Investigating students' proving process in geometry through the commognitive theory

• Main Author: Mendoza, Shawn Dale C.
• Format: text
• Language: English
• Published: Animo Repository 2022
• Subjects: Geometry; Mathematics > Curricula; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etdm_scied/24; https://animorepository.dlsu.edu.ph/cgi/viewcontent.cgi?article=1027&context=etdm_scied
• Institution: De La Salle University

Proving in geometry is fundamental to mathematics (Reid, 2011) and is considered the heart of the mathematics curriculum (Hoyles and Jones, 1998; Oflaz et al., 2016). However, it is one of the essential activities in mathematics classrooms at various educational levels (Nguyen, 2012). Despite its importance, proving has been perceived as one of the most difficult topics to learn (Senk, 1985) and challenging activity in learning mathematics (Shino and Fujita, 2021). While there is much research about proving geometry in the field of mathematics education, less research activity is evident in exploring the student’s proving process from a socially-embedded perspective. Hence, to provide a profound basis for developing the student’s proving skills, the study employed the Commognitive Theory of Sfard (2008). This socio-cultural theory investigates the development of mathematical discourse. In particular, the study aimed to examine the factors that emerged from the students’ discursive activities, such as their proving routines, characteristics of mathematical discourse, and the observed object-level and meta-level learning developments. The participants were 9th and 10th graders of the American School of Ulaanbaatar in Mongolia. The results revealed that students demonstrated diverse construction, substantiation, and recall routines throughout the proving tasks. The results characterized their proving process's applicability, flexibility, and corrigibility. Word use, visual mediators, narratives, and routines utilized and performed in the proving process developed the essential and emergent discourses in teaching geometry, such as learning scaffold, the significance of gestures, understanding of the equal and congruent signs, and alternative perspectives. It was found that culture and identity influenced the meta-level learning development of the students as factors that shaped the learning of mathematics. The transition of the proving tasks in the implementation of the study served as a mechanism in this learning development. Above all, implications of the results exhibited that visualization in geometry facilitated the student’s understanding of relationships, conditions, and other vital components of the proving process. Furthermore, relational understanding is crucial and essential in building the semantic knowledge of proving skills.