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ERIC Number: EJ1299587
Record Type: Journal
Publication Date: 2021-Jun
Pages: 14
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1863-9690
EISSN: N/A
Available Date: N/A
Teaching Calculus with Infinitesimals and Differentials
Ely, Robert
ZDM: Mathematics Education, v53 n3 p591-604 Jun 2021
Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy = 2x·dx is a relationship between increments of x and y, making dy/dx an actual quotient rather than code language for [equation omitted]. An integral [equation omitted] is a sum of pieces of the form 2x·dx, not the limit of a sequence of Riemann sums. One goal is for students to develop understandings of calculus notation that are imbued with more direct referential meaning, enabling them to better interpret and model situations by means of this notation. In this article I motivate and describe some key elements of differentials-based calculus courses, and I summarize research indicating that students in such courses develop robust quantitative meanings for notations in single- and multi-variable calculus.
Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link-springer-com.bibliotheek.ehb.be/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A