In his recent presidential address to the Royal Society of Canada Dr. Cameron of McGill referred to education as "training for living" and technical studies as "training for making a living". I suggest that this is a good place to begin. Your task contains the vital challenge of meeting both these objectives. You will probably agree with me that the former is much more important but the fact remains that you are often judged not by what educative values you have transmitted but by the marks your pupils have obtained on examination, i.e. by the so-called efficiency of your technique. I will have something to say about the real importance of examinations later, but I can tell you this; - the teachers to whom I, as an ex-collegiate pupil, have been most indebted and for whom I retain the greatest respect and affection were a relatively small group who saw things with a wide vision and transmitted much more than mere techniques. There was Madeline Young at Belleville who made Ancient History a living thing by reading to us from Pericles' speeches and from Euripides and from Plato and who got in a jam with the powers-that-then-were because she read part of a comedy of Aristophanes that wasn't exactly polite. There was Peter MacLaurin, my old principal at Belleville High School, who cast chemistry as a matter of observation rather than mere rote and then insisted on careful review of the tabulated observed data however elementary. And perhaps greatest of all, Billy McHugh, the incomparable Maths master at Upper Canada College for whom trigonometry was so much more than "a lot of damned facts about triangles" it was a basis for a measured knowledge of nature: - You see I do remember.
It is fully recognised that you have to east your two-fold objective within the frame of the departmental curriculum, a frame which is essential and necessary as a uniform minimum requirement of the scope of your teaching, which may often be such a large minimum that it occupies all of your endeavour but which becomes an insufferable barrier to both yourself and your students when it assumes the role of a rigid maximum not to be exceeded.
The rejection of a study of science and in the end result of a scientific career by many young people has taken several forms. Scientists are 'egg heads'; science is "too difficult"; scientists have to work too hard; they don't make enough money; are never their own boss; they live in a day-dream and just don't know what goes on in the world; scientists specialize so much that nobody else can understand when they talk their own lingo and they can't talk anything else! Each one of these statements is partly true and largely false. I know some scientists for whose any statement selected from the above is substantially true.
I suggest you don't try to answer this kind of thing directly but that you rather attempt to convey what science is all about. May I suggest one possible definition of science. "Science is finding out things we don't know". If you start trying to find out by asking "I wonder why" or "I wonder how" then you are thinking as a "pure" or "fundamental" scientist. If you start trying to find out the same thing by saying "I wish that" or "I want to" then you are thinking as an "applied" or "practical" scientist. Thus a scientist consciously sets his own course, and the answer he obtains, which will, broadly speaking, be but a part of the whole answer, can only depend on what conclusions he derives frees his observations on the particular course of his own ! selection. Will you tell your students that again and again and again.
The coat of arms over the portal of the realm of science bears its motto in Browning's words - "Ah, but a man's reach should exceed his grasp or what's a heaven for".
Both the objectives, educational and technical, must be met, it seems to me, at the collegiate level more by how you teach your subject than what you teach. The "what you. teach" is largely, but I hope not exclusively, determined by the curriculum. The "how" is much more up to you.
May I suggest your first three "hows" are inseparable and should be combined to bring out a balance of three factors; first the sense of order in nature; secondly the recognition that the validity of that order is dependent on observation; and, third, that there is always an experimental error and a better answer than you have obtained.
When you start teaching so-called scientific laws how do you start? I'd start by asking questions, - questions like "Did the sun come up yesterday Earning?" A stupid question like that should get attention. Then I'd ask "Did the sun come up this morning?", and then "Will it come up tomorrow morning?" and then "Why?". From then on it should be easy to get at the idea of natural law from observed data and then on to the next step that science as we know it would be impossible without the idea of natural law.
