High and low
We find challenges at each end of teaching.
Our tutoring consultant has been out of school a long time, and even applying for grad school seems like a geological age ago. For this reason (mainly) he avoids, as much as he can, getting involved in questions like, “What courses should I take next term?” To answer such things requires a detailed knowledge of syllabi, prerequisites and how college entrance boards look upon High School transcripts, which he lacks almost completely. (Plus, most important, one needs a deep understanding of the student’s capabilities; which he attains only after the fact.) But since he is good at math, he’s assumed to be good at everything else, and he has lately fielded a parent’s question about which Calculus course to take next year. Mostly he expressed unwillingness to go against the High School’s policy, though he did leave open the possibility of supporting a more ambitious scheme.
A separate request came concerning a “math camp,” for which he was given some sample problems. The formal level of knowledge required for this camp was not intimidating; it could be attained by most High School students without trouble. But the use to which these tools would be put was hardly textbook-problem material. Students were invited to do imaginative, creative things, rather like real mathematicians: seeing where a definition led, finding patterns that might be general, eventually proving that something was true or not. The question to him was: can we support this as we do classes in school? The answer was: no, but I wish we could. Every teacher would love to lead (not “teach”) a class in which the students find out everything for themselves, motivated by curiosity and limited only by imagination. For reasons of practicality, few actually do so.
These two requests struck our tutor as the extremes of our educational system. In the first, the fine-grained details of class designations and syllabus were scrutinized. Actual mathematics was almost absent; most important was checking the right boxes and managing perceptions. Practical considerations were uppermost. In the second, there was the prospect of learning and doing quite unexpected, but wonderful, things; though not the certainty. Our tutor can name students (though he never would) who would be quite lost in the math camp, able to solve canned problems but not knowing how to begin open ones.
We’ve mentioned before that different classes can have different purposes. There are those that provide you with tools and those that provide you with inspiration, and confusing the two brings frustration. So perhaps sometimes we need to pay attention to the structure and progression of course-numbers, comparing syllabi and prerequisites, paying attention to college application guidelines; leaving curiosity-driven learning to another time. And good students will thrive in any environment. But now and then we’re still convinced that there’s much to improve in our educational system.
