Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students’ Examination Scripts

Abstract

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the tasks and the lecturers' (also exam setters') assessment practices, and focuses on manifestations of unresolved commognitive conflict in students' engagement with the tasks. Here we note four such manifestations concerning the students' identification of and consistent work with: the appropriate numerical context of the examination tasks; the visual mediators and the rules of school algebra and Set Theory discourses; the visual mediators of the Probability and Set Theory discourses; and, with the visual mediators and rules of the Probability Theory discourse. Our analysis suggests that, despite lecturers' attempts to assist students towards a smooth transition to the different discourses of university mathematics, students' errors at the final examination reveal unresolved commognitive conflicts. A pedagogical implication of our analysis is that a more explicit and systematic presentation of the distinctive differences between these discourses, along with facilitation of the flexible moves between them, is needed.

Textual and Contextual Commognitive Conflict Students in Solving an Improper Fraction

“…This is in accordance with Rabin, Fuller, & Harel (2013), who said that learning mathematics is verbal communication, which is a process of communication that occurs not only with others but also with yourself. Thoma & Nardi (2018) said that there is intra-commognitive conflict, which is a condition where differences occur between words or symbols used by the interlocutor (writing). In addition, Sfard (2008) said that communication can occur through written or spoken language which constitute the primary means for teaching purposes and changes in abilities in learning.…”

“…Departing from this definition, the participants proceeds by dividing again one part of the whole. The participants trie to make adjustments in stages due to the repetition of the settlement process (Sfard, 2007;Nardi, et al, 2014;Thoma & Nardi, 2018). Adjustments made by the participants still produce errors so that the commognitive conflict experienced is still unresolved.…”

“…The commognitive conflict experienced by the participants continues because the previous commognitive conflict has not been resolved. The manifestation of unresolved commognitive conflict is thought to occur because there is involvement in one conversation (Sfard, 2007;Sfard, 2008;Nardi, Ryve, Stadler, & Viirman, 2014;Rabin, Fuller, & Harel, 2013;Thoma & Nardi, 2018).…”

A Trio of Courses to Support Mathematics Transfer Students’ Development of Professional Vision

“…These experiences and activities at universities are starkly different from their prior schooling experiences (Moore, 1994). Even with many universities offering transfer to proof classes, this content remains a significant challenge for students (e.g., Thoma & Nardi, 2017) and a barrier to their retention.…”

El discurso de estudiantes para maestro cuando describen y definen cuerpos geométricos

“…La teoría de la comognición ofrece una perspectiva holística de la enseñanza y aprendizaje de las matemáticas y, dentro de esta teoría, el estudio de los conflictos comognitivos está tomando cada vez más presencia en la investigación (Ioannou, 2018;Jayakody, 2015;Sánchez y García, 2014;Tabach y Nachlieli, 2015;Thoma y Nardi, 2018). En particular, Sánchez y García (2014) y Tabach y Nachlieli (2015) estudiaron conflictos comognitivos que manifiestan los estudiantes para maestro cuando realizan actividades vinculadas a la práctica matemática de definir.…”