Secondary mathematics teachers’ use of students’ incorrect answers in supporting collective argumentation

ABSTRACT

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 correctness of argument components as represented by the diagrams, we developed a potential model of levels of validity in classroom-based argumentation. The model may help the field to identify fine-grained conditions of validity within episodes of collective argumentation. The findings of this study provide insight into how teachers can manage or capitalize on incorrect parts of an argument when they attempt to support classroom-based argumentation as part of a long-term teaching intervention.

KEYWORDS:

• Incorrect answers
• collective argumentation
• toulmin’s model for argumentation
• secondary mathematics teaching

Acknowledgments

The ideas of this paper originate from but are not identical to the first author’s Ph.D. dissertation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. Collective argumentation can involve two or more participants; it is collective in the sense that the participants are working together toward a consensus or a shared understanding; sometimes only one person contributes verbally.

2. We use the word validity in the sense of “the state of being acceptable or reasonable” rather than “the state of being officially true or legally acceptable” (from dictionary.cambridge.org).

Additional information

Funding

This study is based upon work supported by the National Science Foundation under Grant No. 1149436. Any opinions, findings, and conclusion or recommendations expressed in this study are those of the author and do not necessarily reflect the views of the funding agency.

Notes on contributors

Yuling Zhuang

Yuling Zhuang is an assistant professor of mathematics education in the Department of Mathematics and Economics at Emporia State University. Her research focuses on classroom-based collective argumentation in STEM education, including teacher actions, teacher beliefs, and teacher learning of argumentation in terms of teacher education and professional development. Dr. Zhuang’s work investigates ways to empower teachers to support students’ engagement in argumentative discourse as well as help teachers to use argumentation for integrated STEM education.

AnnaMarie Conner

AnnaMarie Conner is a professor of mathematics education at the University of Georgia. Her work research is classroom-based and longitudinal, crossing boundaries between instruction in university courses and classroom teaching in school districts. She investigates teachers’ beliefs and identity construction during teacher education and how teachers learn to support collective argumentation in mathematics classes. These two lines of research come together in findings describing how teachers’ beliefs impact their classroom practice with respect to collective argumentation. Dr. Conner’s work investigates the complex connections between teacher education, teacher characteristics, and teacher practice. She is currently collaborating with secondary mathematics teachers in supporting mathematical arguments as well as investigating how elementary teachers navigate infusing argumentation into integrative STEM instruction.