> _a^` ?bjbjss @@@@@@$I!h#d`...d``y.v``>.>V@``bd0{#>0xK$K$bK$`bhJ5<qddh^....ttttttttt``````1. Some Philosophical Musings
Why do you want to be a teaching assistant? Is it simply because it is a good way of earning some money? Perhaps it because you want to gain experience in teaching in order to be better prepared to be a university professor. Why do we need math teachers anyhow? These topics are discussed in a wise manner in Steven Krantzs book, How to Teach Mathematics. I strongly encourage you to read this, as well as to discuss these questions with your fellow teaching assistants. This sections provides some additional thoughts about these questions.
You should like to do math!
Surprisingly, some people become mathematics teachers even though they do not particularly like doing mathematics, but because that is something that they know how to do and for which there is a demand. That is too bad. Whatever you do teach mathematics, drive a truck, perform surgery, serve food, or help others learn a new language your life will become much more enhanced if you enjoy what you are doing. In the case of mathematics, you should enjoy solving problems in fact, you should find at least some types of mathematical to be intriguing, be excited about discovering patterns, and enjoy the challenge of finding counterexamples to false conjectures. Moreover, these feelings should not just concern the mathematics that you encounter in regular courses, but in all aspects of your life. Many mathematicians do not like all mathematical things. I once had a colleague who loved mathematics, applications, and teaching and he excelled in each of them, but he got absolutely no enjoyment out of working on contrived mathematical puzzles that captivate some of us or in manipulating Rubiks cube (which has group theory as its basis). However, he was fascinated with finding ways to compute, to organize mathematical ideas, and to help students to succeed in their studies. I hope that you have a love for doing mathematics, too. Students need to see that you enjoy it, even if they do not.
You should be good at doing mathematics.
Again, this seems to be obvious, but in my role as a teacher and an observer of teachers, I have found many mathematics teachers who are not very good at doing mathematics. They like teaching and working with students, but do not seem to have any particular insights into mathematics. It seems to me that it would be better if they found another field of work. Otherwise, they may create more students of a similar type. A good teacher should not only be able to solve textbook problems, but also to see why certain techniques work (and not just memorize them by rote), and to be able to see patterns, generalize concepts, and develop insightful hypotheses.
You should like to teach and share what you know with others.
Many people who are good at mathematics work very hard to come up with their own solutions, but then think that everyone should be like that and do not like sharing. In fact, part of their attitude is correct. When you are teaching you need to be careful not to share too much, in order to encourage students to be actively involved in learning. However, you also must be willing to share your knowledge, and enjoy others benefiting from the results of your hard work. I come from an era when most of us who used computers had to learn computer programming and a myriad of related ideas on our own, largely without the benefit of teachers, books, or colleagues. This required us to expend extensive amounts of time and energy in self-directed study.
Consequently, it was easy for some people to exhibit to others their feeling that I spent huge amounts of time learning this, so why should I help others get it with much less effort. I do not believe this is a good attitude, especially for teachers. Whether we realize it or not, we all have benefited from the conscientious efforts of our own teachers. In addition, throughout my career many colleagues have helped me, either through their sage advice or by letting me attend their classes. In turn, I have created and taught voluntary courses and workshops for other faculty members to help them advance more rapidly in areas of my expertise. As a graduate teaching assistant, you can do the same for upcoming undergraduate students, so that they see and respect you as being someone who is willing to help.
You should develop an ability to find alternate ways of explaining things.
Some teachers can only repeat what is in a textbook. If your students can do this themselves, then they do not really need you. If they cannot, then they need to see different reasoning, different explanations, or different examples. You should strive to gain experience in being able to draw pictures, to give plausible arguments, to devise alternate explanations, and to look up other ideas so that you can explain a mathematical idea in several ways. Of course, you need to be correct and know how to give a rigorous proof or derivation, too, but a mark of an effective teacher is being able to present ideas in many different ways. You should not to rely on such statements as, It will be on the examination, so you need to know it or Any good students will be able to follow my presentation, or to teach by intimidation techniques such as looking stern, talking very loudly, or being dismissive.
You should enjoy working with students who are not as mathematically advanced as you, as well as with the academic superstars.
Again, there are plenty of mathematicians who are quite talented, and truly enjoy teaching students who are just as talented as their teacher, but then have no patience for students of a lesser ability. There are a few universities that have only exceptionally gifted students, but most of us will find that much of our teaching involves those who are not quite as gifted in mathematics as their teacher.
In my first year of teaching, I had one very young student who completed virtually all of the principal undergraduate mathematics courses as a freshman, and most first year graduate courses as a sophomore. He was (and still is) much more talented than I, and it was a joy to have him in my classes. However, in over the years I had many more students who were not exceptional in mathematics, but some excelled in other areas such as agriculture, law, languages, the military, and politics, with one even becoming the prime minister of his country
As a teaching assistant, you will encounter brilliant folks who may be more clever than you are, but there will be some on the other end of the mathematical scale, too. Encourage them. Many will turn out to be pretty good in surprising areas, and you can help them, too.
You should be willing to develop new teaching skills, to learn new things, and to discard things that do not work.
