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The Conceptions and Consequences of What We Call Argumentation, Justification, and Proof working group met in 2022 to focus on frameworks for studying argumentation, justification, and proof. Working group participants engaged in conversations interrogating past uses of frameworks and considered potential directions for making progress on both new and longstanding questions involving argumentation, justification, and proof. Discussions revolved around the following topics: the teacher's role in joint sensemaking, student agency, defining validity in proof and proving, the role of emerging technologies, and research and practice related to different audiences and argumentation, justification, and proof. [ABSTRACT FROM AUTHOR]

Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other times, they are inconsistent and even contradictory. Regardless of the descriptions of these processes, however, given the importance of argumentation, justification, and proof to the discipline of mathematics, as well as their valued roles as learning practices, it is critical to query the relationship between engaging students in such processes and the promotion of equitable learning spaces and outcomes. The Argumentation, Justification, and Proof Working Group met for the sixth time at PME-NA 43 in 2021 in Philadelphia, PA. The goal of the 2021 sessions was to facilitate discussions and collaborations among researchers to advance our collective understanding of argumentation, justification and proof through an equity and inclusion lens. A concluding discussion that looked across the sessions occurred on Day 3. [ABSTRACT FROM AUTHOR]

Research processes are often messy and include tensions that are unnamed in the final products. In our attempt to update and generalize a framework used to examine teachers' support for collective argumentation in mathematics education classrooms to examining teachers' work in interdisciplinary STEM contexts, we have experienced significant linguistic tensions because of the context-dependent nature of language. We aim to acknowledge the difficulty of generalizing research beyond the mathematics education community, describe our attempts to resolve the problem we face, and discuss potential conclusions pertaining to the feasibility of generalizing frameworks beyond mathematics education. [ABSTRACT FROM AUTHOR]

Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other times, they are inconsistent and even contradictory. Regardless of the descriptions of these processes, however, given the importance of argumentation, justification, and proof to the discipline of mathematics, as well as their valued roles as learning practices, it is critical to query the relationship between engaging students in such processes and the promotion of equitable learning spaces and outcomes. This year, working group leaders aim to facilitate discussions and collaborations among researchers to advance our collective understanding of argumentation, justification and proof through an equity and inclusion lens. [ABSTRACT FROM AUTHOR]

Argumentation, justification, and proof are essential constructs in the field of mathematics and teaching and learning in mathematics classrooms. Research involving these constructs draws on a variety of definitions and analytic frameworks that include discursive, social, and content factors. This year, we examine frameworks used in research involving these constructs and engage working group participants in critical conversations about how these have been used, with what impact, as well as considering future directions for addressing new questions and making further progress on long-standing ones. [ABSTRACT FROM AUTHOR]

Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other times, they are inconsistent and even contradictory. The inconsistencies in definitions and usages of the terms argumentation, justification, and proof highlight the need for scholarly conversations addressing these (and other related) constructs. Collaboration is needed to move toward, not one-size-fits-all definitions, but rather a framework that highlights connections among them and exploits ways in which they may be used in tandem to address overarching research questions. Working group leaders aim to facilitate discussions and collaborations among researchers to advance our collective understanding and conveyed use of argumentation, justification and proof, particularly the relationships among these important mathematical constructs. The 2018 working group sessions will extend previous conversations into issues of teacher preparation with respect to argumentation, justification, and proof. The group will also discuss how issues of equity, social justice, and marginalized populations intersect with the teaching and learning of argumentation, justification, and proof. [ABSTRACT FROM AUTHOR]

Teachers' questioning is a pivotal contributing factor to support students' engagement in productive mathematical collective argumentation. Following Habermas'(1998) construct of rational behavior, we attempted to demonstrate how teachers' questioning can be framed based on this construct. Adapting Habermas' construct with Toulmin's (1958/2003) model for argumentation, we conducted a case study to analyze how a prospective secondary teacher used questions to support collective argumentation in one of her student teaching classrooms. We also explored how the prospective teacher's interpretations of argumentation related to her use of rational questioning. The results suggested that this theoretical integration can be a useful tool to frame teacher questioning based on teachers' intentions and organizations of argumentation. Some educational implications for teacher professional development are provided. [ABSTRACT FROM AUTHOR]

Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other times, they are inconsistent and even contradictory. The inconsistencies in definitions and usages of the terms argumentation, justification, and proof highlight the need for scholarly conversations addressing these (and other related) constructs. Collaboration is needed to move toward, not one-size-fits-all definitions, but rather a framework that highlights connections among them and exploits ways in which they may be used in tandem to address overarching research questions. Working group leaders aim to facilitate discussions and collaborations among researchers and to advance our collective understanding of argumentation, justification and proof, particularly the relationships among these important mathematical constructs. The 2016 working group sessions will provide continued opportunities for participants to discuss existing definitions and descriptions as well as opportunities to consider how these definitions and descriptions are related to the positionality of researchers and the contexts of their research. Participants will examine data sources through a variety of lenses as a means to investigate the use of particular conceptualizations. [ABSTRACT FROM AUTHOR]