Soft Drinks, Mind Reading, & Number Theory

Proof is a central component of mathematicians' work, used for verification, explanation, discovery, and communication. Unfortunately, high school students' experiences with proof are often limited to verifying mathematical statements or relationships that are already known to be true. As...

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Bibliographic Details
Published in:The Mathematics teacher 2009-11, Vol.103 (4), p.278-283
Main Author: Schultz, Kyle T.
Format: Article
Language:English
Subjects:
Algebra
Classroom discussion
Demonstrative reasoning
Discussion (Teaching Technique)
High School Students
High schools
Mathematical Logic
Mathematics
Mathematics Education
Mathematics Instruction
Mathematics teachers
Number Concepts
Number theory
Numbers
Professional Personnel
Proof theory
Reasoning
Respect
Secondary school mathematics
Teaching methods
Validity
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Summary:Proof is a central component of mathematicians' work, used for verification, explanation, discovery, and communication. Unfortunately, high school students' experiences with proof are often limited to verifying mathematical statements or relationships that are already known to be true. As a result, students often fail to grasp the true nature of what it means to do mathematics. In response to this deficiency, NCTM (2000) has stated clearly that "reasoning and proof are not special activities reserved for special times or special topics in the curriculum but should be a natural, ongoing part of classroom discussions" (p. 342). This article presents a classroom discussion of a mathematical idea that arose spontaneously but that could be used purposefully as a mechanism to develop students' conceptions of proof and the nature of mathematical work. (Contains 2 tables and 1 figure.)
ISSN:0025-5769
2330-0582
DOI:10.5951/MT.103.4.0278