I suggested your first "how" involves a balance of three factors. You have a very ready example of what I mean in the gas laws a Here is a natural "law" that all your students have had to learn. How many of you have dared to emphasize that, except for the inert gases, it only crudely approximates observed facts, and that sometimes students who lose marks because they make an error of small magnitude in dividing out the fractions just might be nearer the observable or measured volume than those who got a "correct" answer. There have, of course, been several reasonable presentations of the gas laws which don't get into too much detail for collegiate use. I'd suggest that given in Cragg and Graham's text for first and second year university. It is particularly good because some of Boyle's original observations are quoted and that is important as it demonstrates another essential factor in science either as education or as technique. For your next "how" should be, I believe, to point out that great scientists (and Boyle was a great scientist) report their measurements as they were observed. There is no such thing as a fudged experimental numerical value in science worthy of the name. Boyle's results do NOT precisely fit his law. Part of the sis-fit is because his "law" is, as I have said, a rather crude approximation and part of the mis-fit is experimental error. Boyle didn't try to hide either. Incidentally also you have, at the collegiate level, a classic example of honestly reported data in Henry Cavendish's measurements on nitrogen. You will recall that many years later the discrepancies which he so meticulously recorded between his observations and what he said should have been obtained were shown to be due to the argon content of nitrogen isolated, as Cavendish had done, from the air. You may theorize about, you may approximate, you may even adjust your conclusions but, in my opinion, an unforgivable sin in the "how" is altering an experimental result. In science accuracy and honesty are synonymous terms as applied to observation. I must add a suggestion which may be quite impractical. Get as many of your students to actually do the experiments (in group parties perhaps) as possible. If this means extra time after school it still has been done.
The fifth "how" requires rather careful planning. Get the idea across that in the scientific order of the natural world the "laws" vary in their accuracy and reliability. The crudest ones are merely technological or industrial sales guideposts - you can make up examples of your own - things like the amount of lighting fluid sold in a given period is proportional to the smoking population, or the quantity of water going over Niagara Falls is proportional to the total rainfall in the Upper Great Lakes. The gas laws are a good illustration of a law that has some genuine mathematical Meaning but is still rather crude. You have a better chance to get the idea across when you start teaching about combining weights and later about isotopes. Before isotopes were discovered many people felt that combining weights should be in the ratio of whole numbers and nature was playing a mean trick because they weren't. Even the ones who wanted to couldn't fudge the atomic weight of chlorine from 35.46 which is just halfway between whole numbers. In the story of the development of knowledge of atomic structure there is a magnificent example of progress towards the truth - of the discovery of underlying principles or laws of progressively increasing validity. I cannot help but think (you may disagree and say I merely want to think) that the real reason why atomic and nuclear study is monopolising so much of the entire field of science today is not the urgency of its applications or military potential but because the underlying fundamentals ~ "I wonder how" and "I wonder why" are being satisfied. Even when he knows his work may be prostituted to the cause of ruin and destruction the idealist in the scientist cannot but try to advance the truth. There is nothing new in this. Christopher Marlow put these words in the mouth of Tamberlaine:
"Nature that fram'd us of four elements,
Warring within our breasts for regiment,
Doth teach us all to have aspiring minds;
Our souls, whose faculties can comprehend
The wondrous Architecture of the world;
And measure every wand'ring planet's course,
Still climbing after knowledge infinite,
And always moving as the restless spheres,
Will us to wear outselves and never rest,
Until we reach the ripest fruit of all,
That perfect bliss and sole felicity,
The sweet fruition of an earthly crown."
Young minds like to be certain about things. I am sure that from my standpoint I have never been as certain about all the answers as I was when I was in my late teens. What I am suggesting is nothing less than giving this attitude a real shock. We are still pioneers. We still, like Cavendish, must be honest enough to note discrepancies, to admit that we don't know, that we make mistakes, that future progress lies before us.
The word "agnostic" has been given connotations of disrepute but in its proper meaning it is a good word with a good meaning. It says very simply and very sincerely "I do not know". The very existence of science is an intelligent agnosticism. This is NOT, ten million times not, a denial of any phase of reality natural or spiritual. It is a statement of a quest. You have got to tell your students sometimes that you don't know. Greater men than you or I have done so -why should you, or I, hesitate. "Ah, but a man's reach should exceed his grasp or what's a heaven for."
