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ERIC Number: EJ1450694
Record Type: Journal
Publication Date: 2024-Dec
Pages: 13
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1863-9690
EISSN: EISSN-1863-9704
Actualizing the Virtuality of the Cauchy-Riemann Equations
Hortensia Soto; Leonardo Abbrescia; Adam Castillo; Laura Colmenarejo; Anthony Sanchez; Rosaura Uscanga
ZDM: Mathematics Education, v56 n7 p1389-1401 2024
In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors, himself, and his students. We found that the mathematician's creative introduction of matrices led to a discussion of transformations which made the CR equations mobile and hence gave him a space to virtualize the CR equations. In our results we summarize how the mathematician's assemblage of "unusual, unexpected, and unscripted," and "without given content" creative acts with materials embedded in algebraic and geometric inscriptions and metaphors "introduced or catalyzed the new"--the virtuality of the CR equations. In our discussion, we highlight how the mathematician bridged the virtual with the abstract via his conceptualizations of the CR equations. Didactic implications include adopting the mathematician's conceptualizations and asking students to bind them. This could stress the mobility of conformal maps which are generally not taught in an undergraduate class. We propose offering professional development for educators focused on learning how to engineer didactic practices that showcase mobility, support binding, and exhibit animation of mathematical concepts.
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://bibliotheek.ehb.be:2123/
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF); National Science Foundation (NSF), Division of Mathematical Sciences (DMS)
Authoring Institution: N/A
Grant or Contract Numbers: 2103136