Technology-Enabled Pedagogy as an Informal Link Between Finite and Infinite Concepts in Secondary Mathematics

dc.creator	Sergei Abramovich
dc.creator	Anderson Norton
dc.date	2000-01-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:22:39Z
dc.date.available	2015-07-20T22:22:39Z
dc.identifier	1062-9017
dc.identifier	https://doaj.org/article/b79a9513028843299390919f7018800a
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/20747
dc.description	This paper is a reflection on activities designed for computer-enhanced in-service training of high school mathematics teachers. The goal of these activities is two-fold: to promote advanced mathematical thinking, and to introduce new uses of existing technology tools. The authors suggest using jointly a computer-based graphing calculator, a dynamic geometry program, and a spreadsheet program in exploring linear algebraic equations to bridge finite and infinite mathematicsstructures. A linear algebraic equation may be introduced in the context of mathematically modeling a uniform movement. In turn, in the technology-rich environment, solving a linear algebraic equation can be introduced through the method of iterations that ultimately leads to the discussion of infinite processes. This opens a window on the complexity of infinite structures, which includes the convergent, divergent and cyclic behavior of iterative sequences. Computerenhanced representations of infinite processes include bisector-bounded staircases and cobweb diagrams, animated pencils of straight lines, and iterations of sequences both in numeric and graphic notations.Finally, by exploring a piece-wise linear recursion, one can arrive at the frontiers of mathematical knowledge, and, in developing mature concepts of convergence, divergence and cycles, experience how chaos—aremarkable phenomena of modern mathematics—can arise in dynamic systems of a surprisingly simple form.
dc.publisher	University of Georgia
dc.relation	http://math.coe.uga.edu/TME/Issues/v10n2/3abramovich.pdf
dc.relation	https://doaj.org/toc/1062-9017
dc.source	Mathematics Educator, Vol 10, Iss 2, Pp 36-41 (2000)
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Education
dc.subject	L
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Science
dc.subject	Q
dc.subject	Mathematics
dc.subject	QA1-939
dc.title	Technology-Enabled Pedagogy as an Informal Link Between Finite and Infinite Concepts in Secondary Mathematics
dc.type	article