochem section)

  • Math 19 (Bio-MWF 1pm)

  • Math 20 (Econ-MWF 9am)

  • Math 21b

3) What is your level of Web savviness? Please check off one of the following Complete neophyte, have walked into spider webs before Able to get around Internet sites without getting lost Able to modify sites, i.e. scan in images, make minor changes Web design savvy, have created web pages before Web god, unlike Al Gore, I really did invent the Internet 4) Do you have other requests, or skills that you think we should know about?

Professional Conduct Meeting

  • Scenario One: It's late one night and the usual crowd is all hanging around shooting the breeze when one of you tells the most amazing story - it turns out it's just a joke, but it's hilarious, definitely top-notch material. Of course it's a bit racy, but not exactly Penthouse level. The next week, your problem session's going pretty well, but you feel that it's a somewhat dull session. You're likely to finish early, so while everyone's working on a few homework problems, you decide to spice things up a bit by telling the joke. Almost everyone in class laughs at it, and you're pleased that you've livened things up. Later that night you receive an e-mail from one of your students, Pat, telling you that they were extremely offended by the joke, and that they feel uncomfortable being in your section anymore. What do you do? What if you had told the joke outside of the classroom? What if you had told the joke at the beginning of the semester, and only found out at the end of the semester that Pat had been so offended?

  • Scenario Two: Fall Heroes section was dull, dull, dull. Perhaps the only bright spot was seeing Sasha, a halogen-lamp in a room full of night lights. Sometime during reading period you see Sasha in the dining hall, over Hoppin John. Apparently neither of you like the stuff very much: confirmation that you have something in common. You are therefore overjoyed when Sasha suggests you both go to the Border Cafe sometime. It doesn't take place until intersession, but the evening goes well. When spring semester begins you see Sasha in the back of the math class you're CAing, taking notes. Ulp. What do you do? What if you were already going out? What if the two of you had already broken up at the beginning of the semester?

  • Scenario Three: You're completely annoyed at Kim, who has been a pain all semester. The two of you are CAs for Math 12ab, a new course offering combining all four semesters of 1a to 21b in a one semester class. It's happened again, the coursehead asked for volunteers, Kim refused to help, and once again you're having to do all the work yourself. Every time changes are made, Kim causes problems, forcing everyone else to be accomodating. Kim constantly complains, refuses to cooperate with either you or with any of the other CAs. You're wondering why the coursehead puts up with it. At one point, the two of you are walking home after a late night meeting with all the CAs, and Kim turns to you and says "Why don't you like me?" Thinking that this is asking for an honest opinion, you respond, "Because you're a real @#$@, and you're a pain in the ass to work with." Days later you begin to hear rumors that Kim is afraid to walk home at night because of your comments. The rumors spread about what you did, and pretty soon you're asked to come in to meet with the Dean. What do you say? Is there anything you could you have done earlier?

Chapter 9. Evaluation

Students have the possibility to voice their oppinion on the course during midterm evaluations as well as on course evaluations run at the end of the semester. Of course, this is not the only way to see whether things go ok, but these two checkpoints are the most important ones. Midterm evalutions are done internally, while final evaluations are arranged by University hall. Since courses have different needs, it can make sense, to include course specific questions in the midterm evaluations.

Online Evaluation Form

  • The Bok center has an online evaluation form:

  • Also the toolkit contains early Evaluations: "The Early Evaluations feature enables instructors to select forms for students in their courses or lectures, sections or labs, to fill out during the term. Links to these forms are displayed in the "Early Evaluations" area of the course Web site. Students fill out the selected form or forms, entering the email address of the course head or instructor to whom the form data should be sent. Instructors receive the form data as anonymous feedback that can be used midway through the term to help improve aspects of the course. These forms have been prepared and presented by the Derek Bok Center for Teaching and Learning, and the Early Evaluations tool links to Bok Center guidance on using the on-line evaluation forms.

  • There are rumours that the CUE evaluations will be done online too.

Some issues to consider when doing online evaluation forms:

  • For the teacher: Who will see the evaluations?

  • For the student: Are the evalutions anonymous?

  • Who assures that the submitter is indeed the student claimed?

  • Who assures that only students submit evaluations who also come to class?

Midterm Evaluation Form Example

Mathematics Department Midterm Course Questionnaire While it is still early in the term, we would like to get your feedback on how your math class is going. In particular, we would like your constructive input while there is still the chance to act on the suggestions made. Please make your comments specific. We appreciate your cooperation!

  • Section Leader's Name

  • Course Name

  • Semester

  • Year

  • Are the classes clear and well prepared?

  • Does your teacher answer questions well?

  • Does your teacher encourage participation?

  • What do you like most/least about the teaching?

  • What changes do you think would make the class more effective?

