The Preparation Needs of New Graduate Teaching Assistants.

paper prepared for the working group
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

http://www.math.ou.edu/~tjmurphy
tjmurphy@math.ou.edu


DRAFT: do not cite without permission.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


Abstract

In the USA, Graduate Teaching Assistants (GTAs, both domestic and international) are critical in the effective mathematics education of undergraduates because they teach a large percentage of lower division courses. A variety of efforts have been implemented to prepare these instructors to teach in a variety of ways with a diversity of students and an evolving curriculum, a context which is often different from the one in which GTAs learned mathematics. The joint Committee on Teaching Assistants and Part-Time Instructors of the American Mathematical Society (AMS) and the Mathematical Association of America (MAA) has held sessions at national conferences in order to explore this issue. I will present: (1) an analysis of themes and emerging ideas from the AMS/MAA sessions and (2) results from an in-depth study of 25 new GTAs at the University of Oklahoma. This latter project will examine the perspective of new GTAs, using journal entries, statements of teaching philosophy, and videotapes of classroom teaching as data.

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Introduction

At postsecondary institutions in the USA, graduate students teach a large percentage of the students in lower division courses. In this paper, such graduate students will be referred to as GTAs (graduate teaching assistants). Many GTAs intend to pursue a career in teaching; some are considering such a career; others are teaching to support themselves through graduate school but have no intention of pursing a career that involves teaching.

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

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.

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Formal Opportunities for Reflection and for Interaction with Other Instructors

Naturally, GTAs need to gain some experience with the mechanics of teaching (e.g., good speaking skills, writing on the chalkboard). These are the details that tend to be addressed by many existing orientation-style training programs. However, there are deeper issues that instructors at all levels need to consider, particularly in the current climate in which ideas about the teaching and learning of mathematics are undergoing "reform". Although some training programs have not tended to address these deeper issues, increasing attention is being paid to such issues.

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)
After being observed by a classmate, another GTA said
"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)
From my experience on the Committee and as a "GTA Trainer", two points have become evident to me: (1) spontaneous reflection and informal conversations are useful, but a designated, department-sanctioned cause to reflect and opportunities to interact are more powerful, and (2) specially designed activities, such as those described by the speakers at the conference sessions, can facilitate reflection and interaction .

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Opportunities to Try a Variety of Instructional Strategies

Many new graduate students are not familiar with the changes taking place in the teaching of college mathematics. For example, after reading Smith (1994) a GTA at OU wrote in her journal:
"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)
These GTAs generally have not previously thought deeply about the use of group work or of technology or of writing. As their teaching careers begin and progress, their beliefs and attitudes evolve based on their experiences (including interactions that they have with other instructors).

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.

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Undergraduate Culture in the USA

Not surprisingly, many graduate students who come to the USA from other countries are self-conscious about their skills at speaking American English. While competent speaking skills are perhaps necessary, they are certainly not sufficient for excellent teaching (which is true of domestic instructors as well as international ones). As Wendell Fleming said (Case, 1989),
"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)
One of the international GTAs at OU wrote in her journal:
"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)
Effective classroom communication is so much more than "correct" pronunciation and grammar. International GTAs have concerns beyond language skills. For example, one GTA at OU wrote in her journal,
"[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)
Another wrote:
"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)
And yet another wrote
"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)
Some institutions (e.g., UIUC) have sessions for international students that are specifically designed to address issues of culture (with speaking skills being just one of the issues). These sessions often occur at an orientation that precedes the semester. I propose that these issues should continue to be addressed, as part of the formal opportunities for reflection and interaction discussed in the first section. By discussing these issues on an ongoing basis, the GTAs can (1) practice their American English -- by both speaking AND LISTENING (listening is another important skill for teaching), (2) hear about the undergraduate culture in the USA from graduate students who experienced the culture first-hand, and (3) share their own perspectives (thus expanding the horizons of the USA graduate students).

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Issues for the Near Future

Most of what I have said in this paper is based more on experience than on research, but this experience compels me to believe that this is an important topic for investigation. Much research has been done with teachers at the elementary and secondary levels. Similar research needs to be done with postsecondary instructors (GTAs, postdoctoral students, adjuncts, faculty). For example, I think that we want a better understanding of such things as: What do GTAs (and other postsecondary instructors) know/believe about math? About teaching? About learning?

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References

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