WGA5: Mathematics Education in Universities

at the conference

ICME-9: International Congress on Mathematics Education

by

Teri J. Murphy, Assistant Professor

Department of Mathematics,
University of Oklahoma

601 Elm PHSC 423

Norman, Oklahoma, 73019 USA

**DRAFT**: do not cite without permission.

Abstract

Introduction

Formal Opportunities for Reflection and for Interaction with Other Instructors

Opportunities to Try a Variety of Instructional Strategies

Undergraduate Culture in the USA

Issues for the Near Future

References

Foremost, the use of graduate students as instructors brings up issues such as:

- Most new GTAs in mathematics are mathematics graduate students, who have a strong background in mathematics, but little if any experience in teaching.
Furthermore, the courses that GTAs are assigned to teach may be very different from the ones that they took as undergraduates, both in intended curriculum and in expected pedagogy. Thus, there is a NEED for extended instructional development.
- As graduate students, GTAs are expected to have as their top priority making progress in their own studies, which primarily are content courses (as opposed to courses on teaching). Therefore, GTAs need to balance their own coursework with their teaching responsibilities. Thus, there is a question of how much time instructional development should consume.

As the importance of such issues has become more clear, the mathematics community in the USA has been to producing documents that begin to address some of the issues (e.g., Case, 1989, 1994; Rischel, 1999). To facilitate continuing conversations within the mathematics community about issues related to GTAs, the joint AMS-MAA Committee on Teaching Assistants and Part-Time Instructors has been holding sessions at national conferences as well as gathering further information. In addition to being a member of this committee, I teach a course for new GTAs in mathematics at the University of Oklahoma (OU): "Teaching College Mathematics" (http://www.math.ou.edu/~tjmurphy/Teaching/5990/5990.html). In the following sections of this paper, I discuss some ongoing themes that I believe are important, based on my background and current position.

At one of the conference sessions sponsored by the Committee, several GTAs gave presentations on their own experiences as beginning and continuing instructors, and some of them discussed their efforts to facilitate GTA development at their institutions. Several of the GTAs "... pointed out that many TAs engage in spontaneous, informal conversations with other TAs as an outlet (often, the sole outlet) for their interest in teaching. They also pointed out that such informal interactions are useful but inadequate for addressing TAs' needs as current and future teachers" (Murphy, et. al., 2000).

Efforts to provide structured opportunities for GTAs to interact with each other and with other instructors (faculty and part-time instructors) range from orientations before the beginning of a term to ongoing "teaching seminars" available to anyone interested. The structure of the opportunities at a particular institution seems to depend on how the mathematics department sees itself. For example, some -- but not all -- departments appear to believe that they are preparing future faculty and that development as instructors is part of this preparation. "[Some] programs hold classes or seminars (some required, some voluntary, some counting for credit), in which participants (varying combinations of TAs, adjuncts, and permanent faculty) explore issues related to teaching. Activities can include readings, dicussions, analysis of case studies [(e.g., The Boston College Case Studies Project at http://www.bc.edu/bc_org/avp/cas/math/publicprojectPI/)], observations and videotaping, consultations with experienced instructors, assignments to experiment, role-playing, modeling activities and further reflection."

The presenters at the conference sessions have primarily been experienced GTAs and faculty. In an effort to represent the voices of new GTAs as I try to understand their needs, I am continuing to examine materials from the population to which I have the easiest access: GTAs at OU. At OU, new GTAs are required to take the course "Teaching College Mathematics." As part of this course, the GTAs keep a "journal" (in the form of e-mail to me). Early in the semester, after reading Krantz (1993), one of the GTAs commented in her journal about provoked reflection:

"I have to say that this book is a very interesting one, not only because it shows many situations that can really happen in a math class, but also because it made us ask ourselves some questions." (female from Romania, graduate student in mathematics) |

"When I realized that I had prepared extra carefully on the day I knew he was observing my class I decided that there was something wrong with that picture. I guess it is human nature to make yourself look your very best when you are being watched, but don't our students deserve that kind of lecture every day?" (female from USA, graduate student in mathematics) |

"This article was very interesting to me because I have heard the phrase 'Calculus Reform' thrown into conversations for some time now but I didn't have a clear definition about what it exactly was. It is nice to now be informed." (female from USA, graduate student in mathematics) |

Many institutions in the USA offer a wealth of instructional experiences. For example, at the University of Illinois at Urbana-Champaign (UIUC), introductory calculus is taught in five formats, each varying in the extent to which it makes use of lectures, small group work, calculators, and computers. New GTAs and postdoctoral students at the University of Michigan are trained in the use of cooperative learning, homework teams, interactive lecturing, and teaching writing (Black, Shure, & Shaw,1997). At the University of California, Berkeley and the University of Texas at Austin, GTAs (new and experienced) attend training programs to learn about teaching in the Treisman-style workshop calculus programs (Treisman, 1985). GTAs at such institutions have opportunities to explore a variety of instructional strategies and approaches to the curriculum, and thus to develop a mature philosophy of teaching.

