Visualizing the Arithmetic of Complex Numbers

Autor/in	Soto-Johnson, Hortensia
Titel	Visualizing the Arithmetic of Complex Numbers
Quelle	In: International Journal for Technology in Mathematics Education, 21 (2014) 3, S.103-114 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1744-2710
Schlagwörter	Arithmetic; Mathematics Instruction; High School Students; Secondary School Mathematics; Geometric Concepts; Algebra; Computer Software; Educational Technology; Numbers; Addition; Subtraction; Multiplication; Teaching Methods; Visualization; Summer Programs; Females; Concept Formation + Suchen Sie Ihr Suchwort? Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematics lessons; Mathematikunterricht; High school; High schools; Student; Students; Oberschule; Schüler; Schülerin; Studentin; Elementare Geometrie; Unterrichtsmedien; Zahlenraum; Subtraktion; Multiplikation; Teaching method; Lehrmethode; Unterrichtsmethode; Visualisation; Visualisierung; Sommerkurs; Weibliches Geschlecht; Concept learning; Begriffsbildung
Abstract	The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and algebraic representations. The purpose of this article is to share Geometer's Sketchpad labs, where students can unearth a geometric interpretation of the arithmetic of complex numbers and their relationship to transformations. With dynamic technologies, students can discover that (1) addition and subtraction of complex numbers corresponds to a translation of the complex plane, (2) multiplication corresponds to a rotation and dilation of the complex plane, and (3) division of complex numbers corresponds to the composition of a reflection about the real axis and dilation of the complex plane. Furthermore, I illustrate how such activities may potentially enrich classroom dialogue. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10