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Lange, 2024 - Google Patents

What are explanatory proofs in mathematics and how can they contribute to teaching and learning?

Lange, 2024

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Document ID
16770445360854243446
Author
Lange M
Publication year
Publication venue
The Journal of Mathematical Behavior

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Snippet

This paper will examine several simple examples (drawn from the mathematics literature) where there are multiple proofs of the same theorem, but only some of these proofs are widely regarded by mathematicians as explanatory. These examples will motivate an …
Continue reading at marclange.org (PDF) (other versions)

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    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
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    • G09B19/00—Teaching not covered by other main groups of this subclass
    • G09B19/02—Counting; Calculating
    • G09B19/025—Counting; Calculating with electrically operated apparatus or devices
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
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    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
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    • G09B7/00—Electrically-operated teaching apparatus or devices working with questions and answers
    • G09B7/02—Electrically-operated teaching apparatus or devices working with questions and answers of the type wherein the student is expected to construct an answer to the question which is presented or wherein the machine gives an answer to the question presented by a student
    • G—PHYSICS
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    • G09B1/00—Manually or mechanically operated educational appliances using elements forming, or bearing, symbols, signs, pictures, or the like which are arranged or adapted to be arranged in one or more particular ways
    • G09B1/02—Manually or mechanically operated educational appliances using elements forming, or bearing, symbols, signs, pictures, or the like which are arranged or adapted to be arranged in one or more particular ways and having a support carrying or adapted to carry the elements
    • G09B1/04—Manually or mechanically operated educational appliances using elements forming, or bearing, symbols, signs, pictures, or the like which are arranged or adapted to be arranged in one or more particular ways and having a support carrying or adapted to carry the elements the elements each bearing a single symbol or a single combination of symbols
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
    • G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
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    • G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
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