  • Comments on the exam?

  • Comments on the text?

  • Have the homework assignments seemed appropriate?

  • Comments on the homework?

  • How often do you attend a Course Assistant's problem sessions?

  • Whose session do you go to?

  • Has the course assistant been good about getting graded homework back to you?

  • How useful are the problem sessions?

  • What do you like most/least about the problem sessions?

  • What is the basic format of the problem session?

  • Would you like to see that format changed? If so, how?

  • What have you done least well so far?

  • Can you suggest one or two changes in your method of study that would improve your learning of mathematics?

  • Anything else that you would like us to know?

CUE Guide

  • The CUE guide is printed and can be viewed online as well. It is possible, that CUE forms will be filled out online in the future.

  • Courseheads will see the students responses after the semester. They should share the main information as well as section specific with their section leader.

Chapter 10. Calendar

Preceptor Annual Calendar of Events

  • August - Preparation for the beginning of the term - Placement Exam review - Syllabus prepared - Midterm Exam dates set and rooms requested. Request sectioning data from Leni.

  • September - Changes to teaching lineup need to be handled (there are always last minute changes) - Coordinate TFs schedules/preferences - Schedule Rooms - Coordinate computer sectioning - Advising - BP and graduate student teacher training/orientation sessions - Bok Center orientation (schedule should be made available to grad students and CAs). Previewing first class lectures for new teachers (and any others who could use it) - CA hiring/administration: interviews, meetings, training sessions, problem session rooms - Introductory meetings are held prior to the first class - Classes begin - Resectioning begins.

  • October - Resectioning continues - Apprentice Program begins - First midterm exam/ grading/ midterm reports to the registrar - Midterm evaluations - CA payroll issues (used to be in November) - CA dinners.

  • November - Apprentice Program underway - Midterm evaluations reviewed - CA payroll issues - Catch up/miscelaneous - Texts ordered for Spring semester - Second Midterm Exam/ grading etc. - Recommendations for Grad applications due.

  • December - Classes end mid December - Start planning for Spring semester: midterm dates need to be set + rooms requested rooms for courses 1st day of spring calculus classes/ sectioning dates need to be determined information for Registrar's poster due.

  • January - Apprentice Reports need to be turned in - CA Reports - TFs Schedules and teaching/time preferences coordinated - Sectioning initiated - Review sessions and final exam for fall term - Final Grades - copy of two midterms and final to Susan - Backing up of websites - CA interviews/ meetings etc... - Introductory Meetings - Sectioning

  • February - see September - Classes begin - Sectioning/Resectioning takes place - CA training and micro teaching - Apprentice Program begins the end of February

  • March - Apprentice Program - First midterm exam/ grading - Midterm Course Evaluations - CA pay issues - CA dinners

  • April - CA Hiring for next year - Grads teaching for next year coordinated/ tentative teaching lineup put together - Course Catalogue prepared including: substantive course descriptions schedule of courses/ sections introductory meetings set up for the following year - Prepare room requests for next years courses - Second midterm exam/ grading

  • May - Hiring process continues (CA and TF) - Scheduling of teaching lineup continues - Review and final exams given/ grading - Midterms and final turned to Susan - Placement Exam review for next fall semester - Backing up of websites -

  • June - Prepairing for Summer school. Meeting if new preceptors come in. - Planning.

  • July-August - Summer school.

Chapter 11. Placement test

The placement test is still done proctored on paper. For many years the same test was used. It has been revised a bit in the years 2001-2002, especially rewritten in LaTeX.

Online Placement Test

An online placement test was written in the spring and summer 2003 by Paul Bamberg and a few students. It was tested in the Summer and Fall of 2003. Like the written test, the online placement test is also given in a proctored environment. The test was running on a local Math department computer: (You will have to install some fonts to run it

Figure 11-1. Online Placement Test

Questions examples

Figure 11-2. Questions Example

1) How many lines pass through the point (1,5) and are perpendicular to both the lines x+y=6 and x-y=-4?

  • a) 2

  • b) 1

  • c) 3

  • d) infinitely many

  • e) 0

2) What are the center C and radius r of the circle with equation x x + y y -2 x+2 y=2?

  • a) C=(-1,1); r=4.

  • b) C=(1,-1); r=2.

  • c) C=(1,-1); r=4.

  • d) C=(-1,1); r=2.

  • e) C=(1,-1); r=2.

