For generations (and also for today), economics students in their first-year education in university have been learning the necessary mathematics by reading one single book, Alpha C. Chiang's Fundamental Methods in Mathematical Economics. I was not an exception.
The book is easy, at least relatively speaking. It is really very suitable for those who have not much mathematics background, with only high-school level general mathematics. The book explains math concepts in detail even for certain basic concepts that a mathematician may find it unnecessary to explain (but it is necessary for laymen). It skips those technical details that may not be helpful for a student to understand certain important results (but mathematicians will find these details necessary for making the presentation complete and rigorous). Hence, it is really helpful for those who want to learn the math and have the patience to read through it. That's why the book has been used in generations and generations.
I have wondered who this economist is. He really knows what students' needs are and concentrate on them. Why there is no other economist doing this (at least in the past)? I believe that he must also be a very good teacher. However, Chiang's other publications are not very well known (though his math book is well known). I do not have much information about him as a researcher or teacher.
Recently, I find that he published a biography Tales from My First 90 Years in 2011 (the book title is already full of humor). There, I eventually find out his own description about his teaching. Expectedly, he was really that type of teachers who care about teaching very much and has his own belief in how things should be taught. Let me share with you some words from him:
"The teaching style that I finally decided on is one where I use a very sketchy outline of topics as a rough guide, but the lecture is always done in an extemporaneous fashion. I of course do prepare the detailed points with diligence. But I try to remember them in my mind, and not have them written down in the outline. This way, not bound by a rigidly formatted outline, I can allow myself the freedom to go with the verbal flow at the moment, making the proceedings spontaneous, even sprinkling a joke or two here and there.
"I had long cultivated the habit of using the blackboard, because the act of writing on the blackboard (which has been replaced by 'greenboard' or even 'whiteboard' over the years) affords relief from the tedium of talking and listening. Besides, writing a few keys words on the blackboard can serve to highlight the concepts I want to emphasize. To allow full view of the blackboard, I usually remove
the lectern from the table, perhaps also symbolically removing the 'demarcation line' between the teacher and the students. A few years into teaching, I introduced the use of colored chalks, making my classroom performance a Technicolor presentation. I intended it to be in CinemaScope, too, since I often write on the blackboard from the extreme left to the extreme right. The colored chalks proved very useful when the analysis in question calls for a graph with three or even more curves, each drawn in a different color to avoid confusion.
"At one time, I asked myself whether I should use transparencies as some colleagues do. I decided against it because, projecting an image on the screen gives the students something not different from a 'reading,' whereas the classroom experience should in my opinion be watching a 'performance,' with an audio aspect involving pitch and intonation variations, and a visual aspect involving facial and body languages. Even in the study of a complicated graph, I want the students to construct it with me from scratch, one curve at a time, seeing how they are related to another, rather than seeing a finished picture projected onto the screen. This adds a 'do it yourself' aspect to the graphical analysis, which, I believe, strengthens the students’ understanding.
"I have never won any teaching award. Perhaps it was because I mainly taught small classes at the graduate level, but teaching awards often go to teachers who teach large classes in big lecture halls, with many student 'voters.' But a couple of my graduate students who adopted my teaching style told me that they had won teaching awards at the colleges where they taught. I was happy for them and appreciated their trust in my teaching style."
I admire this teaching style. In fact, if you are my past students, you know my style was quite similar to this style before the pandemic. "Using blackboard (not slides)", "jokes", "no reading", "drawing graphs" etc are all I did in classrooms. However, pandemic prevents me from practicing these effectively and I eventually succumbed. I have now used a "mixed mode" for teaching, not purely slides and not purely blackboards. Perhaps that's the best I can do in the current "mixed" environment, not purely pandemic and not purely safe in interactions. I will see if further adjustments can be made later but I miss the old days.
Finally, my fate also coincides with Prof Chiang's. I have never won any teaching awards. The reason why I didn't got it is quite different, however. The most obvious reason is that I am not as good as Prof Chiang as a teacher. Meanwhile, I teach large classes at undergraduate level while Chiang taught only small graduate classes. But the number of voters is not really the crucial thing in my university as in Chiang's. What matters is that you need to be nominated for going through the first step (and many more later steps). Though I am confident in my teaching quality (and I, like Chiang, got confirmations from my past students about this), nomination is normally everyone's business and nobody's business.
