Exploring Real Numbers as Rational Number Sequences with Prospective Mathematics Teachers

Autor/inn/en	Belin, Mervenur; Akar, Gülseren Karagöz
Titel	Exploring Real Numbers as Rational Number Sequences with Prospective Mathematics Teachers
Quelle	In: Mathematics Teacher Educator, 9 (2020) 1, S.63-87 (25 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2167-9789
DOI	10.5951/MTE.2020.9999
Schlagwörter	Preservice Teachers; Mathematics Teachers; Pedagogical Content Knowledge; Number Concepts; Mathematics Instruction; Sequential Learning; Mathematics Skills; Fractions; Arithmetic; Division; Visual Aids + Suchen Sie Ihr Suchwort? Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Pädagogische Kompetenz; Number concept; Zahlbegriff; Mathematics lessons; Mathematikunterricht; Didaktische Sequenzierung; Lernsequenz; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Bruchrechnung; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Anschauungsmaterial
Abstract	The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers' understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers. (As Provided).
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