Reflection on Teaching Linear Algebra: Examining One Instructor's Movements between the Three Worlds of Mathematical Thinking

Autor/inn/en	Stewart, Sepideh; Troup, Jonathan; Plaxco, David
Titel	Reflection on Teaching Linear Algebra: Examining One Instructor's Movements between the Three Worlds of Mathematical Thinking
Quelle	In: ZDM: The International Journal on Mathematics Education, 51 (2019) 7, S.1253-1266 (14 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-019-01086-0
Schlagwörter	Mathematics Instruction; Teaching Methods; Algebra; Advanced Courses; Teacher Attitudes; Mathematical Logic; Thinking Skills; Mathematics Teachers; Mathematical Concepts; Decision Making; Teacher Researchers; Reflection; Intervention + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode; Fortgeschrittenenunterricht; Lehrerverhalten; Mathematical logics; Mathematische Logik; Denkfähigkeit; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Decision-making; Entscheidungsfindung; Lehrerforschung
Abstract	Reflection is an important part of teaching and needs to be considered carefully. In this study, we examined a mathematics instructor's reflections on teaching linear algebra. The research team employed Tall's (How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge University Press, Cambridge, 2013) framework to track the instructor's movements between the three worlds of mathematical thinking. The instructor emphasized the importance of symbolic and embodied thinking and made sure the students were ready before entering the formal world. It became evident that moving the class between the worlds appropriately at certain moments was critical to students' understanding of the concept, however at times required much anticipation and careful preparation in advance as well as creating appropriate teaching resources. The instructor's dual role as a researcher and participant resulted a model of instructional decision making which was used to give further insights during his movements between Tall's worlds and afforded him unique opportunities for reflection and subsequent carefully calculated class interventions. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01