Orchestrating Mathematical Classroom Discourse About Various Solution Methods: Case Study of a Teacher’s Development

Abstract

Developing and orchestrating classroom discourse about students’ different solution methods is an essential yet complex task for mathematics teachers. This study reports on the first stages of classroom discourse development of one Dutch higher secondary school mathematics teacher who had no prior experience in including classroom discourse in her teaching practice. Four lessons in analytic geometry were developed iteratively, in collaboration with the teacher. The lessons consisted of students working on a mathematical problem plus classroom discourse concerning students’ different solution methods. Classroom discourse video recordings were collected and analyzed in order to develop a framework to characterize the teacher’s actions, and to describe the change in the teacher’s role in classroom discourse. The results reveal three main changes in the teacher’s role: First, the way the teacher reacted to correct or incorrect solution methods shifted from confirming or setting aside suggestions, toward making the solution methods the subject of discussion; second, the distribution of turns changed such that more students were involved in the discourse and in reacting to each other’s solution methods; third, the teacher’s actions shifted from convergent, teacher-led actions toward divergent, student-led actions. These results show that within four lessons, an important step has been taken toward establishing a discourse community.

Sustainability Education in China: Lessons Learnt from the Teaching of Geography

“…For example, Sugimoto [27] explored the dilemmas faced by a teacher when working with English language learners in a lowincidence school in the US, while Rissanen, Kuusisto, Tuominen and Tirri [28] drew the experience from a Finnish teacher on how she pursued core features of growth mindset pedagogy. Kooloos, Oolbekkink-Marchand, Kaenders and Heckman [29], on the other hand, looked into the problems of teaching mathematics by a Dutch secondary-school teacher. Although they all focused on a single teacher in their studies, such a single-case study is still valuable due to the fact that "single cases can enable the creation of more complicated theories than multiple cases, because single-case researchers can fit their theory exactly to the many details of a particular case" while "multiple-case researchers retain only the relationships that are replicated across most or all of the cases" [30] (p. 30).…”

Dialogische Klassengesprächsführung im Geschichtsunterricht

“…Zusammengenommen lassen sich die Zunahme der divergenten Gesprächshandlungen der Lehrpersonen und der höhere Sprechzeitanteil der Lernenden im Verlauf der Fortbildung als Indikatoren für eine zunehmend dialogischere Gesprächsleitung der drei Geschichtslehrpersonen interpretieren (Alexander, 2018;Kooloos et al ., 2019), wie sie mit der Fortbildung angestrebt wurde . Dabei gehören konvergente Handlungen weiterhin zum Gesprächsleitungsrepertoire der drei Lehrpersonen .…”

“…(2019) übernommen und deduktiv ergänzt . Zusätzlich wurden die divergenten Kategorien vonKooloos et al . (2019) unterteilt in die Oberkategorien "Wissen" und "Reasoning" als folgerichtiges Denken und Argumentieren .…”

Building on student mathematical thinking in whole-class discourse: exploring teachers’ in-the-moment decision-making, interpretation, and underlying conceptions

“…The coding of student-teacher interaction was performed mostly deductively, based on a previous study (Kooloos et al 2020). The coding of interpretation and decisions was inductive, open coding: for each episode, we coded whether and how the teacher interpreted student thinking, and what decision they made.…”