Engaging Students in Proving: A Double Bind on the Teacher

This article uses a classroom episode in which a teacher and her students undertake a task of proving a proposition about angles as a context for analyzing what is involved in the teacher's work of engaging students in producing a proof. The analysis invokes theoretical notions of didactical co...

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Bibliographic Details
Published in:Journal for research in mathematics education 2002-05, Vol.33 (3), p.176-203
Main Author: Herbst, Patricio G.
Format: Article
Language:English
Subjects:
Academic Standards
Classroom Communication
Classroom Environment
Diagrams
Division of labor
Educational Practices
Elementary Secondary Education
Geometric Concepts
Geometry
Knowledge Level
Learner Engagement
Learning
Logical givens
Mathematical Concepts
Mathematical knowledge
Mathematical Logic
Mathematics curricula
Mathematics education
Mathematics Instruction
Mathematics Teachers
Secondary School Teachers
Secondary Schools
Students
Teachers
Teaching
Teaching Methods
Units of Study
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Summary:This article uses a classroom episode in which a teacher and her students undertake a task of proving a proposition about angles as a context for analyzing what is involved in the teacher's work of engaging students in producing a proof. The analysis invokes theoretical notions of didactical contract and double bind to uncover and explain conflicting demands that the practice of assigning two-column proofs imposes on high school teachers. Two aspects of the work of teaching--what teachers do to create a task in which students can produce a proof and what teachers do to get students to prove a proposition--are the focus of the analysis of the episode. This analysis supports the argument that the traditional custom of engaging students in doing formal, two-column proofs places contradictory demands on the teacher regarding how the ideas for a proof will be developed. Recognizing these contradictory demands clarifies why the teacher in the analyzed episode ends up suggesting the key ideas for the proof. The analysis, coupled with current recommendations about the role of proof in school mathematics, suggests that it is advantageous for teachers to avoid treating proof only as a formal process.
ISSN:0021-8251
1945-2306
DOI:10.2307/749724