July 3, 2020

Reflections on Teaching


In my many years of teaching mathematics, I always experienced new teaching and learning situations.  Though I profited much from them, still each new experience brings challenges.  Such challenges make teaching a hard yet a fulfilling and rewarding profession, because it is not a monotonous dead-end job.

I believe that to be successful in teaching, the teacher must sustain throughout his career the same idealistic passion that he initially had in his first year of teaching. His enthusiasm for the subject must not wane (otherwise, everything becomes routine, the drudgery of his job).  Instead, he must at all times possess that burning passion he feels for his subject and share that same passion with his students so that the students will also enjoy, while learning, and eventually love the subject.  Moreover, he should instil in his students the sincere commitment to lifelong, continuous learning, going beyond the confines of the four walled classroom and long years of preparatory education.

First, I care equally about the students’ success in their learning and the course content.  Since math consists of interdependent cumulative topics, it is essential to master the prerequisites in order to be successful in the subsequent topics.  Thus, I make sure that they have sufficiently learned the material through reviews and concept checks before moving on to new topics. When I begin a new section, I try to introduce real-world problems that require or benefit from the use of the material we will be covering.  If these are not possible, since not all materials have real-life applications, I try at least to place the topics in the larger context of its connections with previous results and its applications, so the students more or less have a big picture of what to learn in the subsequent topics. Secondly, establishing a good rapport with the students is essential.  More often than not, students have a not so friendly attitude towards mathematics, as most of them have preconceived notions that they are bad in the subject; hence, dismiss every task as difficult without trying hard enough to even get started.    It is my duty therefore to inculcate in them the value of patience and perseverance inherently essential to their success in doing mathematics.  Lastly, I believe that learning is an active process.  The teacher’s role as a facilitator of learning, acting more as a guide in assisting “discovery” for his students, than as a mere provider of information, is vital.  Thus, I strive to involve the class during lectures.  Class participation is very important.

When students are given assignments or exercises, constant and immediate feedback is very important.  That is why one-on-one or group tutoring supervised by a competent tutor as a supplement to after-school fills in the learning gap to struggling students who are stuck at the assigned tasks and need an expert to guide them through. Using the constructivist approach, rather than spoon feeding my learners, I make my tutees discover the concepts by asking probing questions and let them apply the principles on their own.  By each small effort and the achievement they make, praise is essential because this builds their self-confidence and independence along the way.

Of course, there is much to be learned yet in improving my craft.  The challenges I face are immense.  I recognized that not all of the students share my own love of mathematics.  As such, I try to make the courses I teach a pleasant and enjoyable experience for my students.  Occasionally injecting a sense of humour in some of my lectures, presenting the material with a high level of energy and enthusiasm, and personally connecting with my students to talk about what interests them from time to time work successfully in motivating the students them to excel.  Of course, even if with all these teaching skills, I have a lot yet to learn.  I keenly observe and let each teaching moment become a learning moment too.  I read about best practices from colleagues, and continuously experiment on what works.