Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper's central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require.
%0 Journal Article
%1 Livingston06
%A Livingston, Eric
%D 2006
%J Social Studies of Science
%K cognition discovery ethnomethodology ijceell06 mathematics mythesis philosophy polya proof reasoning situated
%N 1
%P 39-68
%R 10.1177/0306312705053055
%T The Context of Proving
%U http://sss.sagepub.com/cgi/content/abstract/36/1/39
%V 36
%X Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper's central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require.
@article{Livingston06,
abstract = {Discussions of mathematical problem-solving and heuristic reasoning have typically examined how proofs that are already known might be found. This approach has at least three problems: first, provers engaged in discovering proofs for themselves cannot have this perspective; second, if a proof is difficult, formulaic strategies quickly run out; third, beginning with a proof already in-hand separates reasoning about a proof from the actual circumstances in which such reasoning occurs. As an alternative approach to the study of mathematical reasoning, this paper presents a detailed descriptive account of the work of finding a specific proof, including the shifting of perspectives, the wrong paths, the mistakes and the outright errors. Even the appearance of a sketched diagram or of a course of mathematical writing can suggest unanticipated possibilities for finding a proof. This material is used to illustrate the paper's central claim - that the ways that provers go about working on proofs provide the context for continuing that work and for discovering the reasoning that a particular proof is then seen to require.},
added-at = {2008-05-30T05:55:37.000+0200},
author = {Livingston, Eric},
biburl = {https://www.bibsonomy.org/bibtex/22f9395acd26e6d2e31ad9ef73b551c18/yish},
citeulike-article-id = {487275},
doi = {10.1177/0306312705053055},
interhash = {125f4d54ff50383d6a4e855c8ef8e820},
intrahash = {2f9395acd26e6d2e31ad9ef73b551c18},
journal = {Social Studies of Science},
keywords = {cognition discovery ethnomethodology ijceell06 mathematics mythesis philosophy polya proof reasoning situated},
month = {February},
number = 1,
pages = {39-68},
timestamp = {2008-05-30T05:55:39.000+0200},
title = {The Context of Proving},
url = {http://sss.sagepub.com/cgi/content/abstract/36/1/39},
volume = 36,
year = 2006
}