Jake's Conceptual Operations in Multiplicative Tasks: Focus on Number Choice [Konferenzbericht] Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (37th, East Lansing, MI, Nov 5-8, 2015).

Autor/inn/en	Risley, Rachael; Hodkowski, Nicola M.; Tzur, Ron
Titel	Jake's Conceptual Operations in Multiplicative Tasks: Focus on Number Choice [Konferenzbericht] Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (37th, East Lansing, MI, Nov 5-8, 2015).
Quelle	(2015), (8 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
Schlagwörter	Case Studies; Mathematics Instruction; Mathematics Teachers; Concept Formation; Teaching Methods; Multiplication; Computation; Mathematical Logic; Elementary School Mathematics; Number Concepts; Grade 4; Educational Games; Video Technology; Observation + Suchen Sie Ihr Suchwort? Case study; Fallstudie; Case Study; Mathematics lessons; Mathematikunterricht; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Concept learning; Begriffsbildung; Teaching method; Lehrmethode; Unterrichtsmethode; Multiplikation; Mathematical logics; Mathematische Logik; Elementare Mathematik; Schulmathematik; Number concept; Zahlbegriff; School year 04; 4. Schuljahr; Schuljahr 04; Educational game; Lernspiel; Beobachtung
Abstract	This case study examined how a teacher's choice of numbers used in tasks designed to foster students' construction of a scheme for reasoning in multiplicative situations may afford or constrain their progression. This scheme, multiplicative double counting (mDC) is considered a significant conceptual leap from reasoning additively with units of one (1s) and composite units. A researcher-teacher's work with Jake allowed us to center on his gradual cognitive advance as different numbers chosen for the unit rate in problems (e.g., 5 cubes-per-tower) were used in the context of the Please Go and Bring for Me platform task. Our findings show that a child's use of an evolving scheme may initially depend on the numbers used in the task. We discuss the key recognitions that (a) a new way of operating does not evolve in a "once-and-for-all" way for all numbers and (b) the support our study provides for Pirie and Kieren's core notion of folding-back. [For the complete proceedings, see ED583989.] (As Provided).
Anmerkungen	North American Chapter of the International Group for the Psychology of Mathematics Education. e-mail: pmena.steeringcommittee@gmail.com; Web site: http://www.pmena.org/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01