p. 34: "a model is just the intermediary by which a complex reality or theory is idealised or simplified in order to become accesible to more formal mathematical treatment" within a task setting with a purpose. See modelling as See Cobb, Paul (1999) defines it.
Van Calculus & Analysis naar Differential and Integral Methods.
"Neither Calculus nor Analysis is included in this overview, not because I have renounced comprehensiveness, but because both of them, if taught at all, should be preceded didactically by something I propose to call Differential and Integral Methods. This topic deserves a place in an early stage of the learning process where algorithmisation has not yet been developed far enough as to allow teaching Calculus or even Analysis. It is an approach (in principle by graphic representations) initially merely qualitative and later on quantitatively refined (if possible). It aims at understanding and interpreting such ideas as the steepness of a graph and areas covered by the moving ordinate segment, maybe even curvature, in contexts where the drawing of the curve mathematises a given situation or occurrence in primordial reality --we hardly need stress the vast opportunities here for reinvention. In our exposition, Calculus is better discussed alongside with algorithms. Analysis was once invented as a safeguard against false Calculus. It still waits for justifying as a subject at Highschoollevel. By justification I mean guiding the learner to avoid the pitfalls of automatically applied Calculus by reinventing more critical Analysis. As long as I have yet to see any didactical attempt at repeating this very historical origin of Analysis, I think that "Differential and Integral Methods" is a didactically more trustworthy safeguard than Analysis can be trusted to be."
"Calculus was invented as an algorithm"
"Reinvention is here a bigger problem than in the domains I have dealt with so far. Reinventing something that since Archimedes has waited for about two millenia to be invented the first time is not that easy. It requires stronger but nevertheless more subtle guidance. It seems to me that we are just beginning to understand and tackle this problem."