“Self-reading initiative”

In one of the linear algebra classes, I attempted an unconventional approach which lasted for a period of three week. In this initiative, a text book on linear algebra (Matrices by Frank Ayres, Schaum’s Outline series) was selected and students are directed to prepare and study the few selected chapters before coming to the class. Assuming that the students have done their preparation when they entered the class, I would only conduct a very brief introduction to these topics (say for 10-15 minutes). After the brief introduction, I would make the students to attempt problems (which are made known to the students on or before the class) DURING the rest of the lecture hours. Of course I will be guiding them and give hints of how to answer the problems. In the following session (i.e. the next class to come), I would discuss the problem sets attempted by students in the previous session in a more detailed manner. Randomly selected students will be asked to pass up the solutions for grading. Ideally, all students must make preparation for the pre-scheduled topics before coming to the classes, in which they will be forced to attempt questions without going through any formal lecture on these topics. Hence, students will have to understand the contents of these topics by doing the reading and studying for themselves before going to classes, failing which will result in their failure to submit the solutions when asked to do so. This initiative is a bold attempt to provoke self-study pro-activeness in our fellow first year students who are used to the chronic habit of spoon-feeding. Such initiative hopes to promote an active form of learning, (although somewhat forcefully) in which student themselves shoulder a major portion of responsibility in the process of acquiring knowledge. In comparison, learning through lectures (which is the most conventional way teaching is done) is a relatively passive mode of learning. In this initiative, I have to spend quite a bit of effort to specially design a set of original “designed questions” based on Ayer’s book. Ayers’s text book is, like many great mathematicians, highly condensed, precise, no-nonsense yet “unfriendly”. Its “explanations” were mostly in the form of concise mathematical statements beyond the levels for most first year students. My job was to interpreter the theorems using my own approach, basically to illustrate the essential ideas of the theorems via working examples. To this end, a coherent set of problems specially were designed, which were then attempted by the students under my guidance during the lectures. In this learning process, instead of me spending all the time on lecturing, students were asked to go directly to attack the designed questions, after which they will acquire the essential ideas of theorems Ayers tried to tell in his otherwise incomprehensible text book.
I find this approach effective and deliver real understanding, as students were actually playing an active part in the learning process. And it was not as boring as in other mathematics classes as the students were occupied: They were forced to attempt these questions during the lectures as names would be called randomly asking the “lucky ones” to present their answers. I would call this initiative a successful one. However I reckon that not every subject is suitable to adopt such teaching approach. The relatively simple structure of the linear algebra concepts make it easy for students to study by self-reading. In Ayers, the topics were presented in the form of a sequence of theorems, hence was also quite easy to design questions to illustrate them one-by-one. The successful case on linear algebra could be just an incidental result. If this “self-learning” method were to be adopted for other subject, a lot of extra preparation could be required. Anyway, I derived a good sense of personal satisfaction for initiating the experimental approach of teaching. I think many, if not all, of the students in the class had enjoyed a unique learning experience in those three weeks of linear algebra course.