When you begin to teach, you often will find yourself employing two types of teaching techniques: those that your favorite professors used when you were an undergraduate student, and those that seem to work for you. These are wonderful places to begin. However, you cannot stay there. What works for one person, may not work for others. As time passes, what worked with one class may not work with another one. One of the most famous mathematics graduate teachers of all time, R. L. Moore of the University of Texas (see HYPERLINK "http://en.wikipedia.org/wiki/Robert_Lee_Moore" http://en.wikipedia.org/wiki/Robert_Lee_Moore as a place to start to find ways to explore his method), used a radical approach that turned out some of the best researchers who were also successful teachers. Most employed some of his techniques themselves, and many were successful in doing so. However, they developed their own styles, too. Others were less successful in imitating their mentor.
In general, you cannot afford to be stagnant. Initiate discussions youre your colleagues, sit in on classes of master teachers, or attend teaching sessions at professional meetings, and try some of the new things that you see.
Also, do not be afraid to discard things that do not prove to be successful for you. When I taught matrix theory the first time, I used some techniques that seemed to work rather well. However, the next time that I taught the class I tried same things, and found that that approach was failing. I asked an experienced teacher from whom I received some very good advice, You do not have to keep doing things that are not working.
Prepare, prepare, prepare.
You should prepare adequately for every course. This is true even if it your next class deals with a topic in which you excelled as a student. It is especially true if you are teaching something that is new to you, perhaps vector calculus. Never go into class cold. Read, think how you will explain, have alternate explanations, practice doing drawings, computations, examples, and applications. It is theoretically possible to over-prepare and to make everything look to be too easy, but doling this is a rare event that is hard to achieve. It is much easier to appear as if you are unready or even worse that you do not know the material, simply by being unprepared. Always prepare thoroughly for your classes!
Learn to be effective in running recitation or problem sections
At KAIST most of the work of teaching assistants lies in conducting recitation, or problem, sessions. In these classes, the primary focus lies in helping students to solve problems. Although this affords you a lesser chance for giving original presentations, you can nonetheless use these classes to develop useful teaching skills. For example, in addition to simply showing your class how to solve a certain problem, try to provide them with the motivation behind your method, mention other places in which either the underlying mathematical idea of the problem or the solution techniques that you use also arise, or create a different geometric representation or picture for the problem. However, be careful not to depart too far from the basic goals held by the students, who often are primarily interested in learning how to solve a given type of problem. You also can use your answer to a question to reinforce the ideas previously discussed in the lectures.
In addition, at KAIST, professors who design courses encourage students to keep up in their work by having you give quizzes in the weekly recitation sections. However, you should be careful not let the quizzes take up an excessive amount of the class time, or simply dismiss the class when the quiz is over. Use the full extent of the time effectively.
It is a good practice to check with course lecturers periodically especially if they themselves do not contact the teaching assistants regularly. Ask them if they have preferences as to what that want you do or how they want you do things in the recitation sections. If it is possible, attend some of the lectures yourself (after getting permission from the professor), so that you can obtain a feeling for how the professors present concepts and techniques. See if they follow texts approach and use the texts examples, or if they have heir own methods.
You would be wise to work through all of the assigned problems before going to class, if it is at all possible. Some problems will look very easy, but may have hidden subtleties. If it is not possible to work all of them, then at least do some of each type. It is not a good feeling to find out in class that you do not know how to work some of the problems.
Some techniques that you might want to consider in recitation sections
Although not do all of the following techniques will always apply, here are some approaches to try in your classes.
Have available supplies of (i) stories that relate to the various problems and mathematical ideas to which you can relate your discussion, (ii) sets of examples that provide effective illustrations of different topics or solution techniques, (iii) alternate ways to approach a given idea or problem. You will develop these gradually over the years. While you might have a wonderful memory, it is also a good idea to record them in a journal so that you can review them from time to time.
Learn how to draw by hand rather rapidly effective pictures, especially of such challenging things as three-dimensional surfaces in calculus; planes, lines, and vectors in linear algebra; illustrations of the properties of different types of functions in calculus; and ways to visualize such numerical algorithms as Newtons or Eulers Method. Be able to use computer programs to do this, too, and be able to discern which approach is better to use.
Develop skills in creating effective computer demonstrations and being able to use them effectively in your teaching. Be aware that setting up and using a computer in a class can be quite time consuming, and develop a knack for knowing when doing this is worth the effort.
Strive to become continually more knowledgeable of applications, not just of those that arise in the current course, but also of those that your students can expect to encounter in their future studies in mathematics, the sciences, engineering, and business.
Become increasingly adept in handling questions that arise in class. One of the surprises that I have encountered in Korea is how few questions students ask in lectures. Undoubtedly, they are more willing to do so in the recitation sections. As you may know, students in the United States seem generally to be more demanding of their professors, and they ask more questions. [Of course, some of the more common questions do not deal with the actual mathematics. Here are some of the questions that I hear constantly in the US, but have never heard in Korea. (1) What is this topic good for? (Actually, you should know the answer even if they do not ask the question); (2) Will this material be on the examination? (It well could be); (c) How many questions are on the examination? (d) Will class meet the next scheduled day after the exam? (Yes!) However, in answering questions, be sure that you do not allow one student to monopolize the class. Also, strive to keep up the pace needed to cover the required material.
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