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10. Continuing Personal Development
Continuing to improve your teaching should be an ongoing component of your professional life. The Mathematics Department at KAIST provides you with an introductory seminar, access to books and other material, and supervision by faculty members. However, even while you are a graduate teaching assistant, you can begin to embellish your skills in a variety of ways. In this section, we list a few ideas.
Observe the teaching of your teachers. One of the most natural ways to polish your teaching is to observe your own most influential teachers in the classroom. Generally, you will be able to observe a number of techniques of that work for them, and just as importantly, what does not for them or other teachers. Invariably, you will pick up some of their techniques that you can try yourself. However, not every approach that works successfully for one of your own teachers will work as well for you. You may need to make adaptations, or even abandon them. One of the premier research mathematicians who had the reputation of being a great teacher with a very distinctive classroom approach was the topologist R. L. Moore of the University of Texas. I had the privilege of working with several his former PhD students, including opportunities to observing them in the classroom. Many of whom were excellent teachers in their own rights. Although the Moore method had clearly influenced their teaching styles, each also had adopted only certain elements of it as they developed their own teaching styles.
Attend an undergraduate class taught by an experienced professor. While you are still a graduate student, try to arrange with a professor who is giving lectures to an undergraduate course for which you are a teaching assistant to attend his or her classes for a semester. Especially as KAIST adopts the requirement that all first-year classes are to be taught in English, it would be a good idea for teaching assistants to attend lectures in such classes as calculus and linear algebra, especially if they have not received much instruction in the English language in their own undergraduate classes. At the time of this writing, it is unclear whether English or Korean (or both) will be the language used in recitation sections. However, whichever language recitation sections adopt, it would be valuable for you to get an idea of what first-year students are experiencing, and observe where some difficulties might be arising. If the department has not arranged for teaching assistants to do this, then be sure to talk to a professor first.
As a professor, sit in on classes taught by other professors. Although you can observe different presentation styles in seminars, colloquiums, and professional talks, these seldom replicate actual classroom teaching. Although in a regular professorial position, it can be more difficult or awkward for one professor to attend the undergraduate lectures of another, you can often improve your own teaching by doing so. While this is true for even experienced professors (as department chair I have attended classes of all of faculty members and profited from doing so), it especially worthwhile for the less experienced professor. Often you can make the necessary arrangements simply by asking a colleague, either at your university or at another one that is nearby. While I obtained a PhD in pure mathematics (finite groups), for many years I sat in on classes in applied mathematics, industrial engineering, and statistics at Iowa State University, and in computer science at Whitworth College and Eastern Washington University. During this time I saw how some excellent teachers ran their classes, and in the process I also acquired new insights and provide myself with expanded areas of competence that helped me in obtaining future positions as well as in my day-to-day teaching.
Attend mathematics short courses and workshops. Frequently universities or professional conferences provide short courses or workshops on teach techniques, as well as those with a research emphasis that are presented by top rated teachers. You can acquire valuable teaching skills from these opportunities, too. New additions to the list of helpful workshops are those of the National Institute for Mathematical Sciences (see HYPERLINK "http://www.nims.re.kr" www.nims.re.kr).
Attend conferences that have a component on teaching mathematics. Many mathematics conferences emphasize presentations on new research together with overviews of fields presented by respected mathematicians. We attend these to help us remain current in our research, and stay in contact with others in our own disciplines. However, not only do most national and international conferences have sections on teaching university mathematics, each year there are conferences for whom the them is mathematics education at the university level. These can provide you with a number of new ideas, especially in the way of new technologies.
Arrange for joint professor-graduate student presentations. During 2006, I worked with two excellent KAIST students to give joint presentations at international meetings of the Mathematics Association of America in San Antonio, and the National University of Mongolia. These were presentations on the use of spreadsheets in teaching linear algebra in one case, and numerical analysis in the other. The students did an excellent job, presenting in English, and served as excellent representatives of KAIST and their countries, as well as participating in the conference. Arranging for this to happen regularly can be a great opportunity for gaining not only skills, but confidence in ability to present professionally and to help compete late for positions.
Attend conferences of other mathematics education organizations. It is a misfortune if status-related issues arise in our professional lives to deprive us of other valuable opportunities for improving our teaching. Unfortunately, often researchers feel out of place in meeting with organizations that concentrate on high school or community college mathematics. In the United States, while concentrating on pre-university teaching, the National Council of Teachers of Mathematics involved mathematicians of all levels, while the American Mathematical Association of Two Year Colleges focuses two-year colleges. However, each sponsors excellent meetings that involve mathematicians of all levels and interests, allowing us to encounter some novel teaching ideas, and to build relationships with institutions that provide many future students for universities. Over the years, many graduate students and some top mathematics researchers have started out at these universities and schools because of the influenced of their teachers.
