How Can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling

Autor/inn/en	Park, Jin Hyeong; Lee, Kyeong-Hwa
Titel	How Can Students Generalize the Chain Rule? The Roles of Abduction in Mathematical Modeling
Quelle	In: EURASIA Journal of Mathematics, Science & Technology Education, 12 (2016) 9, S.2331-2352 (22 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1305-8223
Schlagwörter	Mathematical Models; Calculus; Mathematics Activities; Mathematical Concepts; Grade 11; Mathematics Achievement; Mathematics Teachers; Mathematics Instruction; Mathematics Education; Logical Thinking; High School Students; Video Technology; Observation + Suchen Sie Ihr Suchwort? Mathematical model; Mathematisches Modell; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; School year 11; 11. Schuljahr; Schuljahr 11; Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Mathematics lessons; Mathematikunterricht; Mathematische Bildung; High school; High schools; Student; Students; Oberschule; Schüler; Schülerin; Studentin; Beobachtung
Abstract	The purpose of this study is to design a modeling task to facilitate students' inquiries into the chain rule in calculus and to analyze the results after implementation of the task. In this study, we take a modeling approach to the teaching and learning of the chain rule by facilitating the generalization of students' models and modeling activities. We assumed abductive reasoning to be one of the key factors which can support the generalization of students' models and modeling activities. We believe that analogical reasoning and diagrammatic reasoning are key factors in fostering students' use of abduction. As a result, we determined that the students' models and modeling activities were generalized to the chain rule by their use of abductive reasoning, and the students found the chain rule to be a generalized rule for describing changes of various quantities. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01