A PROBLEM AND ITS NUMERICAL SOLUTION
W. W. Sleater
1920
School Science and Mathematics
Not long ago when a somewhat unexpected assertion was made in a college physics class, a student inquired whether that result was practical or "only theoretical." That some ideas are practical, useful, and important, while others, though true enough, are theoretical, and therefore of no consequence, has always been a common conviction. No doubt such a distinction exists, but the conviction is objectionable when it is felt, if not precisely maintained, that a result is useless because it is
more »
... etical. The same sort of comparison exists in the public mind between academic results and practical ones, a comparison having its perfect expression in the remark of Mr. Shaw that those who can, do, while those who can^t, teach. No one who recognizes that teaching itself is doing will feel the sting of Mr. Shawls irony. For others it is perhaps intended and by them no doubt deserved. It has, however, been generally supposed that an "academic" result savors of seclusion and perhaps of luxurious other-worldiiness. Though the work of scientists in the war may have modified or partially removed that notion, it still lives, and it is not altogether groundless. Such truth as there may be in the belief that academic conclusions are of negligible importance arises from the fact that the problems assigned and solved in school and college are always selected. They are carefully chosen, made up on purpose even, like chess problems, rather than taken at random from everyday experience. The rigor of the selection is very real to the teacher who supplements his textbook by outside examples. One hesitates to give to his class a problem he himself has not solved he hesitates, at least, after having the not uncommon experience of being unable to answer his own question. There is, of course, a legitimate reason for this selection. One does hot assign to beginners in algebra a problem involving quadratics. But there is also a motive in the exclusion of problems which is at best doubtful. Students have been known to despair of the correctness of a solution because the answer does riot "come out even." To conserve their time, and to keep his pupils in a comfortable and hopeful frame of mind a teacher may exercise more than paternal vigilance over the tasks assigned. The process of selection m^y exclude the common and so to speak unexpurgated questions which arise
doi:10.1111/j.1949-8594.1920.tb07819.x
fatcat:hvbcbakbzrhxnewxn4i6fzud4e