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Organize brown bag meetings. In the United States, people who bring their own noon meals from their residence often carry it in brown paper bags, hence the name used above. In many universities, graduate teaching assistants organize a weekly meeting at lunch, bringing their own food (although in some cases the event is held at a facility where one can buy a meal). The purpose of the meeting is to have participants give presentations (see reference). We can organize several types of meetings designed to help us develop teaching skills.
Talks on teaching techniques. In this approach, one or two people can illustrate how they present a mathematical concept, how they use an item of computer software in teaching, language issues, or how to handle a certain classroom management situation. A general discussion of those attending can follow. The group could also discuss a variety of actual teaching problems that have arisen in classes at KAIST, while avoiding the specific identifications of any people involved.
Talks on elementary mathematical topics given in English. The format of these meetings is similar to those in the previous section, but in this case, the goal is to communicate mathematical ideas effectively in English. The participants can practice their presenting and teaching skills, as well as skills in listening, talking, and analyzing English presentations. A broad range of topics can be included virtually anything that speakers think that the audience will find to be new and interesting. The history of mathematics is a source of many examples that are effective, including those of a rather elementary nature. They need not be very old ideas. The mathematical basis of slide rules and their connection with logarithms, other early computational devices including the abacus, manual and electric calculators, early handheld calculators can make possible topics. Besides introducing others to interesting concepts, the participants learn how to explain elementary concepts in English via topics with which the audience may not be familiar, thus adding an aspect of the classroom experience. Generally, faculty members are not included, so that the participants are not as likely to feel intimidated.
Baby graduate seminars. These are graduate students seminars that are organized, run, and attended strictly by graduate students. We provide examples about these programs on Web sites. While the seminars are on graduate topics, they are at an introductory level (hence the name), with students primarily reporting on their readings about the subject rather than current research. As above, faculty attendance is either significantly limited or forbidden.
General discussion sessions. The topics of these brown bag gatherings are not restricted to mathematics, but are free ranging to allow participants to practice and enhance their skills in English.
Here are some Web sites that provide illustrations of these types of events, with foci on such areas as teaching, research, and the life of a graduate student.
Purdue University: Brown Bag Teaching Seminar
HYPERLINK "http://www.math.purdue.edu/~cowen/BrownBag.html" http://www.math.purdue.edu/~cowen/BrownBag.html
University of Missouri-Columbia: The Preparing Future Faculty Program
HYPERLINK "http://www.missouri.edu/~gradschl/pff/pff.pdf" http://www.missouri.edu/~gradschl/pff/pff.pdf
Morgan State University: Monthly Brown Bag Seminars
HYPERLINK "http://jewel.morgan.edu/~cfemse/programs.php" http://jewel.morgan.edu/~cfemse/programs.php
University of Arizona: Brown Bag Seminar
HYPERLINK "http://math.arizona.edu/department/magazine/mathnews_1999-2000.html#P5" http://math.arizona.edu/department/magazine/mathnews_1999-2000.html#P5
University of Wisconsin: Department Brown-Bag Seminar
HYPERLINK "http://www.math.wisc.edu/~brualdi/vigresemfall03.html" http://www.math.wisc.edu/~brualdi/vigresemfall03.html
Northwestern University: Graduate Student Seminar
HYPERLINK "http://www.complex-systems.northwestern.edu/overview.htm" http://www.complex-systems.northwestern.edu/overview.htm
Massachusetts Institute of Technology: Baby Algebraic Geometry Seminar
HYPERLINK "http://www-math.mit.edu/~kedlaya/stage/" http://www-math.mit.edu/~kedlaya/stage/
Harvard University: Trivial Notions Seminar
HYPERLINK "http://www.math.harvard.edu/trivial/" http://www.math.harvard.edu/trivial/
University of Illinois-Champaign: Baby Logic Seminar
HYPERLINK "http://torus.math.uiuc.edu/cal/math/cal?year=2006&month=03&day=16&interval=year®exp=Baby+Logic+Seminar&use=Find" http://torus.math.uiuc.edu/cal/math/cal?year=2006&month=03&day=16&interval=year®exp=Baby+Logic+Seminar&use=Find
University of Surrey (U.K.): Communicating Mathematics
HYPERLINK "http://www.maths.surrey.ac.uk/personal/st/B.Sandstede/communicating-mathematics.php" http://www.maths.surrey.ac.uk/personal/st/B.Sandstede/communicating-mathematics.php
HYPERLINK "http://www.maths.surrey.ac.uk/personal/st/B.Sandstede/index.php" http://www.maths.surrey.ac.uk/personal/st/B.Sandstede/index.php
Brown University: Attending Conferences and Presenting Papers
HYPERLINK "http://careerdevelopment.brown.edu/grads/succeed_confs.php" http://careerdevelopment.brown.edu/grads/succeed_confs.php
Graduate student conference. This is a more ambitious undertaking, but it could develop into a distinctive KAIST program. The department could organize a national Korean conference with heavy graduate student involvement on the theme of teaching mathematics and giving mathematics presentations in English. This could provide an excellent opportunity for mathematics teaching assistants to give professional-style presentations in English. While the conference would involve both faculty and graduate students in the organizing work, graduate students would give most (or all) of the presentations. One very successful program in this vein in the United States is the Annual Nebraska Conference for Undergraduate Women in Mathematics. The Department of Mathematics of the University of Nebraska organizes this conference (see HYPERLINK "http://www.math.unl.edu/~ncuwm/" http://www.math.unl.edu/~ncuwm/). At the conference, undergraduate women from across the United States are invited to see what graduate in mathematics is all about. This program represents an effort to encourage more women to pursue graduate study in mathematics. The speakers are primarily women graduate students, together with some female undergraduate students talking on their undergraduate research programs.
To provide some illustrations, here are a few more links to previous graduate student conferences
Graduate Student Combinatorics Conference
2006: University of Wisconsin-Madison
HYPERLINK "http://www.math.wisc.edu/~gscc06/" http://www.math.wisc.edu/~gscc06/
Graduate Student Topology Conference
2005: Northwestern University
HYPERLINK "http://www.math.northwestern.edu/~pearsonp/conference.shtml" http://www.math.northwestern.edu/~pearsonp/conference.shtml
Annual Graduate Student Conference in Logic
2006: University of Wisconsin-Madison
HYPERLINK "http://www.math.wisc.edu/~kach/mathematics/gscl7/" http://www.math.wisc.edu/~kach/mathematics/gscl7/
Graduate Student Research Conference on Algebra and Representation Theory
2006: Kansas State University
HYPERLINK "http://www.math.ksu.edu/main/events/grad_conf_2006" http://www.math.ksu.edu/main/events/grad_conf_2006
Midwest Number Theory Conference for Graduate Students and Recent PhDs
2005: University of Illinois at Urbana-Champaign
HYPERLINK "http://www.math.uiuc.edu/mntcg2/" http://www.math.uiuc.edu/mntcg2/
Graduate Student Conference
2001: University of Western Ontario (Canada)
HYPERLINK "http://www.apmaths.uwo.ca/gradinfo/Gradtalks.shtml" http://www.apmaths.uwo.ca/gradinfo/Gradtalks.shtml
Alberta Conference for Young Researchers in Mathematics
2005: University of Calgary (Canada)
HYPERLINK "http://www.pims.math.ca/science/2005/05gradcon/" http://www.pims.math.ca/science/2005/05gradcon/
Case studies approach. The case studies approach, often used in teaching business management and decision making courses, has also been used with teaching assistants at a number of universities. Perhaps the best-known program of this type in mathematics is the Boston College Mathematics Case Studies Project headed by Dr. Solomon Friedberg. A discussion of this project is available on the Web through the URL:
HYPERLINK "http://www.bc.edu/bc_org/avp/cas/math/publicprojectPI/" http://www.bc.edu/bc_org/avp/cas/math/publicprojectPI/
Copies of the faculty and graduate student books for this are available at KAIST in the project library, and a video of Professor Friedberg discussing the program at the 2005 symposium at KAIST is listed elsewhere on this web site.
Skype. Another way to promote the professional growth of mathematicians, including both professors and teaching assistants, is through Internet communication facilities. Currently, the most widely used program of this nature is Skype (see HYPERLINK "http://www.skype.com" www.skype.com). By installing this program on your computer, you can engage in instant online oral conversations with mathematicians around the world. This enables you to talk with colleagues about issues almost as is done in person. It also is easy to connect cameras at each ends, so you can see each other. This facility enables you to participate in some professional conferences from a very remote location. In the autumn of 2004, I was a live co-presenter at a mathematics conference that was underway in New Orleans, USA. I talked via Skype from the study of my KAIST apartment at 3:30 a.m. Moreover, sophisticated programs already exist that can allow you to have live interactive control of a computer from a distant location. Besides these possibilities, the use of a communication device such as Skype enhances your participation in joint research, in sharing teaching ideas, and in listening and responding to different versions of English.
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