Two Students' Mathematical Thinking and Activity across Representational Registers in a Combinatorial Setting

Autor/inn/en	Lockwood, Elise; Ellis, Amy B.
Titel	Two Students' Mathematical Thinking and Activity across Representational Registers in a Combinatorial Setting
Quelle	In: ZDM: Mathematics Education, 54 (2022) 4, S.829-845 (17 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Lockwood, Elise)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-022-01352-8
Schlagwörter	Mathematical Concepts; Thinking Skills; Mathematics Instruction; Adolescents; Mathematical Formulas; Problem Solving; Mathematics Education + Suchen Sie Ihr Suchwort? Denkfähigkeit; Mathematics lessons; Mathematikunterricht; Adolescent; Adolescence; Adoleszenz; Jugend; Jugendalter; Jugendlicher; Mathematische Formel; Problemlösen; Mathematische Bildung
Abstract	In recent decades, there has been considerable research that explores the teaching and learning of combinatorics. Such work has highlighted the fact that understanding and justifying combinatorial formulas can be challenging for students, and there is a need to identify ways to support students' combinatorial reasoning. In this paper, we contribute to research that explores effective ways to foster students' combinatorial reasoning by highlighting the role that shifts in representational registers can play in supporting students' combinatorial reasoning and activity. In particular, we present a case in which two students, aged 12 and 14, reasoned about, and developed a formula for, binomial coefficients. This occurred in a teaching experiment designed to examine their generalizing activity. In these interviews, the students first solved problems about determining the volume of a cube and then shifted to a combinatorial interpretation of this task, leveraging binomial coefficients as a way to consider growth in higher dimensions. The students demonstrated sophisticated reasoning about combinatorial tasks and were ultimately able to generate and understand a formula for binomial coefficients. In framing this case, we focus on the students' use of different representations, highlighting the power of being able to transition between representational registers as a way of supporting students' combinatorial reasoning. In this way, our case demonstrates the value of representational registers specifically as a mechanism by which to potentially improve the teaching and learning of combinatorics. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01