2 canbeinterpr etedassayingthattheareaundertheg raphof between and liesbetweentheareaof theinscribedrectang leandtheareaof thecirumscribedrectangl e.F orinstance, N ewton 0 sproof of theF irstF undamentalT heoremof theC alculus ( FFTC ) usesthisf actfor aninf initesimalinterval, andthenar guesthattheareacanberealiz edastheareaof someintermediaterectanglebetw eentheinscribedandthecirumscribedone see (ibid. I nfact, r elation istakentobeesseantialf orintegr ationandrelation1. While mathematical truths remain, mathematical justifications (proofs) change dramatically and increase in complexity.ģ pez. Sullivan's claim of an observed "advantage" when referring to the improved understanding of non standard calculus students (as opposed to the standard approach of Weierstrass) is a consequence to the accepted fact that mathematical truths remain the same when changes of paradigms ensue, a situation markedly different from that science. ![]() Our proposal is based on ideas of Kitcher and Kuhn and allows us to better understand the didactics of Calculus. In this essay we propose a definition of the notion of cognitive advantage mentioned by Sullivan in expressing the dramatic differences in understanding of students of non standard calculus as oppossed to those of its standard counterpart. ![]() Our research added to her's results related to the teaching of the elementary integral, with similar positive results. Sullivan's initial results as stated in her epoch making study about the effectiveness of teaching elementary calculus using Robinson's non standard approach.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |