Not even suggestions

Our tutor’s activities sometimes depart from the syllabus.

Most of what our tutor does is based on a carefully structured plan.  For support of classwork, especially in math and science, there is the syllabus: what topics will be covered in what order and in what depth and sophistication.  For standardized tests, the material he administers is also compartmented and ordered.  This is all quite necessary.  For students to absorb and remember such a great mass of information and skills, there has to be order and organization.  Mathematics especially is cumulative: one level of learning is necessary for work at the next level.  A very important activity is the detection and fixing of holes in a student’s background.

This does not mean there is always a sort of deductive-mathematical structure.  The days are past when students learned Latin, say, from a set of grammatical rules committed to rote memory; even Geometry is no longer taught by Euclid’s propositions.  Much more effective ways of teaching have been found.  However, what a student needs to master is still well set out, through High School and well into college.

But, like any teacher, our tutor is acutely aware that his students are imaginative and curious.  Of course he very much wants to encourage this.  He is not alone in this desire, and there are approaches to Chemistry and even mathematics in which the student is invited to experiment and find patterns without being told what they are.  His experiences with these have not all been successful.  Insight, he finds, does not come to everyone; the “Aha!” moment cannot be manufactured to order.  Some students just remain confused.

For his part, he has added some activities in the certain knowledge that most students will get nothing from them.  Perhaps some will have no effect whatsoever.  One that takes quite a bit of time and effort is an accumulation of articles from scientific and other magazines, on a wide range of topics but well-written and well-reasoned.  Over the years this has amounted to a couple of shelves of three-ring binders.  Most are never read.  Some are.

Another activity, requiring far less effort, is the posting of a map or chart (from his extensive collection) on his cubicle wall.  It rarely has a specific relevance to any current syllabus; and in any case, over the week or two it stays up, many different students pass by it.  Most do not notice.  Some do.

Then there is the offhand comment, alluding to something outside the current problem but leading on from it.  He may say something like, “This is true with real numbers, but things get more interesting with complex ones.”  Or, “You have just shown that the p-2 series converges, which is right.  Euler showed that it converges to pi-squared over six.”

These are breadcrumbs thrown out on the chance that a passing bird will see one, and be led toward something interesting by curiosity.  There’s no telling where it will end up.  Which is the point.