This paper starts with some philosophical ruminations about perception and notions and moves into a reconstruction of Newton's "thought" that lead him to his proof of the fundamental theorem of Calculus. This reconstruction is highly speculative and relies on no primary evidence. The paper discusses an attempt to encourage students to come to the fundamental theorem of the calculus on their own via intuitions of rate of change, rate of accrual, and Riemann sums. The author concludes that students' difficulties come from three primary factors: inaccuracy in the idea of a function, the tendency to see accruals as solitary objects instead of as accruing at a rate, and inaccuracies in the scheme of an average rate of change. (NS/JDA).
Zie ook de twee artikelen met andere Thompson in JRME 27(1) & JRME 25(3). Die gaan echter meer in op het belang van `conceptual teaching' m.b.v. klassegesprekken en hoe je docenten zo ver kunt krijgen dat ze leerlingen `conceptueel' leren.
Zie ook Thompson (1994) The development of the concept of speed and its relationship to concepts of rate: voor interpretaties van `rate of change' en `average speed' door leerlingen.