"Counting" on Quantitative Reasoning for Algebra

Autor/inn/en	Burch, Lori; Tillema, Erik S.; Gatza, Andrew M.
Titel	"Counting" on Quantitative Reasoning for Algebra
Quelle	In: Mathematics Teacher: Learning and Teaching PK-12, 114 (2021) 6, S.452-462 (11 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0025-5769
Schlagwörter	Algebra; Mathematics Instruction; Calculus; Mathematics Teachers; Mathematical Logic; Error Patterns; Teaching Methods; Mathematical Concepts; Concept Formation; Secondary School Mathematics; Educational Technology; Technology Uses in Education; Manipulative Materials; Problem Solving; Spatial Ability; Geometric Concepts + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Mathematical logics; Mathematische Logik; Fehlertyp; Teaching method; Lehrmethode; Unterrichtsmethode; Concept learning; Begriffsbildung; Unterrichtsmedien; Technology enhanced learning; Technology aided learning; Technologieunterstütztes Lernen; Hilfsmittel; Problemlösen; Räumliches Vorstellungsvermögen; Elementare Geometrie
Abstract	As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a + b)[superscript 3] = a[superscript 3] + 3a[superscript 2]b + 3ab[superscript 2] + b[superscript 3]" can be generalized from quantitative reasoning in the context of combinatorics problems like the Card Problem (Tillema and Burch 2020). The article then illustrates how the combinatorial reasoning students develop in the Card Problem can support them to see combinatorial structure across algebraic computations. Throughout the article, the authors share work from students and teachers with whom the approach was developed. (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: publicationsdept@nctm.org; Web site: https://pubs.nctm.org/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01