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

Abstract

MATHEMATICS TEACHING RESEARCH JOURNAL 186 SUMMER 2022 Vol 14 no 2 This content is covered by a Creative Commons license, Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial purposes only, and only so long as attribution is given to the creator. If you remix, adapt, or build upon the material, you must license the modified material under identical terms. A New Tool for the Teaching of Graph Theory: Identification of Commognitive Conflicts José María Gavilán-Izquierdo1, Inés Gallego-Sánchez1*, Antonio González1, María Luz Puertas2 1Universidad de Sevilla, Spain, 2Universidad de Almería, Spain gavilan@us.es, inesgal@us.es*, gonzalezh@us.es, mpuertas@ual.es 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