If Only They were Athletes, Part 2

Recently, I read a volume which collected various works on the philosophy of mathematics — New Directions in the Philosophy of Mathematics, ed. by Thomas Tymoczko, Birkhauser, 1985. In an article from the 1950 Proceedings of the International Congress of Mathematicians, pp. 258 -271, the mathematician Raymond Wilder talks about

…drill type of teaching [Which he labels ‘symbolic reflex’ teaching] which may enable stupid John to get a required credit in mathematics but bores the creative minded William to the extent that he comes to loathe the subject! What is the difference between teaching a human animal to take the square root of 2 and teaching a pigeon to punch certain combinations of colored buttons? Undoubtedly the symbolic reflex type of teaching is justified when the pupil is very young–closer to the so-called “animal” state of his development, as we say. But as he approaches maturity, more emphasis should be placed on his symbolic initiative.

Let me put this in a different but largely equivalent way. The modern mind is one which likes to settle in well-worn ruts. A human being with such a mind can see nothing outside of his ruts and he’ll consider education to be a matter of training other minds to travel those same ruts. This is a good way to deform and cripple the minds of those who can think more freely.

We need to nurture curiosity and a healthy imagination in those who show a willingness to move outside of set ruts. There might be a few who carve new ruts — the Einsteins or Beethovens. There will be many more who will climb out of their ruts and find a variety of pre-existing ruts to explore. They might end up as the physicists who further develop the theories of an Einstein or the composers who explore the possibilities raised in the works of Beethoven.

Why don’t schools nurture curiosity and a healthy imagination? Why do they suppress giftedness or even lesser talents? The proximate cause seems clear to me. Those who run the vast majority of public elementary and high schools aren’t particularly interested in any academic subjects. Most of my teachers (I graduated from high school in 1973) would have greatly preferred a quiet evening of television to a quiet evening with a good book. Teachers kept up with the pennet-race but didn’t pay much attention to developments in modern physics or mathematics, didn’t even know what was revealed in the glossy pages of National Geographic Magazine.

The obvious exceptions were notable for being so obvious. And I should acknowledge that the older teachers were more likely to be interested in their subjects and seemingly somewhat competent.

In their favor, many of those teachers I observed were interested in the students as human beings. A good percentage of those many could work effectively with students in the middle, raising them to some modest level of literacy and perhaps general knowledge. Some could work wonders with at least the occasional troubled or disabled student. From what I could see, the teachers in the music department were truly interested in nurturing talented students and also helping the other students to develop some level of competence. Of course, many teachers and not just the coaches were concerned that athletes got the proper opportunities to develop their talents. I also have strong memories of the football coach, Chick Patullo, getting very upset that athletes no longer sang in the chorus or participated in the drama club.

Moreover, we have to consider the age of the student and the material he needs to learn as Professor Wilder noted in the quote at the beginning of this entry. At the elementary level, which should probably end at age 8 or so for talented students, it’s probably appropriate for teachers to be student-centered in order to nurture very general abilities.

What about teachers who were interested in their subjects? There were few at my high school. And it’s such teachers that are needed to guide the students with some academic talent and an inborn curiosity. Such a student can be encouraged to develop a good work ethic — math is hard, but hard work can be fun in academic fields and not just on the playing field.

The talented, those who can be our future physicists or the inventors of new computer technology, those who can make sense of our recent history and those who can plumb the depths of the modern soul in poetic forms, also need freedom of a sort not to be found in the modern American classroom. Such talented students, often bad students by many standard measures, need to be given some basic instruction and then encouraged to seek their own way, finding what interests them and learning to ask for guidance. This is a situation which would strike fear deeply into the heart of a bureaucratic school administrator trained to process young human beings as they were raw material and the schools were factories.

In math and physics classes, a talented student would be better off with only an occasional conventional classroom session to set the stage or provide general guidance. Then give him a list of problems culminating in some difficult ones. Let him find a comfortable place to sit with a small pile of books on the subject, a pad or two, several pencils, and a wastebasket. Provide him with a tutor and hold problem-solving sessions with several students where the leader could even be the most advanced student or one from a higher level. In history or literature, a talented student would be better off let loose in the library with some easy questions to answer, then with some harder questions, then with some for which there’s no certain answer. All of this is preceded and interspersed with large amounts of reading of real books and not text-books.

Why do we have a school system in which talented and enthusiastic students are taught to hate even the fields in which they have talent? Because we have a school system staffed by teachers and administrators who do not themselves like to work hard at the core subjects of a high school education, history and writing and mathematics and the sciences. They don’t seem to even truly understand that there are some amongst the young under their care who actually like math or history or disciplined creative writing (based on lots of reading) or lab sciences.

If only those students were athletes, we’d have noticed their development is being stunted long ago and done our best to nurture their talents.

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