Conceptual Knowledge in Introductory Calculus.

摘要: Responses to word problems involving rates of change were collected on four occasions during and after 24 hours concept-based calculus instruction given a group first-year university students, all whom had studied in secondary school. The number students who could symbolize noncomplex situations increased dramatically. However, there was almost no increase the complex items or that required modeling situation using algebraic variables. Detailed analysis revealed three main categories error, which variables are treated as symbols be manipulated rather than quantities related. We surmise developed an "abstract-apart" concept variable "abstract-general" is needed for successful study calculus. Changes technology, qualifications teachers, mathematical competence have led many question role traditional courses curriculum. There is, particular, much concern about large numbers taking rote, manipulative learning takes place (Cipra, 1988; Steen, White, 1990). value skill-based has also come under fire because computers calculators now perform most (if not all) procedures taught such (Steen, Tall, 1987a). Several studies (Heid, 1988, 1989; Hickernell & Proskurowski, 1985; Judson, 1990; Palmiter, 1991) shown how computer tool performing algebra can free explore applications. Other (Hsaio, 1984/85; 1986) used graphics secants tangents curves order build up sound derivative. general tendency less emphasis skills greater underlying concepts. Research into understanding whole spectrum concepts cause students. In student difficulties with