The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

Studies show that supporting argumentation in mathematics classrooms is challenging for teachers. This study reports on the experience of seven elementary and middle-school mathematics teachers in an afterschool classroom-based program where they had the opportunity to facilitate research sessions on students' development of mathematical ideas and…

The authors developed an instructional nudges as part of a larger research project. These instructional nudges are designed to be small but powerful changes to teachers' existing practices. Some instructional nudges focus on modifying tasks used in classrooms. In this article, the authors share Rate and Review. The goal of Rate and Review is to…

The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…

This study illustrates how two secondary mathematics teachers used students' incorrect answers as they supported students' engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the…

This article shares a paper presented as the keynote for the Terry L. Wood Memorial Conference that was held virtually on May 20, 2022. This paper starts with a reference to the project, The Coordination of a Psychological and Sociological Perspective, that was funded by the Spencer Foundation. The results of the research in this project are…

This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the…

How teachers can experience adaptive professional development (PD) experiences is still understudied in the literature on teacher learning, which for the most part reflects an emphasis on learning outcomes rather than the process of learning. In this study, we use a situated perspective on teacher learning to investigate the coevolution of a…

This study investigates teachers' perspectives on the use of a mathematical argumentation teaching strategy in elementary mathematics in which students disprove mathematical statements they already know to be false. Mathematical argumentation is a process through which students develop an argument about a mathematical concept and rationalize its…

To leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question, "How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers' knowledge and practices for teaching?" In this paper, we offer a model called…

This paper presents research on the argumentation that preservice teachers perform when designing and teaching geometry. Argumentation is associated with speech acts carrying didactical intentions. This research study features of preservice teachers' argumentation when explaining geometry tasks both to peers, during preparation and discussion of…

The aim of this study is to examine the argumentation-based problem solving processes of 10th grade students in the context of quadratic equations. The study was carried out in a public high school in Istanbul. The study group consists of three male students selected by the method of "homogeneous sampling". In the research, special case…

One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

Mathematical argumentation is generally thought to be the paradigm of cogent reasoning. The concept of mathematical proof thus seems to be associated with necessity and enforcement, but not with freedom; however, in various ways a reference to freedom is also needed to understand the phenomenon of mathematical proof, for example, to distinguish it…