Generalization across Multiple Mathematical Domains: Relating, Forming, and Extending

Autor/inn/en	Ellis, Amy B.; Lockwood, Elise; Tillema, Erik; Moore, Kevin
Titel	Generalization across Multiple Mathematical Domains: Relating, Forming, and Extending
Quelle	In: Cognition and Instruction, 40 (2022) 3, S.351-384 (34 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Ellis, Amy B.) ORCID (Lockwood, Elise) ORCID (Tillema, Erik) ORCID (Moore, Kevin)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0737-0008
DOI	10.1080/07370008.2021.2000989
Schlagwörter	Generalization; Mathematics Instruction; Algebra; Advanced Courses; Trigonometry; Cognitive Processes; Thinking Skills; Problem Solving; Middle School Students; Calculus; High School Students; College Students; Taxonomy; Grounded Theory; Task Analysis; Mathematics Skills; Student Attitudes + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Fortgeschrittenenunterricht; Trigonometrie; Cognitive process; Kognitiver Prozess; Denkfähigkeit; Problemlösen; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; High school; High schools; Oberschule; Studentin; Collegestudent; Taxonomie; Aufgabenanalyse; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Schülerverhalten
Abstract	Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students' generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support more productive generalizations. In response, we report on results from 146 interviews with 93 participants in middle school through college in the domains of algebra, advanced algebra, trigonometry/pre-calculus, and combinatorics while solving complex problems. Our findings yielded the Relating-Forming-Extending (RFE) Framework, which distinguishes multiple related forms and types of generalizing. We also present two aspects of mental activity that promote generative generalizations: operative activity, and building and refining activity. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01