Now it is obvious that a pursuit of the kind of "how" we are talking about soon leads far beyond the confines of the collegiate curriculum so the sixth "how" mist be concerned with supplementary reading for yourselves and for your better students. I'd strongly recommend Cragg and Graham's book to which I've already referred. For a mixture of mathematics including an understandable explanation of the square root of minus 1, physics from stars to nuclei, heredity and genes, outrageous fun, and some of the most remarkable photographs I have ever seen collected in one book, your school library should have George Gaiaov's "One-two-three ... infinity". Your school library should also have "The World of Mathematics", the four-volume set edited by James Newman. Another thing that is equivalent to supplementary reading is the possibility of some of your students attending some technical society meetings. I personally think there are too many technical societies in this area but at least you can't complain that they are unavailable. There is the Canadian Institute of Chemistry, about every kind of engineering society imaginable, and all kinds of trade associations like the Canadian Pulp and Paper Association. Student nights are pretty such an untapped field here.
Get your school library to get "Endeavour". This is published in England by the I.C.I., and you can ask C.I.L. for it here. A lot of it will be over your head and mine but I'll bet that there will be half a dozen articles a year from which some of your students (and this time I did not say pupils) will really learn. In the case of Endeavour I'm talking about science as a whole and specifically including Zoology and Botany.
Suggesting supplementary reading involves work because, to be intelligent about it, you must have read it yourself. But you will get very close to the ideal of teaching which Kahlil Gibran set out in "The Prophet",
"No man can reveal to you aught but that which already lies half asleep in the dawning of your knowledge.
The teacher who walks in the shadow of the temple, among his followers, gives not of his wisdom but rather of his faith and his lovingness.
If he is indeed wise he does not bid you enter the house of his wisdom, but rather leads you to the threshold of your own mind."
The seventh "how" brings us face to face with examinations. What is the object of examinations? If you answer "to find out what the pupils know" I can give you at "best only a minimum pass mark. If you add "and to find out how much I've taught him" that will add to your rating. To get a really good mark on my marking scheme you will have to add - "and especially find out how well he can tell somebody else what he does know". Speaking from experience in the fields of my own competence, there is nothing which holds back individual progress, both as scientific accomplishment and as monetary reward, to a level below the individual's capabilities more than inability to convey information lucidly and accurately. So I suggest you get your students to regard examinations as a problem in communications! It can be done. Peter MacLaurin in Belleville didn't put it just that way but he had his own schemes to do the trick. One was to have a few bonus marks (perhaps five) available. I still remember his teaching in third form (now Grade XI) the "law" of multiple proportions. We talked about it in almost seminar fashion. We wrote down on the blackboard some ways of saying the ideas involved. Then he dictated the way he would say it and then he added "On the next exam there is going to be a question asking for several of the laws which state how chemical elements combine. If you give me back the words I have dictated I'll give you full marks but there will be one bonus mark for each law which you formulate correctly in your own words".
A second method is to try to get your students to answer exam questions as if they were explaining things to a stranger or, better still, as if they were teaching things to a stranger. I'd suggest you keep and compile examples where examination answers don't get full marks because of poor explanation (not just plain ignorance). You can use these in later years without embarrassment to anyone and in particular cases may be a little private coaching with the student concerned wouldn't be asking too much. The knowledge that there were departmental exams ahead to be marked by a stranger did a lot in my collegiate days to help this.
Thomas Traherne showed the importance of communications well in his quaint poetry:-
"All things to Circulations owe
Themselves; by which alone
They do exist; they cannot show
A sigh, a word, a groan,
A colour or a glimpse of light;
The sparkle of a precious stone,
A virtue, or a smell; a lovely sight,
A fruit, a bean, an influence, a tear,
But they another's livery must wear;
And borrow matter first,
Before they can communicate."
When communications fail sometimes people get hurt. And this reminds me about a little girl - a little girl about five. She had a couple of older brothers. From them she'd learned to communicate in a very colourful language - so colourful as to be a source of considerable anxiety to her parents - as well as to parents of her playmates. She was invited to a party at the home of a playmate whose parents were particularly careful people. Her mother and father cautioned her early in the morning to be on her good behaviour and threatened her with dire things if she should stray from the straight and narrow. They went further - they called the parents of her playmate to request that she be sent home immediately if her language got out of bounds.