3) If a particle moves according to the equations x=2 cos(2 t),y=sin(2 t) for 0 < t < 2, its path is

  • a) a line segment

  • b) a circular arc

  • c) an elliptic arc

  • d) a parabolic arc

  • e) a spiral

Handout with written Placement test MOPE

More Placement Information from the Mathematics Department. Welcome to Harvard! As a supplement to the pencil-and-paper placement exam, the Mathematics Department is making available a system of online placement exams. These exams are sponsored by a grant from the Provost's Fund for Innovation in Information Technology. The Mathematical Online Placement Exam offers students:

  • Individual course tests to decide your readiness. We have separate tests to place into 1a (first semester of calculus), 1b (second semester of calculus), or 21a (multivariable calculus). We also have a test to help if you are trying to decide between Math 21a and the more theoretical first-year courses Math 23, 25, and 55.

  • Mastery tests to determine satisfaction of prerequisites. If you are interested in taking a course with 1b, 21a, or 21b (linear algebra) as a requirement, you can take a test to verify your background knowledge.

  • Feedback after each test to show what specific skills you need extra practice in before being fully equipped for a course, and

  • The opportunity to take the test more than once to improve your score after a bit of review Each online exam consists of 3040 multiple-choice questions and can be taken at any time from any networked computer. We invite all first-year students to take the online placement exam, as it offers extra, more detailed advice on choosing your first math course. The exam is strongly encouraged for students who: - Have scored a 4 or 5 on the Calculus BC Advanced Placement Exam, or - Have completed coursework on the level of 21a before enrolling at Harvard, The online exam covers topics not in the paper exam but which are necessary for several higher-level math courses.

Both the pencil-and-paper and online exams are informational and do not by themselves grant or prevent enrollment. Please talk to any of the Math Department's advisors or your freshman proctor if you have further questions about choosing a course. For more information or to take the online placement exam, visit: We look forward to your enrollment in any of our courses. (Tear this page off before you turn in the test.)

Chapter 12. Summer and Extension school

Some preceptors teach in the extension school and/or the summer school. The audience in those courses differs from the studentbody. While in the summerschool, one can see many high school students who want to get a head start in calculus, the extension school students include adults who brush up their knowledge in the evening. The summer school and extension school have informative websites and also publish a booklet every year.

Summer school peculiarities

  • CA's are hired by Sergan Divac. About a mongth before classes start, you will hear the name of your CA.

  • Midterms take place during regular class times, the final is administered by proctors.

Extension school peculiarities

  • CA's (if required) are hired by the instructor

Chapter 13. Computer stuff

In this chapter we list some initial information for computer needs. Most of the information can be found on the Math department website.

Getting started

Our system adminstrator is Arthur Gaer. Most preceptors are computer savy too and can help out too. Information technology changes extremely fast. Here are three things to get started with:

  • Get a computer account

  • Apply online for a FAS account too. This is handy if you want to use the kiosk computers or lab computers in the science center or if you want to connect to Harvard from home using a modem.

  • Get your computers connected in your office.

  • In case you have a laptop, it is convenient to have a wireless connection. This is especially useful if you want to use it for teaching.

  • Learn how to hook up your computer in the classroom.

  • Locate the printers in the 3rd,4th and 5th floor.

  • Walk through the computer labs in the science center to see what students can use. Knowing this can be useful if you plan to use new software.

  • Learn about the resources which are available.

  • Familiarize yourself with the ICG toolkit for course websites. Evenso you might not want to use it for your class, it has useful features like facebooks. You can send email to all students. It is also good to make questions and answers.

  • Make sure your machine is always up to date with respect to operating system patches.

  • If you have a laptop, it is advisable to lock it when unattended.

Course webpages

What are the possibilities to setup a course website? When setting up a course website, you have the following options:

  • Use the toolkit on FAS website: go to

  • Use the toolkit with direct editing on FAS website: ssh, ftp

  • Edit directly the FAS website: example: ssh

  • Redirect the website to a private website on an other webpage.

The Toolkit

The documentation of the toolkit is quite good:




Figure 13-1. Toolkit

Without Toolkit

To edit the FAS website directly: telnet to go to the directory public_html and edit the files. An other possibility to keep a local version of the website, which is copied regularly to the fas account fia FTP. Some course heads set up their course website in abel and redirect the course URL to a directory in the personal URL. The advantage to do so is that you don't have to login to an other account to update the website. The disadvantage is that the need of a URL redirection which disrupts the history path of a surfer.

Necessary ingredients of a course website

What information has to go onto the course website? A course website does not need to be complicated nor fancy. Most important is that all the information can be found easily and that the website is updated regularly.

  • A syllabus with topics, grading policy, textbook information etc.

  • A place for announcements, news

  • Important calendar dates, midterm and final announcements

  • Course head and section leader data

  • Homework and solutions

  • Additional handouts

  • Labmaterial used in class

  • Previous exams for practice

  • Links to relevant websites about the topic

Basic formats of the web

  • HTML, the markup language of the web is learned fast, especially for people who know Latex. One can learn a great deal from looking at existing documents to see how things are done.

