Algebraic Thinking through Koch Snowflake Constructions

Autor/in	Ghosh, Jonaki B.
Titel	Algebraic Thinking through Koch Snowflake Constructions
Quelle	In: Mathematics Teacher, 109 (2016) 9, S.693-699 (7 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Leitfaden; Unterricht; Lehrer; Mathematics Instruction; Grade 11; Secondary School Mathematics; Algebra; Geometric Concepts; Generalization; Foreign Countries; Mathematical Logic; Mathematical Formulas; Spreadsheets; India + Suchen Sie Ihr Suchwort? Lesson concept; Instruction; Unterrichtsentwurf; Unterrichtsprozess; Teacher; Teachers; Lehrerin; Lehrende; Mathematics lessons; Mathematikunterricht; School year 11; 11. Schuljahr; Schuljahr 11; Elementare Geometrie; Ausland; Mathematical logics; Mathematische Logik; Mathematische Formel; Spread sheet; Spredsheets; Spreadsheet; Tabellenkalkulation; Indien
Abstract	Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both kinds, which are essential for algebraic reasoning. The activity involved thirty grade 11 students exploring the Koch snowflake as a part of the sequences and series topic in their math course. The primary goal was to enable them to visualize geometric sequences by exploring various patterns in the snowflake construction through pictorial, tabular, and symbolic representations and to make connections among them. The activity provided students with opportunities to engage in explicit as well as recursive reasoning. The importance of such reasoning has been articulated in the Common Core State Standards for Mathematics, which states that students studying algebra in grades 9-12 should be able to "write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms" (CCSS1 2010, p. 21). (ERIC).
Anmerkungen	National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01