Physics has been a difficult subject not only to students but also to the teachers. There have been many causes leading to such impression, such as the structural deficiency in our education systems and the poor appreciation for an intellectual culture. The university education in many ways is simply yet another secondary school sitting in a larger campus. Students memorise the formulas and concepts, vomiting them out again in the exam halls, but never appreciate the intellectual process of how these concepts are formulated. To many students physics is merely a collection of formulas that can be used to calculate certain problems. When given a physics problem, what first come to their minds is to scan for the right formula from their memorised data base, instead of analysing it with a more robust approach. Such a mechanical practice is a norm among the students and has saved many’s “lives” in the exam halls. But it has also deprived them the opportunity to think like a physicist.
In a typical classical mechanics course for example, various “must know” concepts or theories are taught, such as how to describe the translational and rotational motion of a point particle or a rigid body, the classical concepts of forces, gravity etc. These are specific knowledge that has to be learned by students (and to be tested in the exam hall). However, these specific concepts and theories are different in nature from the more general, and somewhat more abstract, aspect of the physics methodology used to formulate them. At this point, I would like to make a distinction between physics concepts (or theories) and physics methodology, a.k.a. “the way how physicists think”, or “physicist’s paradigm”. Teaching physics and mathematics should not only involve presentation of fact, concepts, formulas and technique to perform calculation. Equally important is to teach the students how to think like a physicist.
Physicists’ paradigm is characterised by clear logic. They think along a logical track when formulating a quantitative description of a physical system. They are able to distinct one line of logical thread from the other, and see the connection between them. Logics are spoken in the language of mathematics, hence physicists are intensive users of mathematics. They have to translate an idea or a theory precisely using the language of mathematics because physical reality is represented using mathematical symbol and equations in physics. Physicists must know how to abstract information from observations and put them coherently into a mathematical form for further logical manipulation. They do experiments on a physical system and make measurement, then use mathematics to build model to describe the physics as inferred from the experimental data. Physicists have to make smart simplification when building models to describe a physical system. They need to know how to deduce physical consequences or inferences from a set of mathematical equations. They often apply tricky mathematical procedures such as making approximation at different levels of accuracies when approaching a complex system. Very often they need to be smart enough to spot the underlying similarities between two disparately different systems so that the theoretical treatment used for one system lends a helping hand to describe the others. Sometimes physicists simply have to be clever enough to put forward a smart guess to tackle a clueless problem. The set of methodology used by physicists as briefly mentioned above is an art practiced by all, yet is not mentioned explicitly in most physics textbooks. It is only to be acquired after a long time working in the physics research business. Making student to at least be aware of the physicist’ paradigm is one of my agenda in my teaching.
When I teach physics, of course I will explain the mathematical formulas and theories, or illustrate the physical laws by working examples, as every physics teacher will conventionally do. On top of that, I also insist on explaining the way a physicist thinks, and the physicists’ methodology when dealing with a physics problem. This, I reckon is an aspect less emphasised by most physics teachers who used to feed the students with formula without properly explaining their origin or the thinking process behind them. Our education system inclines to force students to memorise the outcome of the thinking process (i.e., the formulas formulated by the physicists) but never teach them to appreciate and comprehend the thinking process itself. Having said that, to teach and train students to comprehend the physicist’s thinking are no easy task. Translating a physics concept into a mathematical form is an abstract and highly intellectual process. To apprehend the paradigm requires certain level of intellectual maturity. I myself was not even aware of the existence of such paradigm when I was a physics undergraduate. The usual way to teach the paradigm is by ways of examples, in which I elaborate and commentate on the process and approaches used by physicists when solving a specific problem. I reckon that the inclusion of physicist’s paradigm in my teaching makes me slightly distinct from other physics teachers.
