Algebraic Reasoning in Years 5 and 6: Classifying Its Emergence and Progression Using Reverse Fraction Tasks

Autor/inn/en	Pearn, Catherine; Stephens, Max; Pierce, Robyn
Titel	Algebraic Reasoning in Years 5 and 6: Classifying Its Emergence and Progression Using Reverse Fraction Tasks
Quelle	In: ZDM: Mathematics Education, 54 (2022) 6, S.1257-1271 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Pearn, Catherine)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-022-01426-7
Schlagwörter	Logical Thinking; Elementary School Students; Grade 5; Grade 6; Fractions; Algebra; Multiplication + Suchen Sie Ihr Suchwort? School year 05; 5. Schuljahr; Schuljahr 05; School year 06; 6. Schuljahr; Schuljahr 06; Bruchrechnung; Multiplikation
Abstract	This paper builds on our previous research and investigates how students' fractional competence and reasoning can provide clear evidence of non-symbolic algebraic thinking and its progressive transition towards fully generalised algebraic thinking. In a large-scale study, 470 primary students completed a written paper and pencil test. This included three reverse fraction tasks which required students to find an unknown whole when presented with a quantity representing a fraction of that whole. Seventeen students from one participating primary school undertook a semi-structured interview which included reverse fraction tasks, similar to those on the written test, but with progressive levels of abstraction, starting with particular instances and becoming more generalised. Two important products of the study are the Classification Framework for Reverse Fraction Tasks and the Emerging Algebraic Reasoning Framework. The interview results highlight two critical transition points for the emergence of students' algebraic reasoning. The first is the ability to transition from additive strategies to multiplicative strategies to solve reverse fraction problems. Students reliant on diagrams and additive strategies struggled to solve more generalised tasks that required multiplicative rather than additive strategies. The second transition is the shift from multiplicative thinking to algebraic reasoning where students could generalise their multiplicative knowledge to deal with any quantity represented in a reverse fraction task. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01