Valuing Informal Arguments and Empirical Investigations during Collective Argumentation

Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not...

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Bibliographic Details
Published in:PRIMUS : problems, resources, and issues in mathematics undergraduate studies resources, and issues in mathematics undergraduate studies, 2012-12, Vol.22 (8), p.643-663
Main Author: Yopp, David A.
Format: Article
Language:English
Subjects:
argumentation
Classroom Communication
Classrooms
Cognition & reasoning
College Faculty
College Mathematics
Colleges
Empirical analysis
empirical investigations
Evidence
Geometry
High Schools
Higher education
Inquiry
Instructors
Learning Strategies
Linear algebra
Logical Thinking
Mathematical analysis
Mathematical Logic
Mathematics education
Mathematics Instruction
Middle School Teachers
Personal development
Persuasive Discourse
Proof
Proof theory
proving
reasoning
Secondary School Mathematics
Secondary School Teachers
Students
Teacher Educators
Teachers
Teaching Methods
Training
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Summary:Considerable literature has documented both the pros and cons of students' use of empirical evidence during proving activities. This article presents an analysis of a classroom episode involving in-service middle school, high school, and college teachers that demonstrates that learners need not be steered away from empirical investigations during collective argumentation. The analysis demonstrates that empirical investigations and subsequent informal reasoning during collective argumentation can provide opportunities for the instructor to introduce important mathematical tools and conceptions, and opportunities to discuss various levels and types of arguments and their individual importance to mathematical thinking, all the while progressing toward formal proof. Implications for the training and professional development of those who prepare students for college mathematics and those who teach college mathematics are discussed.
ISSN:1051-1970
1935-4053
DOI:10.1080/10511970.2011.621164