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Leading Students towards the Formal World of Mathematical Thinking: A Mathematician's Reflections on Teaching Eigentheory

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Bibliographic Details
Title: Leading Students towards the Formal World of Mathematical Thinking: A Mathematician's Reflections on Teaching Eigentheory
Language: English
Authors: Stewart, Sepideh, Epstein, Jonathan, Troup, Jonathan
Source: International Journal of Mathematical Education in Science and Technology. 2019 50(7):1011-1023.
Availability: Taylor & Francis. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 13
Publication Date: 2019
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Mathematics Instruction, Professional Personnel, Teaching Methods, Reflection, Mathematical Logic, Thinking Skills, Mathematical Concepts, College Mathematics, College Freshmen, Algebra, College Faculty, Mathematics Teachers, Undergraduate Students
DOI: 10.1080/0020739X.2019.1657598
ISSN: 0020-739X
Abstract: In this study, we analysed a mathematician's teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall's ["How humans learn to think mathematically: Exploring the three worlds of mathematics." Cambridge University Press] three-world model of embodied, symbolic and formal as a framework for understanding the mathematician and teacher's pedagogical reflections as he led the class to the formal world. In order to reach the formal world, he used a sequence of tasks that emphasized embodied and symbolic, as well as formal thinking. The analysis of the journals showed that the mathematician faced challenges in leading the class towards the formal world. The study also revealed that the mathematician strived to build a concept image, that, while perhaps mirroring his own, did not resonate with the students.
Abstractor: As Provided
Entry Date: 2019
Accession Number: EJ1228550
Database: ERIC
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Abstract:In this study, we analysed a mathematician's teaching journals on eigenvalues and eigenvectors in a first-year linear algebra course. The research team employed Tall's ["How humans learn to think mathematically: Exploring the three worlds of mathematics." Cambridge University Press] three-world model of embodied, symbolic and formal as a framework for understanding the mathematician and teacher's pedagogical reflections as he led the class to the formal world. In order to reach the formal world, he used a sequence of tasks that emphasized embodied and symbolic, as well as formal thinking. The analysis of the journals showed that the mathematician faced challenges in leading the class towards the formal world. The study also revealed that the mathematician strived to build a concept image, that, while perhaps mirroring his own, did not resonate with the students.
ISSN:0020-739X
DOI:10.1080/0020739X.2019.1657598