Bridging the gap between mathematical conjecture and proof through computer-supported cognitive conflicts

In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to...

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Bibliographic Details
Published in:Teaching mathematics and its applications 2008-03, Vol.27 (1), p.1-10
Main Authors: Lee, Chun-Yi, Chen, Ming-Puu
Format: Article
Language:English
Subjects:
Adolescents
Cognitive Processes
Computer Uses in Education
Computers
Conflict
Geometry
Heuristics
High School Students
Inferences
Learner Engagement
Logical Thinking
Mathematical Aptitude
Mathematical Concepts
Mathematical Logic
Mathematics Curriculum
Mathematics Education
Mathematics Instruction
Metacognition
Problem Solving
Progress Monitoring
Science Instruction
Teaching Methods
Thinking Skills
Validity
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Summary:In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students’ conviction based only on empirical experience and to create a need for deductive explanations, we developed a problem-solving activity with technology support intended to cause cognitive conflict. In this article, we describe the process conducted for this activity that led students to contradictions between conjectures and findings. The teacher could create familiar problem-solving situations and use students’ naïve inductive approaches to make students think mathematically and establish the necessity for proof via computer support.
ISSN:0268-3679
1471-6976
DOI:10.1093/teamat/hrm014