It is the responsibility of the teacher to actively involve his or her students in the
learning process. The most important thing he or she should do is avoid giving clear,
concise, organized lectures. If the presentation of a lesson is too easy to follow, most
of the class will not need to learn the new material on their own. They will have
a certain degree of confidence in their new knowledge, and this will tend to stifle
their intellectual pursuits. If, on the other hand, the lecture is vague, rambling and
disorganized, the students will leave with their heads full of questions. In fact, they
will be so filled with curiosity that they will try to expand their knowledge on their own.
There are many ways to present a thought-provoking lecture. One of the easiest techniques is to use a foreign accent. If the accent is thick enough, even a well organized lecture will produce expressions of intellectual wonder among the students. Effective accents can be acquired in Alabama, New York City, China, India, Latin America, Germany, or other foreign countries.For natives of Kansas, that is, for individuals who cannot speak anything but perfect Midwestern English, this technique may offer difficulties. There are two possible solutions: (1) one can teach in a foreign country, or at least in New York or Texas; or (2) one can incorporate a new syllable into one's language. Two very effective syllables to use are "um" and "uh." The chosen syllable should be uttered every second or third word. This reduces the possibility that any coherent concept will be given to the class. For example, one could say, "Um, today, um, we will be, um, discussing, um,..., um, determinants." After a couple of sentences, most of the class will be staring at their watches or out the windows. Very quickly, they will become very anxious to go out and learn the material on their own.
In addition to being aware of one's own speech patterns, the teacher should also pay close attention to the written word. Illegible handwriting can stimulate a student's interest in new material almost as effectively as incoherent lectures. Often students will meet outside of class to exchange interpretations of lecture notes. Thus illegible handwriting encourages students to work together and share ideas.Writing illegibly requires a great deal of practice to be effective. If one does not have satisfactory handwriting (that is to say, if one's handwriting is suitable only for formal invitations and eye charts), certain "tricks" can be learned:
The above "tricks" may be used separately or combined. It is a good idea to change them occasionally to add some variety to the classroom routine.It is very important that the professor lecture to the blackboard. This helps to demonstrate to students how involved the teacher is with the subject. This enthusiasm will most assuredly rub off on the class. This has the added benefit of making it easy to ignore questions which forces students to go home and answer the questions themselves.
There is one last point on teaching technique. It is important that one does not over prepare for a lecture. Generally, one should arrive at class a few minutes early, open the book, and glance at the topics to be covered that day. Lectures prepared in this manner have a certain freshness and spontaneity that is often missing in carefully prepared lectures. In addition, students will gain a greater appreciation for a correct proof if they see how much time can be spent on a wrong approach.The first part of this guide dealt with actual teaching, concentrating on lecturing "tricks," techniques and preparation. The subject of the last part is general appearances.
Students tend to have more confidence in an instructor if they believe he or she has a thorough understanding of mathematics. This confidence is enhanced if the instructor appears to be "spaced-out." Being "spaced-out" implies one is so involved with abstract mathematics that one has lost touch with the real world. There are several ways to project such an image:
By being properly "spaced-out", one will gain the confidence and respect of one's students. This will make it easier to help inspire them in their study of mathematics. Being properly "spaced-out" will also help one acquire tenure at any reputable college or university.