The world in my classroom


One of the most satisfying pedagogy experiments I did was in the monsoon semester of 2017-18 at the School of Engineering and Applied Science at the Ahmedabad University.  I am especially surprised by the success of the experiment because it seemed to occur effortlessly and due to spontaneity, demanded by lack of time for planning.  My pedagogy came about as a culmination of multiple factors, following were the major ingredients,

  • I had just come back after spending a semester at the Olin college, where I was involved in a flurry of insightful activities around student centric learning. My major takeaways from that semester were as follows:
    • Design the interaction keeping student background and aspirations in mind, get to know their culture, their fears and their dreams
    • Make students co-creators of your course
    • Give students freedom to express themselves and encourage them in the process
    • Encourage peer to peer interactions
    • Experiment
    • Humanize delivery (can’t stress this enough)
  • Listen to students: This is another point which is very, very important. Students usually are not very free in their interaction with the teachers, due to the power-play involved. So when someone speaks up, it is really useful to make that person feel respected and valued and it is equally useful to show that you are ready to address the point raised by them. I am especially indebted to Prof. Lynn Stein who during her visit at Ahmedabad University and to Prof. Jonathan Stolk during the summer collaboratory at the Olin college in 2015, impressed upon me the importance of listening, encouraging and being non-judgmental.
  • As a result of decades of reading and observing I had come to realize the importance of having a playful and relaxed mind in effective learning. I tried to bring it to practice by starting my classes with music,  TED talks, a short video clip or discussion about a favorite news item by students. Once we played with a ball in the class while discussing very useful mathematics (internally I was quite freaked out, wondering if the youngsters will stay serious about learning while playing but it worked out very well)
  • Encouraging teamwork: This was supported by allowing a lot of discussion time when I discussed a topic that students found conceptually hard. Peer to peer interactions not only as a method of learning but also for social and cultural exchange and psychological well being, was very much stressed on, during the course.
  • Engaging with the class informally, by sharing personal experiencing doing impromptu projects, for example I discussed poetry that I write and one Saturday afternoon a bunch of us went to the workshop and spent several hours designing and laser cutting, card-board earrings
  • Encouraging class to ask “why?” for any curricular component that did not make sense to them, when they did not ask why, I usually asked them as to why did they think they were learning the topic and where were they likely to use it.

Since the course was co-created with students being responsible for their own education and because of having a class which was not traditional, the atmosphere was much more cordial. We laughed a lot, talked about topics from ranging from movies and politics to literature, sports and businesses. It would be great to see if I can better that experience in the coming semester.

Here is a link to my github page with course-notes.

Animated Mathematics

As an experiment in pedagogy in the winter semester of 2016-17, I offered a course on discrete mathematics as a project based course. Students worked as teams in the lab on three projects, while there were some quizzes and a few lectures too. There were 66 students in the class. I offered three types of projects. Groups were formed randomly and were required to come up with their own project idea. Here is a sample of one of the game projects


This project was created by a my students Chaitya Sanghavi, Freya Shah, Nikhil Balwani, Purvang Shah

  • Create a game traditional or your own, using the MIT software scratch and analyze it.
  • Study an application of a finite state machine (FSM) and write a code to implement it.
  • Create a code that implements a graph-theory algorithm.

Project:1  Games

I got the students, most of whom had no programming experience, to learn scratch from using simple examples from the scratch website and then code for a game that was logic based, the last point was needed to be stressed because many groups had game ideas that used chance, speed and knowledge with not much logical reasoning required from the students. We worked on the first project in the lab for about a month, during which about one hour every week I taught discrete mathematics theory but rest of the time talked to students about getting their code to work and resolving logical and coding errors. I have a feeling that quite a bit of learning took place during this time which would be very hard to quantify. There were 3 students per group and the projects were graded by me as well as fellow students. The idea was to get students to enjoy the learning process.

Some of the games made were, Pacman, encroach and capture, word play etc.

Project:2 FSM

  On the project on finite state machines, I asked students to find applications of finite state machines and write codes that would either implement the application or make a new application that addresses a real world problem. Some examples were designs of traffic lights for six-roads junctions for efficient flow of traffic, control system for washing machines, lifts, design of survival games amongst others.

Project:3 Graph theory algorithms

   Before starting on this project, I taught students some basic matlab coding and showed how to run simple programs. I also gave them some challenging codes, like coding for the Koch curve efficiently.  Students either found an existing application or created their own application of graph theory and wrote a code in their preferred coding language.  The projects mostly rotated around matching algorithms with some search and coloring algo.s thrown in.

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.