The party was to be held at three. At five minutes after three, Sal was home. Her mother met her at the door. When Sal attempted to speak, she said, "Not one word out of you, young lady - straight upstairs until your father comes home." When the father came home, he was told what had happened - as he went upstairs he rolled up his sleeves to administer the spanking. As he walked in the door, Sal tried again to speak, but again she was told, "Not one word out of you, young lady - you're going to get the spanking of your life." When it was an over, she said, "And now can I speak?" At the nod of her father's head, she said, "The God-damned party ain't until tomorrow!"
A third method, and one of the best, involves reading well written books. These should not be scientific. Old classics like Treasure Island, the Jungle Books, and Lorna Doone are classics precisely because they are well written. Read them. Read Winston Churchill's books. And especially - very especially - read poetry, although I admit that poetry should be read aloud..
Now please don't tell me that this ideal kind of communications cannot be accomplished under examination conditions. This year at this collegiate Donna Youngblut wrote ten Grade XIII papers and had an average mark of over 90 on the ten. As far as I could judge from the printed results in the paper, she was first in the school in seven of these ten papers. No one is denying that Donna Youngblut is a very exceptional student, but you cannot tell me that anyone, exceptional or not, can get marks like 96 in French and 94 in chemistry and in the high 80's in English and 97 in geometry without both knowing her work exceedingly well and being able to "communicate" in the very finest sense of the word. Incidentally Donna intends to become a collegiate English teacher. I would be delighted if she should later decide to switch to science!
The eighth "how" is also a problem in communications from your standpoint. Some of you may not like what I am going to say but it is one of the more important things I want to bring out. Typical collegiate teaching is 99-1/2% directed to the low average mentality of your pupils (and this time I didn't say students). Maybe this is "democratic". I think it is foolishness of the most rankly stupid kind. The magnificent scientific achievement of Sputnik both as pure science and applied science wasn't reached on that basis. Now I don't, even for a moment, believe that this achievement was reached for the propaganda reason of the environment of a socialist-communist system either. But it was reached by orienting capable and brilliantly intelligent minds, the best minds, to a problem of their competence and providing the reward of a standard of living within the economic system of their environment which is competitively desirable and relatively free (and I say relatively) from the dangers attendant on political success under the same system of government. To give attention only to your better students would, of course, be undesirable, short-sighted, and even morally wrong. But the present approach is far too far on the opposite side. It then becomes much worse when mass production methods require dictated notes to be memorized and parroted back for marks on examinations set and corrected by the same teacher. Now some facts have to be memorized but if you want to induce failures at a subsequent university level of those who go on, presumably because they are your more capable students, I can't think of a more effective way to do it. I personally blame an appreciable part of the distressing failure rate in early university years on this kind of hack unthinking that only does dishonour to the word "teacher" and the profession of teaching.
Maybe this is the place to review the suggested "hows", -
I cannot close, however, without combining the "how" with the "what". Somewhere you must correlate science with humanity. I can illustrate best by an example, as example in poetry because it is often in poetic language that such truths are best given. In his Testament of Beauty Robert Bridges wrote,-
"Lov'st thou in the blithe hour of April dawns - nay marvelest thou not - to hear the ravishing music that the small birdes make in garden or woodland, rapturously heralding the break of day; when the first lark on high hath warn'd the vigilant robin already of the sun's approach, and he on slender pipe calleth the nesting tribes to awake and fill and thrill their myriad-warbling throats praising life's God, until the blissful revel grow in wild profusion unfeign'd to such a hymn as man hath never in temple or grove pour'd to the Lord of heaven?
