Over the semester I have been reading and enjoying Michael Strong’s The Habit of Thought: From Socratic Seminars to Socratic Practice. I was struck today by a quotation Strong draws from Peter Drucker’s Innovation and Entrepreneurship:
“We have known, for instance, for several hundred years that mathematics is a problem subject in school. A small minority of students, certainly no more than one-fifth, seem to have no difficulty with mathematics and learn it easily. The rest never really learn it … . In every generation there is a mathematics teacher of genius who somehow can make even the untalented learn, to at least learn a great deal better. But nobody has ever been able, then, to replicate what this one person does. The need is acutely felt, but we do not understand the problem” (quoted in Strong, p. 166).
An analogous anecdote from my experience teaching Logic to college students. After the first few years of teaching the course, I noticed a grade pattern that has remained consistent over the years:
A minority group of students will get an A in the course, apparently without much effort.
A majority of students will, with effort, get a C or a low B.
Another minority will either drop the course early on or not try consistently and get an F.
Thoughts?
My wife has been in math education for 5 years and I have taught for two. In our experience the 20/80 principle is in play.