Students' Distributive Reasoning with Fractions and Unknowns

Autor/inn/en	Hackenberg, Amy J.; Lee, Mi Yeon
Titel	Students' Distributive Reasoning with Fractions and Unknowns
Quelle	In: Educational Studies in Mathematics, 93 (2016) 2, S.245-263 (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-016-9704-9
Schlagwörter	Mathematics Instruction; Mathematical Logic; Fractions; Algebra; Interviews; Middle School Students; High School Students; Multiplication; Mathematical Concepts; Semi Structured Interviews; Mathematics Tests + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Bruchrechnung; Interviewing; Interviewtechnik; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; High school; High schools; Oberschule; Studentin; Multiplikation
Abstract	To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students' fractional knowledge and algebraic reasoning are explored. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01