What is the aim of school?

A recent comment on one of our posts raises the question of what teachers are trying to achieve in school.  The answer varies.  In a comment on our recent post about students’ strategies for surviving school, Mr. Celarier raised the question of what school was trying to achieve.  Considering as an example a physics class, he asks (quite reasonably) “what is a thorough understanding of F=ma?” and suggests that one aim of education is to have the student realize that no education is finished.  With this idea we haven’t the faintest quarrel.

But having been classroom teachers ourselves we are painfully aware of some practical limitations involved.  There is always the limit of time (hours in a day and weeks in a term) and the fact that a class will have students of diverse types, both in raw ability and in style of learning.  Moreover, as we’ve mentioned before, the purpose of a class will vary.

A beginning calculus-based physics class in college will normally be taken by science and engineering majors.  For each of them, a grounding in basic mechanics and electromagnetism will be followed by later courses building on it.  The student must be able to deploy the Newtonian arsenal of concepts and mathematics in other contexts.  An appreciation of the historical context of Galileo and Newton and of their intellectual achievement would be nice, but is not essential.

A prerequisite for such a class is a semester or more of calculus, taught of course by a mathematician.  The students in follow-on courses must be able to use calculus to solve problems in physics; an appreciation of the rigor of the definition of a limit would be nice, but not necessary to learn the physics.  In the calculus class and the beginning physics class the aim is to give students tools for later use.  There is rarely time for much more, though the occasional historical sidelight may help humanize the subject.

Later courses may bring in an appreciation of the historical context, and of the intellectual achievement made by Newton and everyone else.  Courses in quantum mechanics are especially good at getting students to ask what they do understand, and how.

It would seem obvious that pre-college courses in mathematics aim at the same kind of “toolbox” learning.  Algebra is, after all, utterly vital to calculus, as is trigonometry, and many a physics problem rests on a diagram whose essence is geometry.  But not all students in algebra go on to calculus, and a minority of geometry students will wind up doing physics.  Here the aim (expressed or implied) must be different.  We have suggested that the value in having all secondary school students master a level of mathematics many will never need is indirect.  You may never need to prove some obscure fact about triangles, but the idea of a rigorous deduction from premises is itself invaluable.  And flexing the mental muscles in any way probably helps them gain and keep strength.

There are no doubt other aims for other classes, some of which you can come up with yourselves.