Abstract:

We are given a class of 15 graduate students and we are asked to teach them Graph Theory focusing on its practical aspects, i.e., highlighting how graph theory has and can be used to address real world problems. Students are of various undergraduate profiles including computer science and engineering, mathematics, civil engineering, business administration and of various backgrounds regarding graph theory. The objective is to motivate them appropriately so that at the end of the semester they all appear a homogeneous, high-level background on this particular area of graph theory. What could be an efficient approach towards this objective?.

A possible direction could include intense teaching and lectures on advanced topics coupled with assignment and study of relevant published work. Using this approach, a successful outcome would be heavily based on personal effort put from individuals: a teacher, who would have to prepare and present detailed, rigorous lectures and students, who would have to work hard on an individual basis on relevant research work.

However, given the various scientific background of students, such an approach would suffer an important drawback. A teacher would have to assume a minimum class background level as a starting base for further discussion on advanced topics. Using a very low "minimum" is inefficient in terms of time; using a very high "minimum" is ineffective in terms of maintaining class homogeneity. No matter how this initial decision is made, what usually happens then is that part of the students through hard individual work manage to catch up contributing to achieving the course goals while the rest of the students get lost in the way and either fail or hardly pass.

What if an alternative approach were used according to which a class is not seen as a set of individuals but, instead, as a society where the overall objective is finally obtained via the development of a “course culture”. A culture is not just a collection; there is a mode of relationship operating between the individuals of the culture, namely, communication. The culture of the group consists of the totality of the individual world views united by bonds of communication.

We implemented this approach for a semester period in the context of our graph theory graduate course in a graduate program on computer science and engineering. In particular, all course activities were conducted in a cooperative way. Lecturing was replaced with extensive discussion on new terms and concepts. Problem-solving sections were replaced with detailed brainstorming before suggesting and analyzing a solution to a particular question. Assignments were conducted only in groups.

Our findings are indeed impressive and encouraging. Having started with a rather heterogeneous class of very weak background in elementary graph theory, we ended up with a pretty strong, homogeneous class showing clear evidence of a common graph-theoretic culture. Knowledge and experience was communicated within the class creating a cultural environment shared by all participants. This induced cultural environment not only did it promote understanding, skills and potential of individual participants but also further enabled creativity and highly elevated the research potential of the whole class.

Keywords:

Culture, teaching, computer science, higher education, graduate program.