I am grateful for the opportunity today to discuss with you some aspects of physics teaching. Dr Tong Shiu-sing and Dr Wong Wing-hung suggested that I should say a few words on the contextual approach to the teaching of physics. I must first of all confess that this is only a personal view, random thoughts not informed by theory or research. What I have to say is unlikely to be all correct; I may perhaps be permitted to entertain the hope that it is not all wrong. The purpose is to arouse interest and provoke discussion. Surely an important element of the education reform now being mooted is that the speaker on the podium (I here, you in the classroom) need not be correct all the time, and education is very much a process of two-way interaction involving the participation of the audience in order to arrive at the truth, or a closer approximation to the truth.
The proposed reform of the education system and of the curriculum structure has stirred intense debates in the community. It is gratifying to see so many teachers here today; teachers' concern and involvement bodes well for the reform ahead.
There has recently been a suggestion to revamp the physics syllabus, to introduce the contextual approach to the teaching of physics. The proposal has much to commend it: by starting with realistic examples and familiar contexts the students can more easily relate abstract concepts to their experience and intuition. You have more experience than I in utilizing such an approach, and you understand better than I its theoretical underpinnings, so I need hardly belabour the obvious. Indeed, the whole point of the Physics World
website has much to do with the advantages of the contextual approach. For example, there are many demonstration experiments in Physics World
, in the hope that students can come into contact with reality (if only virtual reality) as they learn physics.
Nevertheless, I believe that some cautionary remarks are in order, attention to which would allow the contextual approach to be more effective.
The theory of knowledge
It would not be out of place to begin with the theory of knowledge. Plato believed that humans trying to make sense of the natural world are like cavemen with their backs to the entrance of a cave. They only see the shadows on the walls of the caves, but not the real objects outside casting these shadows - this is the famous "fallacy of the caveman" well known to students of philosophy. (In much the same way, you can see the shadow of my hand on the screen now.) Cavemen studied the shadows, drew conclusions, and thought that they had come to know the real world - which is of course far from true. (Just as the shadow of my hand on the screen is not the real object; it is only a shadow produced by the object.) Plato believed that what we see (the sensible world, i.e., the contexts we are talking about) is not knowledge; knowledge is the reality responsible for the sensory perceptions.
Plato illustrated with another example. When we teach pupils about geometric objects, e.g., a square, we do not refer to this red, slightly distorted and incompletely closed square shown on the left here, with lines of uneven thickness and interior angles of 89.5 o
or 90.5 o
; neither do we refer to this blue square on the right with similar problems. We expect students to grasp the abstract
concept of a square. In the conceptual world, a square has no color and its lines have no thickness; it is perfect, exact, impossible to draw. Real knowledge must be sought at the conceptual level of Platonic ideals, not at the sensible level where we can see, touch, feel and draw. Pupils in learning geometry generally manage to transcend the sensible, contextual level and attain the abstract, ideal level.
When we teach numbers to young children, we begin with concrete objects, that is, contexts: three apples, three oranges, three blocks. When children are in primary one or two, they finally grasp the abstract concept of the number "3", and no longer need to associate the concept with apples, oranges and blocks anymore. This abstraction and generalization from contexts represents real learning and growing up.
There are good examples in secondary school physics as well. We demonstrate collisions with trolleys. The trolleys are made of wood, are coloured, has three or four wheels, and may also contain other components. This is the situation and the context that students see. We hope that students would eventually abstract from the contexts to develop concepts such as the mass m
, the velocity v
and the momentum p
. To know all about trolleys but fail to grasp the concepts of m
is to miss the whole point of learning physics. In contrast, once the students have grasped the concepts of m
, the trolley hardly matters.
When TS Eliot wrote in The Love Song of J Alfred Prufrock
Let us go then, you and I,
When the evening is spread out against the sky
Like a patient etherised upon a table;
he was not talking about the evening, the sky, much less about a patient etherized. He was attempting to portray an overall scene, almost a state of mind, a state that cannot be seen, touched or smelt. The tangible is only the shadow, the intermediary through which one tries to reach the intangible. The essence of poetry is in the intangible; the essence of science is also ultimately in the intangible.
May I quote a discourse about the art of painting. "I realized that the distinction between the abstract and the concrete may not be clear-cut." (In our terms: the concrete is what we call "context" and the abstract is the ideal or theoretical level.) "Some see my paintings as concrete, but they also see abstractions within; it is image and it is also form; this is exactly my ideal in painting - the art is within the orbit of my paintbrush but also goes beyond it. Every dot, every line and every surface has to carry the delight of the paintbrush. I am not bothered by the distinction between the abstract and the concrete, and I am not fettered by such boundaries. I do as I wish." The writer believes that a good painting should integrate the two levels and transcend the boundary between them. The teaching of science is no different. If we can help students to start with the concrete and the context, and then move on to the abstract and general, integrating the two as one, our objectives would have been achieved. The discourse quoted above is from "Reflections on Painting" by Gao Xingjian, July 1995. (All quotations above are originally in Chinese, translation by the present author.)
Religion is similar. We live in the material world, and religion attempts to guide us to the spiritual world, where we can gain wisdom and enlightenment. In teaching, we also want to guide our students to the spiritual world of wisdom and enlightenment in science.
Context as a tool
Thus context is merely a tool, not the goal; it is the starting point of the learning process, not its end. A toddler learning to walk needs a baby-walker, a very effective tool. Though effective, paradoxically it should be abandoned as soon as possible, and not held on to - not to belittle its value, but to recognize that it has accomplished its mission.
Teaching is no different. We have to distinguish between teaching and examinations. Teaching is a device, a process; examinations assess whether students have attained the instructional objectives. It is as if learning to walk is a device and the ability to walk is the goal. In a track meet, speed is the goal, and one would not worry whether the athlete can ride a baby-walker well, which baby-walker he used as a toddler, nor indeed whether he ever used one at all. This precept should be recognized in setting examination questions. Unfortunately, many examination questions confuse the means and the end, and focus on the devices in the learning process, leaving the instructional objectives untested.
Take the example of ticker-tape-timer, familiar to all of you. After the experiment, we cut the dotted paper tape into segments, and then paste them to produce a velocity-time graph; or we may use a paper tape to record a collision, to study the conservation of momentum. But some examination questions asked about the cutting of the paper tape and the structure of the trolley. Not even Newton reborn can answer these questions. Should questions in mechanics that challenge even Newton be a learning goal in physics? Ripple tank demonstrations are very effective in teaching wave motion, but if the detailed operations of the ripple tank are to be examined, even Huygens may fail. Such questions are not unlike asking athletes to demonstrate their prowess with a baby-walker.
In the Advanced Level physics syllabus on electricity, there is a demonstration on "spooning charge". What it attempts to show is actually very simple - that charge is real and can be transported. Surprisingly, some textbooks explain in some considerable detail a rather complicated instrument that is used - the electrometer. Many students are then left with the impression that the design and operation of the instrument are crucial, and thus make an effort to understand it (or, worse yet, to simply memorize the part of the text); no wonder they find physics difficult. Not only is attention focused on the details of the instrument, but the crucial physics concepts are then sidelined and neglected. Such textbooks can only be characterized as ridiculous. I say "ridiculous" without fear of giving offense, for I am one of the authors in question. The textbook was written that way precisely because public examinations tend to be oriented that way - assessing the context more than the physics.
To emphasize context at the expense of physics is one mistake. To pose contrived contexts that obviously depart from reality is another. Thus one sometimes sees (and laments) problems the solutions to which lead to a person with a mass of 1000 kg, or wave speeds in a ripple tank of 104
. One also encounters questions such as the detection of a single
-particle with a gold foil electroscope - a real example from the Certificate of Education Examination some years back. Such ludicrous contexts merely expose ignorance on the part of the setter. Of course, occasionally we would deliberately postulate unrealistic data, in order to make the point that the laws of physics are universal. For example, we might say "A Martian with mass 1000 kg is in a gravitational field of g = 300 m s-2
..." The reference to a Martian signals that the data are admittedly unreal, and that students should not rely on their experience in the laboratory - and with this implied warning, there would be no problem with this approach.
Context is specific
These examples underscore the importance of not being mesmerized by the specificity of a context; rather, we should guide our students to move forward from specificity to generality. Context is specific; science is general. Their relationship can be explained as follows. At the bottom left of Fig. 1, a
represent some contexts; they combine to generate the content in the top box, i.e., a general law of science. Further downwards interpretation, explanation and prediction then apply to the new phenomena at the bottom right and the contexts x
. This representation of the scientific process, with contexts generalized to a law which is then interpreted and applied to new contexts, is what we need to teach.
If we start from one context and generalize it to a theory, but fail to apply the theory to another
context, we would have failed; that is not even science. If we forget about the theory and only linger around the original context, that is worse. After secondary school students carry out experiments with a trolley, they often cannot apply the knowledge to nuclear collisions and are still confused about momentum; yet they remember vividly that the trolley is made of wood, not iron, that it has three wheels, not four - this is the farce we daily witness in physics teaching.
