By Melvin D. George (auth.), Susan L. Ganter (eds.)

ISBN-10: 1441933344

ISBN-13: 9781441933348

ISBN-10: 1475746989

ISBN-13: 9781475746983

Calculus Reform. Or, as many would favor, calculus renewal. those are phrases that, for larger or worse, became part of the vocabulary in arithmetic departments around the state. The flow to alter the character of the calculus direction on the undergraduate and secondary degrees has sparked dialogue and controversy in methods as varied because the genuine adjustments. Such interactions variety from "coffee pot conversations" to college curriculum committee agendas to important periods on calculus renewal at nearby and nationwide meetings. yet what's the value of those actions? the place have we been and the place are we going with calculus and, extra importantly, the whole scope of undergraduate arithmetic schooling? In April 1996, I bought a fellowship from the yank academic study organization (AERA) and the nationwide technological know-how origin (NSF). This fellowship afforded me the chance to paintings in place of abode at NSF on a couple of assessment initiatives, together with the nationwide impression of the calculus reform circulate considering that 1988. That venture ended in numerous communications with the math group and others in regards to the prestige of calculus as a direction in isolation and as an important participant within the total undergraduate arithmetic and technological know-how adventure for college kids (and faculty). whereas at NSF (and via a moment NSF provide got whereas on the American organization for larger Education), I additionally used to be a part of an assessment venture for the Institution-wide Reform (IR) program.

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In the plane ofthe Kolb cycle (Fig. 1) there are two primary axes, the actionreflection axis (AE-RO) and the concrete-abstract axis (CE-AC). Those axes Renewal in Collegiate Mathematics Education 31 CE Diverger Accommodator AE action reflection Converger RO Assimilator AC Figure 1. Kolb learning cycle. ,15 pp. 131-132): • • • • Converger (AC, AE): strengths include practical applications, single correct answers; unemotional, prefers things rather than people; deductive, focuses on specific problems; likely to specialize in physical sciences or engineering.

The classical application of calculus to such fundamental problems as planetary motion is an important part of its historical development, and modern applications to fluid dynamics or population biology, for example, inspire students with the power of calculus as an analytical tool. Even for students going on to theoretical mathematics, it is important to under- The Goals of the Calculus Course 21 stand the roots of calculus in science; furthermore, the mental exercise of thinking through the interpretation of a concept in realistic contexts helps build understanding of the concept itself.

1). The four stages of this cycle are • • • • Concrete Experience (CE) Reflection/Observation (RO) Abstract Conceptualization (AC) Active Experimentation (AE) The ideal learner cycles through these stages in each significant learning experience. The AE stage represents testing in new situations the implications of concepts formed at the AC stage. Depending on the results of that testing, the cycle starts over with a new learning experience or with a revision of the current one. The ideal learning environment is designed to lead the learner through these stages and not allow "settling" in a preferred stage.

### Calculus Renewal: Issues for Undergraduate Mathematics Education in the Next Decade by Melvin D. George (auth.), Susan L. Ganter (eds.)

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