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Teaching First: A Guide for New Mathematicians

Teaching First: A Guide for New Mathematicians

By Thomas W. Rishel

Catalog Code: NTE-54
Print ISBN: 978-0-88385-165-4
150 pp., Paperbound, 2000
List Price: $29.95
MAA Member: $23.95
Series: MAA Notes

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In this volume Thomas Rishel draws on his nearly forty years of teaching experience to address the “nuts and bolts” issues of teaching college mathematics. This book is written for the mathematics TA or young faculty member who may be wondering just where and how to start. Rishel opens the readers’ eyes to pitfalls they may never have considered, and offers advice for balancing an obligation “to the student” with an obligation “to mathematics.” Throughout, he provides answers to seemingly daunting questions shared by most new TAs, such as how to keep a classroom active and lively; how to prepare writing assignments, tests, and quizzes; how exactly to write a letter of recommendation; and how to pace, minute by minute, the “mathematical talks” one will be called upon to give.

This book is Rishel’s answer to those who may suggest that good teaching is innate and cannot be taught. This he emphatically denies, and he insists that solid teaching starts with often overlooked “seeming trivialites” that one needs to master before exploring theories of learning. Along the way he also covers the general issues that teachers of all subjects eventually experience: fairness in grading, professionalism among students and colleagues, identifying and understanding student “types,” technology in the classroom. All of the subjects in this book are considered within the context of Rishel’s experience as a mathematics teacher. All are illustrated with anecdotes and suggestions specific to the teaching of mathematics.

Teaching First is a comprehensive guide for a mathematics TA, from the first semester preparations through the unforeseen challenges of accepting a faculty position. Its aim is to prepare the new TA with clear suggestions for rapidly improving their teaching abilities.

Table of Contents


First Steps
1. Types of Teaching Assistantships: Recitation, Lecture, Grading
2. Before You Teach: A Checklist
3. Day One
4. What Goes On in Recitation
5. What Should be in a Syllabus
6. Lesson Planning: Survivalist Tactics
7. Grading Issues
8. The Semester in Five Minutes
9. Cooperative Learning
10. Technology
11. Writing Assignments
12. Making Up Exams and Quizzes
13. The Active Classroom
14. “What Was That Question Again?”
15. Motivating Students
16. How to Solve It
17. Course Evaluations
18. Get Along with Colleagues
19. How to Get Fired
20. What is a Professional?

More Advanced Topics
21. Teaching Methodologies for Various Types of Classrooms
22. Problems of and with Students
23. Student Types: Who is the Audience, Anyway?
24. Advice to International T.A.s
25. Some Silly Stuff
26. …And Not So Silly Stuff
27. Using Cognitive Models to Make Appropriate Problems (Co-author Mary Ann Malinchak Rishel)
28. The Perry Model
29. Finding Voice Through Writing in Mathematics

Professional Questions
30. Letter of Recommendations
31. Jobs, Jobs, Jobs
32. Mathematical Talks
33. University and College Governance
34. What Does An Evaluator Evaluate, Anyway?
35. Becoming a Faculty Member
36. The Essence of Good Teaching

Case Studies

Excerpt: Types of Teaching Assistantships: Recitation, Lecture, Grading (p. 3)

Most teaching assignments for graduate students fall into one or another of the three categories listed in the title of this section.

Probably the most common T.A. assignment in mathematics, and the one with which the majority of the faculty began their careers, is that of recitation instructor. Those of you who have received an undergraduate degree from a large university will be familiar with the lecture-recitation format: a faculty member lectures to a large class of students two or three times a week on an assigned topic from a textbook, after which a graduate student answers questions about the lecture and discusses assigned homework problems. In this format, the lecturer decides which problems to assign and often determines the structure of the recitation. By this I mean he or she may say “Don’t do all the problems; just the ones that are designated ‘not to be turned in for grading.’” Alternatively, the lecturer may suggest that you begin each recitation with a couple of “examples problems.” Generally, however, most instructors will give you little or no advice, except to say something like “Just do a standard recitation.” (For a sample “standard recitation,” whatever that may be, see the later section, What Goes On in Recitation.)

Another common assignment for T.A.s is to be asked to lecture. Schools vary as to when in a graduate student’s career this is to be done; at some institutions you are handed an algebra and trigonometry text and told, “Go teach this. Don’t mess up!” (I won’t say what I personally think of a school that puts a beginning graduate student in such a position, but it’s probably pretty clear.) Other schools wait for a year or two until you have had some less demanding assignments before they ask you to plan lessons, make up your own exams, decide grading policy, and generally deal with the problems of teaching undermotivated freshmen (or worse, undermotivated seniors!) the joys of precalculus.

It is probably worth pointing out here that at some stage of your graduate career you should actively pursue a lecturing assignment, for a number of reasons:

  • A graduate student who has lectured has a real advantage in the job market (see the section Jobs, Jobs, Jobs).
  • By lecturing before you take a first faculty position, you remove some of the stress over teaching that goes into the tenure-pressure.

A third common T.A. assignment is that of grading, sometimes in an elementary course, more often in an advanced undergraduate or even a graduate course. Many T.A.s describe such assignments as “easy” or “boring.” While the assignments can be either or both, however, grading jobs can teach you how far you have come since the days when this course’s material was a real effort. These assignments can also show you how hard it is to teach others to write clear, concise answers and proofs. A third benefit to a grading job is that you yourself can use it to review the material you may be asked on a graduate comprehensive examination. I will say more about the questions involved in grading papers later on in the section titled Grading Issues.

For now, thing about:
Which type of T.A. assignment appeals to you the most now? Is there one that you think you might never want to do? Do you think that your opinions might change later on in your career, or are they set in stone?

About the Editor

Tom Rishel received his PhD in topology at the University of Pittsburgh. He has taught at a community college, two four-year institutions, and two graduate departments. This year he moved from his position as Director of Undergraduate Teaching at Cornell University to Associate Director at the MAA. Tom is also the co-author with John Meier of Writing in the Teaching and Learning of Mathematics, published by the MAA.


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