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From Collaborative Construction, through Whole-Class Presentation, to a Posteriori Reflection: Proof Progression in a Topology Classroom

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Title: From Collaborative Construction, through Whole-Class Presentation, to a Posteriori Reflection: Proof Progression in a Topology Classroom
Language: English
Authors: Igor' Kontorovich (ORCID 0000-0002-3353-5445), Sina Greenwood (ORCID 0000-0001-6013-4981)
Source: International Journal of Research in Undergraduate Mathematics Education. 2024 10(2):516-546.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 31
Publication Date: 2024
Document Type: Journal Articles
Reports - Research
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Topology, Cooperative Learning, Active Learning, Classroom Techniques, Class Organization, Classroom Communication, Reflection, Learning Processes
DOI: 10.1007/s40753-023-00217-z
ISSN: 2198-9745
2198-9753
Abstract: Coming from a social perspective, we introduce a classroom organizational frame, where students' proofs progress from collaborative construction in small groups, through whole-class presentation at the board by one of the constructors, to a posteriori reflection. This design is informed by a view on proofs as successive social processes in the mathematics community. To illustrate opportunities for mathematics learning of proof progressions, we present a commognitive analysis of a single proof from a small course in topology. The analysis illuminates the processes through which students' proof was restructured, developed previously unarticulated elements, and became more formal and elaborate. Within this progression, the provers developed their mathematical discourses and the course teacher seized valuable teachable moments. The findings are discussed in relation to key themes within the social perspective on proof.
Abstractor: As Provided
Entry Date: 2024
Accession Number: EJ1437093
Database: ERIC
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  Data: Coming from a social perspective, we introduce a classroom organizational frame, where students' proofs progress from collaborative construction in small groups, through whole-class presentation at the board by one of the constructors, to a posteriori reflection. This design is informed by a view on proofs as successive social processes in the mathematics community. To illustrate opportunities for mathematics learning of proof progressions, we present a commognitive analysis of a single proof from a small course in topology. The analysis illuminates the processes through which students' proof was restructured, developed previously unarticulated elements, and became more formal and elaborate. Within this progression, the provers developed their mathematical discourses and the course teacher seized valuable teachable moments. The findings are discussed in relation to key themes within the social perspective on proof.
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