Research to Practice: Developing the Amplitwist Concept. Issue 5 (28th May 2019)

• Record Type: Journal Article
• Authors: Soto-Johnson, Hortensia; Hancock, Brent
• Is Part Of: PRIMUS. Volume 29:Issue 5(2019)
• Page Start: 421
• Page End: 440
• Publication Date: 2019-05-28
• Subjects: Amplitwist -- complex analysis -- derivative -- GSP; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2018.1477889
• Languages: English
• ISSNs: 1051-1970

Abstract

Abstract: Although students may develop extensive geometric intuition about derivatives during calculus, many complex analysis texts avoid geometric connections between the real and complex derivative. In this report, we discuss our implementation of, and student responses to, a Geometer's Sketchpad lab that was informed by mathematics education research. This lab served to guide students towards discovering a geometric description of the complex derivative known as the amplitwist, and connecting this interpretation to the derivative of a real-valued function. We hope that instructors adopt aspects of this lab to promote a more dynamic, geometric perception of complex differentiation.