Hast thou then thought that all this ravishing music, that stirreth so thy heart, making thee dream of things illimitable unsearchable and of heavenly import, is but a light disturbance of the atoms of air, whose jostling ripples, gather'd within the ear, are tuned to resonant scale, and thence by the enthron'd mind received on the spiral stairway of her audience chamber as heralds of high spiritual significance? and that without thine ear, sound would have no report, nature have no music; nor would there be for thee any better melody in the April woods at dawn than what an old stone-deaf labourer, lying awake o' night in his comfortless attic, might perchance be aware of, when the rats run amok in his thatch?"
Yes, I dare to suggest that you read that to your science classes.
You teach about light. Do you teach, as you should, that when it is required to specify
fully the colour of any object, this colour must be defined wave length by wave length
throughout the spectrum, and, at each wave length, the significant quantity is the product
of three factors, namely the intensity of the light emitted from the source multiplied by
the capability of the object to reflect the light received by it and the product of these in
turn multiplied by the ability of the human eye to see the light so reflected.
Mathematically
Yw = Ew
Rw Sw
Having done that, do you suggest also what this means? There is no knowledge for
us (because light symbolizes knowledge) save that which (directly or indirectly) is sent
towards us, and of this only that portion which the whole universe around us is capable of
reflecting, and of this only that portion which we are capable of receiving. And this is
true wave length by wave length - entity of knowledge by entity of knowledge.
Finally - if you teach, as you must, that the method of science is necessarily seeking that which we do not know, also remember that we search towards that which is ultimately true. la this search the knowledge of order, of cosmos and not chaos, overwhelms us with a sense of wonder. Don't be ashamed to express that wonder. The whole testimony of the ages confirms it. Thus many years ago the Psalmist proclaimed in his own tongue and continues to proclaim in ours -
"The Heavens declare the glory of Godj and the firmament sheweth his handywork.
Day unto day uttereth speech, and night unto night sheweth knowledge.
There is no speech nor language, where their voice is not heard.
Their line is gone out through all the earth, and their words to the end of the world. In them hath he set a tabernacle for the sun.
Which is as a bridegroom coming out of his chamber, and rejoiceth as a strong man to run a race.
His going forth is from the end of the heaven, and his circuit unto the ends of it; and there is nothing hid from the heat thereof."
If you find that too old fashioned or the language too symbolic, and I do not, the same kind of thing is being said today. Robert Bridges said it:-
"Yeas and how delicat! Life's might mystery sprang from eternal sseds in the elemental fire, self-animat in forms that fire annihilates: all its selfpropagating organisms exist only within a few degrees of the long scale rangeing from measured zero to unimagin'd heat, a little oasis of Life in Nature's desert; and ev'n therein are our soft bodies vext and harm'd by their own small dlstemperature, nor coud they endure wer't not that by a secret miracle of chemistry they hold internal poise upon a razor-edge that may not evsn be blunted, lest we sicken and die."
Your task as teachers has, I think, never been better set out than by Kahlil Gibran.
There came to the Prophet a woman who held her babe against her bosom and she said: - "Speak to us of Children." And he said;
"Your children are not your children.
They are the sons and daughters of
Life's longing for itself.
They come through you but not from you,
And though they are with you yet they belong not to you.
You may give them your love but not your thoughts,
For they have their own thoughts.
You may house their bodies but not their souls,
For their souls dwell in the house of tomorrow, which you cannot visit, not even in your dreams.
You may strive to be like them, but seek not to make them like you.
For life goes not backward nor tarries with yesterday.
You are the bows from which your children as living arrows are sent forth.
The archer sees the mark upon the path of the infinite, and He bends you with His might that His arrows may go swift and far.
Let your bending in the Archer's hand be for gladness;
For even as he loves the arrow that flies, so He loves also the bow that is stable."
Here then are the challenges and rewards of science - a dynamic becoming, never a
passive being and with all that this implies, -
all its eggheadedness and all its simplicity,
all its frustrations and all its joys,
all its poverty and all its riches,
all its failures and all its triumphs,
but ever and always "Ah, but a man's reach should exceed his grasp or what's a
heaven for" for science is a part of the stream of life.
A presentation to the Ontario Secondary School Teachers' Federation Science section, Niagara Region.