RETHINKING CALCULUS : LEARNING AND THINKING

1. REMODELING CALCULUS THE INSTITUTION. Surely the renewal of Calculus is a good idea, one good enough to attract the attention and energy of many good people. But this is Calculus the Institution that peculiarly American academic event and all its supporting structures and expectations. Professor Knisely, however, barely hints at matters of institutional implementation, so I conclude that he is addressing Calculus, the System of Knowledge and Technique. As such, his paper is, perhaps, a warm-up exercise to a deep and long overdue reconsideration of the appropriate intellectual content of Calculus, one that has been postponed while we attempt to remodel Calculus the Institution. This remodeling has proven to be an arduous task for two reasons: (1) the renovation is taking place whilst the owners and stakeholders continue to inhabit the institution (a constraint applying to most educational reform); and relatedly (2) we have left all the larger structural features of the institution intact, including those features that connect it to the outside world, e.g., to the rapidly changing K-12 education. The basic architecture and its place in the larger world are untouched. I suggest that we embark on the more fundamentaJ rebuilding towards which Knisely points. In so doing we need to come to terms with the relations, existing and possible, between Calculus the Institution (C-INST) and Calculus the System of Knowledge and Technique (C-KNOWL). And we need to look more deeply and critically at the assumptions, largely tacit, that hold the status quo in place and provide some concrete, implementable alternatives.