Tag: education

An interesting thought: people aren’t stupid

I don’t generally talk or write about being a doctor – it’s mawkish and tedious, and I’ve no desire to preach from author­ity – but working in the NHS you meet patients from every conceivable walk of life, in huge numbers, discussing some of the most important issues in their lives. This has consistently taught me one thing: people aren’t stupid. Anybody can understand anything, as long as it is clearly explained – but more than that, if they are sufficiently interested. What determines an audience’s understanding is not so much scientific knowledge, but motivation: patients who are ill, with an important decision to make about treatment, can be very motivated indeed.

But journalists and miracle-cure merchants sabotage this process of shared decision-making, diligently, brick by brick, making lengthy and bogus criticisms of the process of systematic review (because they don’t like the findings of just one), extrapolating from lab-dish data, misrepresenting the sense and value of trials, carefully and collectively under­mining the nation’s understanding of the very notion of what it means for there to be evidence for an activity. In this regard they are, to my mind, guilty of an unforgivable crime. [335]

The “baffled boffins” narrative

My basic hypothesis is this: the people who run the media are humanities graduates with little understanding of sci­ence, who wear their ignorance as a badge of honour. Secretly, deep down, perhaps they resent the fact that they have denied themselves access to the most significant developments in the history of Western thought from the past two hundred years; but there is an attack implicit in all media coverage of science: in their choice of stories, and the way they cover them, the media create a parody of science. On this template, science is portrayed as groundless, incompre­hensible, didactic truth statements from scientists, who themselves are socially powerful, arbitrary, unelected authority figures. They are detached from reality; they do work that is either wacky or dangerous, but either way, everything in science is tenuous, contradictory, probably going to change soon and, most ridiculously, ‘hard to understand’. Having created this parody, the commentariat then attack it, as if they were genuinely critiquing what science is all about. [225]

Science teaches thinking

The idea of the outward-looking, self-transcending stance expressed itself in two connected ways for Russell. One related to science, the other to personal relationships and the individual’s attitude to others in general. In regard to science, the objectivity and scope of science is obviously such as to make individual self-concern a very minor if not indeed nugatory thing. In the essay ‘The Place of Science in a Liberal Education’ Russell worte, ‘The kernel of the scientific outlook is the refusal to regard our own desires and interest as affording the key to the understanding of the world’, and this immediately entails that the disciplines of reason and evidence are the sole legitimate determinants of thinking in general. [69-70]

The chief end of man

His own culture—the unfolding of his nature, is the chief end of man. [271]

Measuring student progress

After teaching 10 years, the only good measure of student progress I know is the number of open problems they can successfully characterize.

What counts in the future

Perhaps the greatest of all pedagogical fallacies is the notion that a person learns only the particular thing he is studying at the time. Collateral learning in the way of formation of enduring attitudes, of likes and dislikes, may be and often is much more important than the spelling lesson or lesson in geography or history that is learned. For these attitudes are fundamentally what count in the future. The most important attitude that can be formed is that of desire to go on learning. If impetus in this direction is weakened instead of being intensified, something much more than mere lack of preparation takes place. The pupil is actually robbed of native capacities which otherwise would enable him to cope with the circumstances that he meets in the course of his life. We often see persons who have had little schooling and in whose case the absence of set schooling proves to be a positive asset. They have at least retained their native common sense and power of judgment, and its exercise in the actual conditions of living has given them the precious gift of the ability to learn from the experiences they have. What avail is it to win prescribed amounts of information about geography and history, to win the ability to read and write, if in the process the individual loses his own soul; loses his appreciation of things worthwhile, of the values to which these things are relative; if he loses the desire to apply what he has learned and above all, loses the ability to extract meaning from his future experiences as they occur? [48-9]

Theirs not to reason why

The traditional scheme is, in essence, one of imposition from above and from outside. It imposes adult standards, subject-matter, and methods upon those who are only growing slowly toward maturity. The gap is so great that the required subject-matter, the methods of learning and of behaving are foreign to the existing capacities of the young. They are beyond the reach of the experience the young learners already possess. Consequently, they must be im­posed; even though good teachers will use devices of art to cover up the imposition so as to relieve it of obviously brutal features.

But the gulf between the mature or adult products and the experience and abilities of the young is so wide that the very situation forbids much active participation by pupils in the development of what is taught. Theirs is to do—and learn, as it was the part of the six hundred to do and die. Learning here means acquisition of what already is incorporated in books and in the heads of the elders. Moreover, that which is taught is thought of as essentially static. It is taught as a finished product, with little regard either to the ways in which it was originally built up or to changes that will surely occur in the future. It is to a large extent the cultural product of societies that assumed the future would be much like the past, and yet it is used as educational food in a society where change is the rule, not the exception. [18-9]

How to train your chimpanzee

The main problem with school mathematics is that there are no problems. Oh, I know what passes for problems in math classes, these insipid “exercises.” “Here is a type of problem. Here is how to solve it. Yes it will be on the test. Do exer­cises 1−35 odd for homework.” What a sad way to learn mathematics: to be a trained chimpanzee.

But a problem, a genuine honest-to-goodness natural human question—that’s another thing. How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them).

A good problem is something you don’t know how to solve. That’s what makes it a good puzzle, and a good oppor­tunity. A good problem does not just sit there in isolation, but serves as a springboard to other interesting questions. A triangle takes up half its box. What about a pyramid inside its three-dimensional box? Can we handle this problem in a similar way?

I can understand the idea of training students to master certain techniques—I do that too. But not as an end in itself. Technique in mathematics, as in any art, should be learned in context. The great problems, their history, the creative process—that is the proper setting. Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea, then give them some technique. But not too much. [40-2]

The art of explanation

By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity—to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs—you deny them mathe­matics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m com­plaining about the lack of mathematics in our mathematics classes. [29]

An educational utopia

If I thought of a future, I dreamt of one day founding a school in which young people could learn without boredom, and would be stimulated to pose problems and discuss them; a school in which no unwanted answers to unasked ques­tions would have to be listened to; in which one did not study for the sake of passing examinations. [40]