Context is subjective
Context is moreover relative, subjective and distinctive. First, it is relative in terms of degree. For secondary school students, the collisions of trolleys and ripple tank demonstrations are appropriate. For undergraduates, the concepts m
are already part of their experience and knowledge; these can be taken as the context. For research students, you only have to mention the action integral, and they should know the rest. In short, what is within one's experience is context, but the ambit of experience varies from one person to the next. Second, context depends on background and preparation. This story may be apocryphal. It is said that when Newton was sitting under a tree, he was hit on the head by a falling apple. Newton thought about the velocity and acceleration of the apple, and from that inspiration developed the science of mechanics. Anyone else probably would have been thinking about the colour of the apple and whether it was ripe and fit to eat. With the same context but different background knowledge, people zero in on different parts and different contents. The next speaker will demonstrate some fascinating experiments; as physics teachers, you will know the essence once you see them. But primary school students would come up with other thoughts after seeing the experiments, just like those who wonder about the taste of the apple instead of its velocity. Thus context and background are related. The contextual approach to teaching must make use of actual experience in order to enhance intuitive perception.
There is a demonstration experiment in the Form 5 physics syllabus adopted over a decade ago, in which a feather falls together with a coin in an evacuated glass cylinder. Since the syllabus was largely adapted from the UK, and mother-tongue teaching was not yet encouraged in those days, the name of the experiment, "the feather and guinea experiment", was taken directly from the UK, and it was even written into the syllabus. The guinea is an old English coin worth 21 shillings, that is
1.05. Students had no clue what a guinea was and the more conscientious among them would look it up in the dictionary, wasting time and effort and more importantly distracting attention from the real learning. It was unfortunate that the experiment was not renamed "feather and coin" at that time, to take care of the practical experience of the students and the relative nature of contexts.
When my son was in primary one, he asked me to help with his arithmetic homework: R + G = ? I said I had no clue. He thought I was pulling his leg: how could a university teacher fail to do a problem in primary one! But I truly had no clue. Later I learnt that teachers used toy blocks as teaching aids in the classroom. A block one unit tall is red (R), a block two units tall is green (G) and a block three units tall is blue (B). Thus R + G = B is used to explain 1 + 2 = 3. The letters R, G and B are only symbols. In the actual school environment, such a contextual approach is fine in principle (though one may question whether primary one students in Hong Kong understand "red", "green" and "blue" in English). But at home without the blocks around, students were supposed to memorize the colour code, worse yet, to do so in English. To disregard the actual experience was mindless; to blindly transplant the context of one to another was downright dumb. No wonder students lost interest and confidence.
To build upon the practical experience of the students, we have to be responsive and spontaneously utilize contexts that crop up, in order to arouse attention and interest. For example, a traffic accident near the school can be used to motivate the topic of collisions. This will arouse the interests of the students and is the most effective. Just now I waved my fingers above the overhead projector to generate a shadow on the screen, in order to explain the "fallacy of the caveman". There was no overhead projectors for Plato, so the use of overhead projector to introduce Plato's theory is an extemporaneous use of context. I used words from Gao Xingjian to make a point, because in these few days just after he won the Nobel Prize, a quotation from him may leave a deeper impression. In the original Chinese version of this paper I referred to a poem by Li Bai; for English-language readers of this version, I have changed the reference to some lines from TS Eliot, which makes the same point, but in a context to which an English-language reader can better relate.
Key role of teachers
Therefore, the actual contents and examples in the contextual approach to teaching should not be planned and dictated by a central authority, but principally designed and promoted by individual teachers, so that the examples used could be different in every classroom in every school. Then, extemporaneous discussion based on situations actually encountered by individual students can be included. Of course the examination design must also be considered. Examinations (at least public examinations) have to be uniform for all students, but this does not matter. Teaching methods may differ, but as long as the examination questions focus on the teaching goals rather than the particulars of the examples or context used in teaching, it does not matter if different examples and teaching strategies are adopted in different schools.
The contextual approach to teaching should not be the one and only teaching strategy and moreover it should not be set in stone. Different tactics need to be adopted at different stages of learning, and within one stage there could be different methods and examples, addressing the problem from different perspectives. Different teachers would also benefit from using different methods to teach different students. The rationale behind the contextual approach lies in the integration of theory with practical experience, but since practical experience depends upon the particular people, time and place, so the teaching methods must necessarily be similarly diversified in order to be effective.
To move towards this goal, teachers would do well to reflect upon the rationale behind the contextual approach to teaching. If on the other hand a particular novel teaching method is adopted by a central authority and it is decreed that all teachers and students must adhere to this single approach, then the novelty would be lost and there would hardly be any point. Unfortunately this happens all the time. If the contextual approach to teaching is to be successful, front-line teachers must take the lead. The presence of so many teachers here to participate in the dialog gives us confidence that curriculum development would go forward.
Postscript and Acknowledgment
I am grateful to Prof Gilbert Fong for introducing me to Gao Xingjian's discourse on art. The original oral presentation was first transcribed by Mr Chan Wan-mo, and Ms Janny Leung produced the first draft of the English translation. Prof SY Mak gave valuable comments on an initial draft, in the light of which I have made some corrections and elaborations.