  • JAVASCRIPT is a simple yet powerful programming language which allows to make dynamic websites. See Since Javascript is not compiled, one can learn quite a bit from existing pages by looking at the source code.

  • JAVA allows the creation of interactive applets.

  • PDF allows to publish documents in such a way that the format, fonts, style is preserved. People need a plugin or external viewer when hitting a PDF document on the web.

  • FLASH allows to deliver multimedia content like sound, animations, video to the user.

  • REAL/Quicktime/WindowsMedia are the current popular choices to deliver streaming video to the user.

Converting existing documents to webpages The following possibilities are the most commonly used ways:

  • Writing the document directly in HTML

  • Writing the document in SGML and translating it to LaTeX, HTML with sgml2latex, sgml2html

  • Writing the document in LaTeX and translating it to HTML with latex2html

  • Writing the document with a textprocessor like Abiword, Staroffice, Word perfect, MSWord and exporting it to HTML.

  • Writing the document with a publishing software like LaTeX, Pagemaker, Quarkpress or Word processor and exporting the PDF document.

Computer resources

Figure 13-2. Projector in Hall 507

Figure 13-3. Public Computer Room with Scanner

Figure 13-4. Meccah

  • For most tasks, a generic PC or Mac will suffice. Many preceptors use Mac OS X, some PC's others the Linux operating system.

  • For CPU intensive tasks, there is a Unix cluster available at the Mathematics department. It is called "meccah". See William Stein if you want to use it.

  • One of the Sun servers called "neron" is equipped with 22 Gig of memory. If you should have a task which needs this, run it there.

  • In particular, avoid the use of the main server Abel for CPU intensive tasks.

  • It is good to know what students for their disposition. In the basement of the science center as well as in the second floor, there are Unix labs, PC labs and Mac Labs. While at the Math departement, we have Magma, Maple, Mathematica, students can get access to Mathematica. There is a cite licence. site-licence for Mathematica. In multivariable calculus and linear algebra, the computer algebra system Mathematica was used routinely since many years.


We keep old course websites archived on abel. Most of these pages are not linked, some not accessible. If you want some material not public on the archive, just restrict access on the website. This restriction will be inherited in the archive. You always can access from within abel those pages with "cd /usr/local/Web/archive".

  • Manual acces of documents in /usr/local/Web/preceptor/docs and /usr/local/Web/archive

  • Access through the web on using the login name "preceptor" and the password "nolimits".


A typical groupware application contains a subset of

  • calendar

  • todo list

  • sync with handhelds like palm

  • project lists

  • document database, document exchange

  • email, mailing lists, newsgroups

  • workflow systems

  • shared whiteboards

  • chatsystems, discussion system

  • news forums

  • collaborative writing systems, wikis

Available groupware resources at Harvard are

  • ICG toolkit: discussion list, email to groups

  • The myharvard tool is a decent collaborative tool. It is not very sophisticated, but is completely web based and simple.

  • Harvard uses Meeting maker at some places. Webevent is an addition to meeting maker which is used in the physics department for example but it is quite expensive.


  • We experimented with online calendars on our own servers but preceptors have not used it extensively yet.

  • The most effective groupware for a small group we are seems meeting in person or organizing by email.

  • Group management tools need support and maintainance. Most have a database like MySql or PostSQL under the hood.

  • Users have to learn how to use it. The complexity is similar to the one of a word processor ( has a fraction of the complexity of some commercially available groupware projects.

  • Many open source projects are under heavy development like phpgroupware. It seems hat at this moment there is a choice between pretty robust but expensive commercial products (with frequent upgrades and associated relearning and maintainance and costs) and open source projects (with glitches and which are mostly "work in progress" and which need a lot of configuration and maintainance.) A newer option is the Suse OpenExchange Server, 4.1 (about 400 Dollars for 50 users), which allows interaction with MS Exchange.

For teaching

Especially for reviews or introduction meetings, people often use slides to review some material. The main lecture halls are well equiped for that. Many classrooms are also pre-wired with projectors. Sometimes a cable is needed to hook up your computer. If you have a wireless card on your computer, you can use it in all classrooms. If the connection should be too weak, you might have to open the door of the lecture hall a bit. Students appreciate the change of an occasional presentation but one should not do it too often. It can be helpful once to present a little Mathematica animation, but getting draged too much into the inner workings of the program defeats the purpose. Often it makes more sense to post an applet or graphics on the website with instructions and information how to use or interpret it.

Useful Websites

We live in the Google age. Google answers most questions better than any guide can do. Things change fast on the web. Make sure, you get to know the Harvard website, the FAS websites as well as the Math department website. It is also a good idea to look through existing course websites in order to get to know what is taught here and what syllabi are used.