Other institutions, however, do not have the resources to offer such a variety. Nevertheless, GTAs often have some leeway to experiment. Thus, it is useful at least to introduce ideas that are different from the dominant ones within a department. As the GTAs gain experience and confidence, they can try new strategies with their classes. For example, at the University of Oklahoma, courses in mathematics are primarily traditional (mostly lecture). But several GTAs experimented with using small group work in a college algebra course; one of them is finishing a dissertation about that experiment. Another GTA worked on incorporating a computer algebra system into a linear algebra course; she is also finishing a dissertation on that experiment. (OU has a doctoral program in undergraduate mathematics education.)

Given that many GTAs intend to pursue careers in teaching, experience with a variety of instructional strategies might increase their choices of career path after graduation. Even GTAs who are not in departments with a variety of programs can still experiment, if their departments are willing to be supportive of such efforts.

"Undergraduate students use the excuse that they are not doing well because of the TA's accent; however, from looking at the individual cases, I'm convinced this is just an excuse. Okay, there are some really bad cases occasionally, but this is often not the meat of the problem. The cultural aspect is very important. Some foreign students misunderstand what our educational system is about and how weak the standard really is to let a student get by. Things like that I believe are as important as the accent. Some of our most successful TAs, in fact, have some kind of an accent." (p.5) |

"According to my experience, international students usually don't have a big language problem ... and I've heard so many Americans with bad, and very poor language, so my point is that I don't understand all complains [sic] about international students, TA's, professors, etc." (female from Russia, graduate student in mathematics) |

"[The first week of teaching] was a learning experience for me because the classroom situation and atmosphere are a lot different from those in my country." (female from India, graduate student in computer science) |

"I have also talked to my students in both classes about the fact that I am Russian, and thus we may have some cultural differences. I said 'Even though I have lived in USA for 5 years, I still may not be familiar with all aspects of culture ..." (female from Russia, graduate student in mathematics) |

"When I came here, I was always thinking about how could it be inside the class ... I saw many of classes in my country, my parents were professors and, like you said, I grew up with this ... but I never saw any American class until you invited us [to observe each other]." (female from Romania, graduate student in mathematics; not yet "language qualified" when she took "Teaching College Mathematics", so she was not teaching yet) |

- Black, B., Shure, P., & Shaw, D. (1997).
*The Michigan Calculus Program Instructor Training Materials for Cooperative Learning, Homework Teams, Interactive Lecturing, and Teaching Writing.*New York: John Wiley & Sons, Inc. - The Boston College Mathematics Case Studies Project. Website: http://www.bc.edu/bc_org/avp/cas/math/publicprojectPI/.
- Case, B. A. (Ed.) (1989).
*Keys to Improved Instruction by Teaching Assistants and Part-Time Instructors,*MAA Notes #11. Washington, DC: Mathematical Association of America. - Case, B. A. (Ed.) (1994).
*You're the Professor, What Next: Ideas and Resources for Preparing College Teachers,*MAA Notes #35. Washington, DC: Mathematical Association of America. - Krantz, S. G. (1993).
*How to Teach Mathematics: A Personal Perspective.*Washington, DC: American Mathematical Society. - Murphy, T. J., Branson, W., Friedberg, S., Kappe, L. C., Madden, J., Manderscheid, D., Mantini, L., Marchisotto, E., McCreary, P., Nestler, A., Novak, J., Plisch, S., Speer, N., Wilson, J., & Zia, L. (May/June, 2000). Innovative programs address professional development of teaching assistants and adjuncts.
*FOCUS: The Newsletter of the Mathematical Association of America, 20*(5), p. 9. - Rishel, T. W. (1999).
*A Handbook for Mathematics Teaching Assistants (Preliminary Edition).*Washington, DC: Mathematical Association of America. - Smith, D. (1994). Trends in Calculus Reform. In A. Solow (Ed.),
*Preparing for a New Calculus: Conference Proceedings,*MAA Notes #36. Washington, DC: Mathematical Association of America. - Treisman, P. M. U. (1985).
*A study of the mathematics performance of black students at the University California, Berkeley.*Unpublished doctoral dissertation, University of California, Berkeley.