A Framework for Understanding and Cultivating the Transition from Arithmetic to Algebraic Reasoning

Autor/inn/en	Nathan, Mitchell J.; Koellner, Karen
Titel	A Framework for Understanding and Cultivating the Transition from Arithmetic to Algebraic Reasoning
Quelle	In: Mathematical Thinking and Learning: An International Journal, 9 (2007) 3, S.179-192 (14 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1098-6065
Schlagwörter	Mathematics Education; Classrooms; Mathematics Teachers; Economic Opportunities; Arithmetic; Algebra; Teaching Methods; Thinking Skills; Models; Elementary School Mathematics; Research Reports; Workshops; Colorado; Wisconsin + Suchen Sie Ihr Suchwort? Mathematische Bildung; Classroom; Klassenraum; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Teaching method; Lehrmethode; Unterrichtsmethode; Denkfähigkeit; Analogiemodell; Elementare Mathematik; Schulmathematik; Research report; Forschungsbericht; Lernwerkstatt; Schulung
Abstract	Algebraic reasoning stands as a formidable gatekeeper for students in their efforts to progress in mathematics and science, and to obtain economic opportunities (Ladson-Billings, 1998; RAND, 2003). Currently, mathematics education research has focused on algebra in order to provide access and opportunities for more students. There is now a growing awareness that the essential concepts that make up school algebra are accessible to students before secondary-level education, and that earlier introduction could facilitate students' algebraic development (Carpenter, Franke, & Levi, 2003; Kaput, Carraher, & Blanton, 2007; National Council of Teachers of Mathematics [NCTM], 2000, National Research Council [NRC], 1998; RAND, 2003). In order to understand middle school students' transition from arithmetic to algebraic reasoning, and to develop and evaluate effective educational approaches to improve the learning and teaching of increasingly complex mathematics, future efforts need to be grounded in sound theory. This theory needs to encapsulate both how students develop algebraic reasoning and acquire domain knowledge, and the beliefs, knowledge, and existing practices of teachers. The theory must also acknowledge the complexity of this area of study, including its multi-tiered nature, diversity of settings and participants, and the high degree of interconnectedness among important components. What does it mean to reason algebraically? How can this reasoning be cultivated in middle school classrooms? In this article, the authors address these questions by turning to the theoretical underpinnings, and relevant empirical findings within each of the three tiers: (1) Student Algebraic Reasoning; (2) Middle School Algebra Teaching Practices; and (3) Research on Teacher Learning and Teacher Change. (Contains 1 footnote and 2 figures.) (ERIC).
Anmerkungen	Lawrence Erlbaum. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10