In this article I discuss my experience in teaching UQR2206 "Simplicity", a module in the University Scholars Programme. UQR2206 is a science/ technology-based module without prerequisites and open to USP students from all faculties. A typical class would consist of students from their first semester at NUS to those in their third year of study.

The objectives of the module are to introduce students to (i) the scientific method as used by practitioners, and (ii) the various qualitative concepts and quantitative tools researchers use to understand and model observed phenomena. Some of the challenges of teaching such a module are likely to be common to other cross-disciplinary modules. I shall discuss these challenges below and the various approaches I have experimented with.

The first problem is that students come from diverse disciplines, with very different science and mathematics backgrounds. Thus the subject matter chosen for weekly discussions must be neither too easy nor too advanced. In other words, the discussion subject should ideally sustain the interest of all students over long periods and encourage them to participate enthusiastically.

However, by choosing interesting, and sometimes unconventional, material to solve the first problem, one may face a second problem-the highly pragmatic nature of some students who want to know how what they are learning is useful to them.

The third problem with "Simplicity" as a module in quantitative reasoning is the aversion many humanities students have to mathematics. Many of these students have terrifying memories of how they spent their pre-university days mindlessly memorising countless formulae that were then used with little understanding to solve highly artificial examination problems. Surprisingly, many science and engineering students also think that memorising and using formulae is what mathematics, physics and engineering are all about. However, science and engineering students differ in that they are slightly more accepting of mathematics than the humanities students.

I solve the first problem by choosing readings from various disciplines and try to use non-standard examples to illustrate the concepts. In this way, even students from physics or mathematics, who may have covered similar basic material elsewhere, would learn something new. Furthermore, I constantly relate the abstract concepts to real life examples and point out connections between similar ideas in different disciplines. In this way, students are reminded that science is ultimately about understanding the real world and how understanding something at the conceptual level in one discipline can help solve similar problems in another. Hence, the second problem mentioned above is also resolved.

To address the third problem, I introduce the mathematics gradually, with a liberal use of simple examples, computer simulations, judicious analogies and fun activities (e.g. mathematical modelling of the love between Romeo and Juliet)-all meant to lull students into a relaxed frame of mind and help them forget their preconceptions of quantitative reasoning. At the end of the day, I hope to have taught students something new and useful that they could remember for a longer period than some meaningless formulae.

An example of a computer simulation used in teaching the module is the Game of Life¹ that illustrates how remarkably simple rules can give rise to both diversity (as a result of different initial conditions) and emergent complexity, but how difficult it would be to guess those rules just by looking at the end result. This simulation illustrates with minimal fuss why there is merit in the scientific method used by explorers in seeking simple universal rules underlying natural phenomena.

Another example is Boids²-a computer simulated program that produces very realistic f locking behaviour of digital birds, illustrating the concept of self-organisation. When students learn that the techniques used in Boids are also used in many blockbuster movies and animations, students realise that science can be both serious and fun.

There is, of course, no substitute for the real thing - the group project (the most challenging part of the module). This is where students are asked to select a recently published paper that uses quantitative reasoning and the scientific method and do a critical review of that paper. Thus, students have to first understand what the paper is about, master the mathematical tools the authors used, surface the various underlying theoretical assumptions in the mathematical models, critique those assumptions and conclusions, and finally, suggest improvements for a potential future study. For many students, the critical reading of a technical journal article is often their first experience in taking the indispensable preliminary step in academic research. To make the experience even more realistic and memorable, students are to give an oral presentation of their project to the whole class, after which presenters will be 'grilled' just as in any science workshop for professionals.

Anecdotal evidence indicates that the group project comes in handy for students whose future project work involves mathematical modelling. Even for those who do not intend to further their studies in science, the project arguably brings students as close as possible to the way actual science is done and perhaps, dispels their naïve thoughts that scientists can easily make breakthroughs by day-dreaming.

In addition to the group project, each student has to make another 3-minute oral presentation on 'scientific method or quantitative reasoning in the news'. Students search for a recent news item and then give a concise but intelligible talk to the whole class. This teaches students how to digest everyday scientific news, distil its essence and communicate it to their peers.

Some of the resources used in "Simplicity" are available at the course website: http://staff.science.nus.edu.sg/~parwani/sim/simindex.html.

¹ The Game of Life is available online: http://www.math.com/students/wonders/life/life.html and students can play it before or after class discussions.

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² Boids (http://www.red3d.com/cwr/boids/) was a computer program originally developed by Craig Reynolds in 1986 to simulate the flocking behaviour of birds.