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Discouraging "Proof by Example"

Author

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  • Thomas Mitchell

    (Southern Illinois University at Carbondale)

Abstract

One of the difficult and frustrating aspects of teaching mathematics is getting students to think logically and develop an ability to prove theorems. Too frequently, students resort to what might be called "proof by example." A classic illustration of "proof by example" comes from years of teaching "mathematics for economists." The exercise is to prove a general principle about sets; for example: "show that for arbitrary sets A and B, the sets A \setminus B, B \setminus A, and A \intersect B are pairwise disjoint." Too frequently the student "proof" begins with: "Let A = {1,3,5,7} and B = {2,4,6,8}. Then ..." Other examples, in other areas of mathematics, no doubt abound. This note presents an obviously preposterous "theorem" and "proves" it with many examples. This "theorem," once "proved" in class, successfully discourages future proofs "by example."

Suggested Citation

  • Thomas Mitchell, 1995. "Discouraging "Proof by Example"," GE, Growth, Math methods 9506001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpge:9506001
    Note: 10 pages; LaTeX 2.09; three files FTP'ed: DVI, PostScript, and TeX input file; Report_no: SIUC Discussion Paper #90-07
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    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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