Teachers' Contextualization of Argumentation in the Mathematics Classroom

• In Event: 52.045 - Argumentation Within and Beyond K–12 Classrooms

Abstract

A mathematical argument is “a line of reasoning that intends to show or explain why a mathematical result is true” (“Argument,” 2014). Mathematical argumentation is a practice that involves a range of activities such as conjecturing, testing examples, thought experiments, representing mathematical ideas, taking another’s point of view, analyzing, and revising (see Lakatos, 1976). Mathematical arguments (some in need of revision) are produced repeatedly as a group engages the process of argumentation.

The importance of argumentation in K-12 mathematics education is generally asserted based on its critical role in the discipline of mathematics as evidenced by various standards and curricular documents (e.g., Common Core State Standards in Mathematics [CCSSM] (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). CCSSM, as well as other math standards and curricular documents, however, say little about the importance of mathematical argumentation in the teaching and learning of mathematical topics.

This paper presentation examines multiple purposes for engaging students in argumentation in the mathematics classroom, and explores how different purposes are shaped by, and shape, the opportunities students have to participate in argumentation at the classroom level. Using a situative perspective (Lave, 1996; Greeno & MMAP, 1997) to view the classroom, we unpack the different opportunities students have to make sense of argumentation as they engage various tasks and activities. We seek to understand how teacher’s choices during task implementation may reflect different valued purposes of argumentation, ultimately shaping students’ understanding of the practice of mathematical argumentation and its role in the discipline.

Drawing on classroom video data from an NSF-funded research project, we document how argumentation - a practice that is central to establishing new knowledge of the mathematics community – can be contextualized in secondary mathematics classrooms to serve different purposes. We document two complementary purposes – argumentation for concept development and argumentation for mathematical practice development. Argumentation for concept development is prioritized as teachers engage students in argumentation as a practice to develop students’ conceptual understanding of a topic such as area, congruence, the distributive property, etc. Argumentation for mathematical practice development is prioritized as teachers engage students in argumentation in order to support them in becoming more proficient at mathematical argumentation (an important process skill (practice) central to mathematics). We conclude with a discussion of tensions and recommendations related to offering students a robust view of this crucial practice.

By providing a nuanced analysis of classroom interactions on the same task that lead to different experiences with the practice of argumentation, this analysis extends our understanding of the role of mathematical argumentation in classrooms, building on literature on the role of proof in mathematics and the role of justification (e.g., de Villiers, 1990; Hanna, 2000) and argumentation in mathematical classrooms (Author, 2012, 2014).

Authors

• Megan E. Staples, University of Connecticut

• Jill Annette Newton, Purdue University