Rituals and explorations in mathematical teaching and learning: introduction to the special issue

Abstract

This special issue comprises seven studies and a commentary piece, which relate to various aspects of rituals and the Britual-exploration^dyad in learning, teaching and learning-to-teach mathematics. The theme of the special issue arose from Sfard and Lavie's (Cognition and Instruction, 23(2), 237-309, 2005) Britual^vs. Bexplorative^dyad, on which a Working Session was held during the PME conference in 2016. Three central themes are addressed in the papers of this special issue: (1) the logic of ritual, and why rituals are so persistent in mathematics classrooms; (2) the coexistence of rituals and explorations, including the question of whether rituals and explorations are a binary or a continuum; and (3) alternative theoretical conceptualisations of the ritual-exploration dyad, focusing in particular on what can be learned about rituals from social and critical theory, as well as socio-linguistics. In this introduction, we first give an overview of each of the papers and its unique contribution. We then synthesise the answers given by the papers to the three themes described above.

Machine Learning for Non-Majors: A White Box Approach

“…In practice, we should ask: How do learners build their mental representations of mathematical objects, and how do they advance their representations along the process-object continuum? A current mathematical education theory suggests that the learning of mathematical concepts is accomplished by participating in mathematical routines, which can be viewed as repeated executions of mathematical tasks (Heyd-Metzuyanim & Graven, 2019;Sfard & Lavie, 2005). There are two types of mathematical routines: rituals and exploration (Lavie et al, 2019).…”

Commognition as an approach to studying proof teaching in university mathematics lectures

“…Moreover, interviews with students took place exploring the operationalization of these opportunities. Later on, a special issue with seven studies was published, where the researchers explored rituals solely but also as a dyad with explorations in learning, teaching, or learning-toteach contexts (Heyd-Metzuyanim & Graven, 2019). Heyd-Metzuyanim and Graven (2019) synthesized the studies of this issue in three main themes: the logic of rituals and their persistence in class (Coles & Sinclair, 2019;Lavie et al, 2019;McCloskey et al, 2019;Nachlieli & Tabach, 2019), questions about the co-existence of rituals and explorations and whether they are binary or in a continuum (Heyd-Metzuyanim et al, 2016;Nachlieli & Tabach, 2019;Viirman & Nardi, 2019), and the different conceptualizations of rituals and explorations (Coles & Sinclair, 2019;McCloskey et al, 2019;Robertson & Graven, 2019).…”

Rituals and Explorations in Students’ Mathematical Discourses: The Case of Polynomial Inequalities

“…Therefore, the analysis of learning has grown more discursive (Nardi, 2005). These studies, which emphasize the relevance of the context in which learning occurs, are largely based on Sfard's (2008) commognitive approach (Emre-Akdoan, Güçler, & Argün, 2018;Heyd-Metzuyanim & Graven, 2019;Nachlieli & Katz, 2017;Nachlieli & Tabach, 2019;Viirman & Nardi, 2019;Sfard, 2017). Classroom communication, according to these studies' findings, is equal to thinking.…”

“…The literature on mathematics education studies exploring the mathematical discourses of students and instructors has grown in recent years (Baccaglini-Frank, 2021;Heyd-Metzuyanim & Graven, 2019;Heyd-Metzuyanim & Shabtay, 2019;Heyd-Metzuyanim, Tabach & Nachlieli, 2016;Nachlieli & Katz, 2017;Nisa, Lukito & Masriyah, 2021;Roberts & le Roux, 2019;Sfard, 2017). While most of these studies (Heyd-Metzuyanim & Graven, 2019;Heyd-Metzuyanim & Shabtay, 2019;Nachlieli & Katz, 2017;Sfard, 2017) investigate the mathematical discourses of teachers and teacher candidates, a limited number of them (Baccaglini-Frank, 2021;Nisa et. al., 2021;Roberts & le Roux, 2019) focus on students' mathematical discourse.…”

“…Some studies focusing on teacher discourse also draw attention to the effect of teacher discourse on students' discourse (Heyd-Metzuyanim & Graven, 2016;Tabach & Nachlieli, 2012;Sfard, 2017). Researchers have also analyzed the discourses of pre-service teachers in learning environments that offer explorative learning opportunities (Heyd-Metzuyanim & Graven, 2019;Nachlieli & Katz, 2017). In addition to analyzing pre-service teachers' discourse, these studies aimed to identify learning opportunities that foster exploratory engagement.…”