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A New Tool for the Teaching of Graph Theory: Identification of Commognitive Conflicts

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Title: A New Tool for the Teaching of Graph Theory: Identification of Commognitive Conflicts
Language: English
Authors: Gavilán-Izquierdo, José María, Gallego-Sánchez, Inés, González, Antonio, Puertas, María Luz
Source: Mathematics Teaching Research Journal. Sum 2022 14(2):186-212.
Availability: City University of New York. Creative Commons. 205 East 42 Street, New York, NY 10017. Web site: https://commons.hostos.cuny.edu/mtrj
Peer Reviewed: Y
Page Count: 27
Publication Date: 2022
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Descriptors: Undergraduate Students, Engineering Education, Computer Science Education, Graphs, Teaching Methods, Mathematics Instruction, Geometry, Cognitive Processes, Conflict, Foreign Countries
Geographic Terms: Spain (Madrid)
ISSN: 2573-4377
Abstract: In this exploratory work, the discourse of first-year computer engineering undergraduate students of graph theory was analyzed with the aim of improving the teaching of this branch of mathematics. The theoretical framework used is the theory of commognition, specifically, we focus on commognitive conflicts because they are learning opportunities since they foster the learning process when resolved by students, and so teachers should consider them in their practice. A qualitative analysis of the written responses to a questionnaire dealing with definitions and the concepts of path and cycle graphs was performed. Thus, several commognitive conflicts were found, coming from the confluence of discourses governed by different discursive rules. Furthermore, the conflicts encountered were classified according to their origin, into object-level and metalevel conflicts. Concretely, the object-level conflicts had to do with the school discourse of geometry or sequences, and with the discourse of directed graphs; the metalevel commognitive conflicts were associated with the school discourse of the mathematical practice of defining. Finally, our findings are contrasted with related works in the literature, and also a series of implications for the teaching of graph theory are presented.
Abstractor: As Provided
Entry Date: 2022
Accession Number: EJ1350527
Database: ERIC
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  Data: In this exploratory work, the discourse of first-year computer engineering undergraduate students of graph theory was analyzed with the aim of improving the teaching of this branch of mathematics. The theoretical framework used is the theory of commognition, specifically, we focus on commognitive conflicts because they are learning opportunities since they foster the learning process when resolved by students, and so teachers should consider them in their practice. A qualitative analysis of the written responses to a questionnaire dealing with definitions and the concepts of path and cycle graphs was performed. Thus, several commognitive conflicts were found, coming from the confluence of discourses governed by different discursive rules. Furthermore, the conflicts encountered were classified according to their origin, into object-level and metalevel conflicts. Concretely, the object-level conflicts had to do with the school discourse of geometry or sequences, and with the discourse of directed graphs; the metalevel commognitive conflicts were associated with the school discourse of the mathematical practice of defining. Finally, our findings are contrasted with related works in the literature, and also a series of implications for the teaching of graph theory are presented.
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