Speaking Mathematics

The way we learn has changed drastically over the last decade or so. I consider myself fortunate for having access to so much high quality learning material with very little effort.  I am a physicist by training but have been teaching Mathematics to engineers for quite sometime now. There are many lines of thought on how Math should be taught to engineers. Three main views are

(1) Teach in the usual lecture, problem solving style with a lot of emphasis on concepts, rigor and formal methods.

(2) Classroom teaching in an intuitive manner with lots of games and real life examples involved.

(3) Teach Math hands-on while students work in the lab on real life projects.

A proponent of the first method is the well known computer scientist Djikstra He holds the view that learning formal methods without interpreting the symbols is a great way of preparing students to work with novel realities. In physics such an approach of working with mathematics without well decided interpretation (in terms of analogies) has been quite useful, especially in quantum mechanics.

The second view is a favorite of many educators, if one is to go by online platforms. John Conway is a proponent of this style of Mathematics teaching, where he tries to either develop or understand mathematics using a lot of analogy and tools. Conway

The third view, being followed by many educational institutes is that of project based learning, where the students work in teams to solve real life problems and pick up mathematical skills as and when needed PBL While some engineering institutes have used this pedagogy very successfully, when it comes to Math learning there are also voices that express doubts about effectiveness of this method.

I have used each of this style to some extent in my classes and here is what my experience tells me.

In an average classroom usually the second style of teaching mathematics intuitively works out very well. It gets students interested in learning and enthusiastic about the subject.

I believe the first style have many positives, for a higher level learner who has come to appreciate the abstract nature of Math and its power. In a regular classroom less than 10% of students usually have this appreciation. When mastered, this method can be utilized to application of mathematics in quite diverse fields.

The PBL method of learning is relatively new. It requires appropriate infrastructure and manpower. It has the advantage that the learning is driven by student motivation and it happens in the real world context. However this method also requires learning of new tools, machines and computational, searching for and using appropriate materials and working on open ended projects. These considerations mean that students get to focus only on limited aspects of mathematical details and learn fewer concepts compared to a student taught by the other two methods.

When it comes to my view, I would be flexible and change my methods based on the students involved, the motive of the course and the infrastructure available. When the students are advanced and have developed appreciation of abstract concepts and have the ability to apply their knowledge effectively, formal method is very good. In general it would work out very well for students wanting to major in Math. The second method would be fun and effective in an average classroom, whereas the PBL method is good for students who want to apply the knowledge gained in real life situations and are prepared to learn, take challenges and deal with uncertainties.



Saved in Time ?

Reading about single person acts of terrorism (I don’t like the name lone wolf, there is a hint of heroism in that, senseless violence does not deserve it) makes me think of a sequence of events years ago. Most of what I describe here was told to me by friends whose interpretations I trust.

The story is of a friend. A very quiet, sincere and deeply religious guy, I shall call him “I”. We all were mostly a bunch of rebels (not too extreme, but compared to the Indian back-grounds we came from). Criticizing and making fun of fellow friends was a normal part of the day. “I” was while generally well accepted, did get laughed at a lot (…and  also criticized)  due to his deep religious beliefs.  During the course of time, for some reasons (possibly due to a strong difference of opinion with a senior) “I” moved out from the housing complex where we all lived. He, with his newly married wife went to live in a much inferior place, to be closer to his spiritual support system. He started donating regularly to the religious cause from his tiny income and appeared to be content with his new lifestyle.

A year or two later, his wife fell seriously ill. The community to which he was making regular donations distanced itself from him (In India most religious institutions have very little money). It was the bunch of old friends, including those who regularly ridiculed him, who stood by him. It changed his perspective and brought him back to live in our housing complex.

There are times, I have wondered, what if things went slightly differently ? How different a person would “I” have become ? But then I don’t want to think about it.

Why this blog

This is the excerpt for your very first post.

With time I have come to appreciate the importance of dialogues in variety of situations. I have also realized  the power of internet and it’s role in spreading and evolving ideas and in bringing like minded people together. So this page for me is to initiate dialogues with known and unknown people in the hope of learning, understanding and finding friends.

I am thankful to my friends, Ananthkrishnan, whose blog I happily criticized and like a true good friend, he happily ignored my criticism, Jeemol, for reminding me the therapeutic effect of rambling and finding friends, Ratnik for introducing me to the blog by Terence Tao.