Convergence of Numerical Sequences: A Commentary on "The Vice: Some Historically Inspired and Proof Generated Steps to Limits of Sequences" by R.P. Burn

Burn (2005) proposes a genetic approach to teaching limits of numerical sequences. The article includes an explanation of the Method of Exhaustion,¹ a generalization of this method, and a description of how this method was used for obtaining areas and lengths in the seventeenth century. The author u...

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Bibliographic Details
Published in:Educational studies in mathematics 2006-03, Vol.61 (3), p.395-402
Main Author: Berge, Analia
Format: Article
Language:English
Subjects:
Analysis
Approximation
Convergence (Mathematics)
History instruction
Infinity
Learning
Mathematical completeness
Mathematical knowledge
Mathematical problems
Mathematical sequences
Mathematics education
Real numbers
Sequences (Mathematics)
Study and teaching
Citations: Items that this one cites
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Summary:Burn (2005) proposes a genetic approach to teaching limits of numerical sequences. The article includes an explanation of the Method of Exhaustion,¹ a generalization of this method, and a description of how this method was used for obtaining areas and lengths in the seventeenth century. The author uses these historical and mathematical analyses as a basis for proposing an alternative definition of the limit of a sequence. The paper focuses on the fine mathematical and historical detail of the notion of limit. Reading it made me reflect on the explicitly or implicitly involved didactical aspects, which I would like to share with ESM readers.
ISSN:0013-1954
1573-0816
DOI:10.1007/s10649-006-8754-9