%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 }