I’ve been teaching math at the local community college for several semesters now. My first course was a finite math course, with non-math, non-science majors being the primary target. One of the things that immediately struck me about the book was its apparent backwardness: in introducing a new concept, the book would invariably present some examples, then posit a definition of sorts, then enumerate any steps or processes involved. I was extremely puzzled by this order of presentation. Why on earth throw up some examples before defining or even describing whatever it is that you wish to illustrate? I simply didn’t get it.
Since then, I’ve had several other courses: business calc, probability & stats, “quantitative literacy,” math for elementary ed teachers (the latter being a whole ‘nother story in itself). All of these books followed the same order of presentation – bass-ackwards. I couldn’t fathom why, and I merely continued preparing my lectures in a more logical format: definition, example, steps, problem.
Concurrently, I’ve been reading more about the current state of the American educational system. A common theme seems to be how the progressive-constructivist philosophy has by and large supplanted the traditional, instructivist methods in the classroom. This philosophy, in turn, has resulted in less and less actual learning taking place in our schools, a phenomenon I’ve noticed as a community college instructor and as a private tutor.
I didn’t put two and two together, though, until the other day, then it dawned on me: the textbooks for the courses I’ve been teaching have all been written by authors who have imbibed from the constructivist well. They’ve bought into Piaget’s odd little notion that knowledge is not “true” knowledge unless you’ve “constructed” or discovered it yourself. Aha – so that’s why these crazy books obdurately insisted on placing examples before giving any definitions or enumerating any steps. That explains that.
I still don’t get it, though.