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We analyze the vigorous debates among mathematicians concerning the idea of infinitesimals.", "publicationTitle": "Educational Studies in Mathematics", "publisher": "", "place": "", "date": "2010/03/25", "volume": "74", "issue": "3", "section": "", "partNumber": "", "partTitle": "", "pages": "259-273", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Educ Stud Math", "DOI": "10.1007/s10649-010-9239-4", "citationKey": "", "url": "http://link.springer.com.ezproxy2.library.arizona.edu/article/10.1007/s10649-010-9239-4", "accessDate": "2016-10-22T03:44:06Z", "PMID": "", "PMCID": "", "ISSN": "0013-1954, 1573-0816", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "link.springer.com.ezproxy2.library.arizona.edu", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2016-10-22T03:44:06Z", "dateModified": "2016-10-22T03:44:06Z" } }, { "key": "47DHUJD6", "version": 42, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/47DHUJD6", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/47DHUJD6", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/WJGVADS7", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "47DHUJD6", "version": 42, "parentItem": "WJGVADS7", "itemType": "attachment", "linkMode": "imported_url", "title": "Full Text PDF", "accessDate": "2016-07-19T03:14:39Z", "url": "http://sss.sagepub.com/content/33/2/301.full.pdf", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Giere and Moffatt - 2003 - Distributed Cognition Where the Cognitive and the.pdf", "md5": "16d167c8eb8dede9c0660c9b589fbcd6", "mtime": 1468898083514, "tags": [], "relations": {}, "dateAdded": "2016-07-19T03:14:39Z", "dateModified": "2016-07-19T03:14:43Z" } }, { "key": "EABRNC49", "version": 42, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/EABRNC49", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/EABRNC49", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/WJGVADS7", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } } }, "data": { "key": "EABRNC49", "version": 42, "parentItem": "WJGVADS7", "itemType": "attachment", "linkMode": "imported_url", "title": "Snapshot", "accessDate": "2016-07-19T03:14:39Z", "url": "http://sss.sagepub.com/content/33/2/301.short", "note": "", "contentType": "text/html", "charset": "utf-8", "filename": "301.html", "md5": "4fbe506ab7601904064f63ac5b65405c", "mtime": 1468898080458, "tags": [], "relations": {}, "dateAdded": "2016-07-19T03:14:39Z", "dateModified": "2016-07-19T03:14:39Z" } }, { "key": "WJGVADS7", "version": 41, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/WJGVADS7", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/WJGVADS7", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Giere and Moffatt", "parsedDate": "2003-04-01", "numChildren": 2 }, "data": { "key": "WJGVADS7", "version": 41, "itemType": "journalArticle", "title": "Distributed Cognition: Where the Cognitive and the Social Merge", "creators": [ { "creatorType": "author", "firstName": "Ronald N.", "lastName": "Giere" }, { "creatorType": "author", "firstName": "Barton", "lastName": "Moffatt" } ], "abstractNote": "Among the many contested boundaries in science studies is that between the cognitive and the social. Here, we are concerned to question this boundary from a perspective within the cognitive sciences based on the notion of distributed cognition. We first present two of many contemporary sources of the notion of distributed cognition, one from the study of artificial neural networks and one from cognitive anthropology. We then proceed to reinterpret two well-known essays by Bruno Latour, `Visualization and Cognition: Thinking with Eyes and Hands' and `Circulating Reference: Sampling the Soil in the Amazon Forest'. In both cases we find the cognitive and the social merged in a system of distributed cognition without any appeal to agonistic encounters. For us, results do not come to be regarded as veridical because they are widely accepted; they come to be widely accepted because, in the context of an appropriate distributed cognitive system, their apparent veracity can be made evident to anyone with the capacity to understand the workings of the system.", "publicationTitle": "Social Studies of Science", "publisher": "", "place": "", "date": "04/01/2003", "volume": "33", "issue": "2", "section": "", "partNumber": "", "partTitle": "", "pages": "301-310", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Social Studies of Science", "DOI": "10.1177/03063127030332017", "citationKey": "", "url": "http://sss.sagepub.com/content/33/2/301", "accessDate": "2016-07-19T03:14:39Z", "PMID": "", "PMCID": "", "ISSN": "0306-3127, 1460-3659", "archive": "", "archiveLocation": "", "shortTitle": "Distributed Cognition", "language": "en", "libraryCatalog": "sss.sagepub.com", "callNumber": "", "rights": "", "extra": "", "tags": [ { "tag": "Bruno Latour", "type": 1 }, { "tag": "Edwin Hutchins", "type": 1 }, { "tag": "cognitive versus social", "type": 1 }, { "tag": "distributed cognition", "type": 1 } ], "collections": [], "relations": {}, "dateAdded": "2016-07-19T03:14:39Z", "dateModified": "2016-07-19T03:14:39Z" } }, { "key": "S9RUEJGH", "version": 39, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/S9RUEJGH", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/S9RUEJGH", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Oehrtman", "parsedDate": "2009-07-01", "numChildren": 1 }, "data": { "key": "S9RUEJGH", "version": 39, "itemType": "journalArticle", "title": "Collapsing Dimensions, Physical Limitation, and Other Student Metaphors for Limit Concepts", "creators": [ { "creatorType": "author", "firstName": "Michael", "lastName": "Oehrtman" } ], "abstractNote": "This study investigated introductory calculus students' spontaneous reasoning about limit concepts guided by an interactionist theory of metaphorical reasoning developed by Max Black. In this perspective, strong metaphors are ontologically creative by virtue of their emphasis (commitment by the producer) and resonance (support for high degrees of elaborative implication). Analysis of 120 students' written and verbal descriptions of their thinking about challenging limit concepts resulted in the characterization of 5 clusters of strong metaphors. These clusters were based on the objects, relationships, and logic related to intuitions about (a) a collapse in dimension, (b) approximation and error analyses, (c) proximity in a space of point-locations, (d) a small physical scale beyond which nothing exists, and (e) the treatment of infinity as a number. Students' reasoning with these metaphors had significant implications for the images they formed and the claims and justifications they provided about multiple limit concepts.", "publicationTitle": "Journal for Research in Mathematics Education", "publisher": "", "place": "", "date": "July 1, 2009", "volume": "40", "issue": "4", "section": "", "partNumber": "", "partTitle": "", "pages": "396-426", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Journal for Research in Mathematics Education", "DOI": "", "citationKey": "", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/40539345", "accessDate": "2015-10-21T18:48:14Z", "PMID": "", "PMCID": "", "ISSN": "0021-8251", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "JSTOR", "callNumber": "", "rights": "Copyright © 2009 National Council of Teachers of Mathematics", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2015-10-21T18:48:14Z", "dateModified": "2015-10-21T18:48:14Z" } }, { "key": "UMF88GM7", "version": 37, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/UMF88GM7", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/UMF88GM7", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/FNX3VVPP", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "UMF88GM7", "version": 37, "parentItem": "FNX3VVPP", "itemType": "attachment", "linkMode": "imported_url", "title": "JSTOR Full Text PDF", "accessDate": "2015-09-30T21:13:50Z", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/pdfplus/10.2307/40539345.pdf?acceptTC=true", "note": "", "contentType": "application/pdf", "charset": "", "filename": "", "md5": null, "mtime": null, "tags": [], "relations": {}, "dateAdded": "2015-09-30T21:13:50Z", "dateModified": "2015-09-30T21:13:50Z" } }, { "key": "WR7U53KN", "version": 36, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/WR7U53KN", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/WR7U53KN", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/D5DT5TBD", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "WR7U53KN", "version": 36, "parentItem": "D5DT5TBD", "itemType": "attachment", "linkMode": "imported_url", "title": "JSTOR Full Text PDF", "accessDate": "2015-09-30T21:07:08Z", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/pdfplus/10.5951/mathteaceduc.1.2.0172.pdf?acceptTC=true", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Conner - 2013 - Authentic Argumentation With Prospective Secondary.pdf", "md5": "d13f8ce9299a299eab09352ee899b851", "mtime": 1443647233000, "tags": [], "relations": {}, "dateAdded": "2015-09-30T21:07:08Z", "dateModified": "2015-09-30T21:07:13Z" } }, { "key": "D5DT5TBD", "version": 35, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/D5DT5TBD", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/D5DT5TBD", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Conner", "parsedDate": "2013-03-01", "numChildren": 1 }, "data": { "key": "D5DT5TBD", "version": 35, "itemType": "journalArticle", "title": "Authentic Argumentation With Prospective Secondary Teachers: The Case of 0.999 …", "creators": [ { "creatorType": "author", "firstName": "AnnaMarie", "lastName": "Conner" } ], "abstractNote": "Engaging prospective secondary teachers in mathematical argumentation is important so that they can learn to engage their own students in creating and critiquing arguments. Often, when we attempt to engage prospective secondary teachers in argumentation around topics from secondary mathematics classes, the argumentation is not authentic, as they believe they already know the answers. There are problems related to the secondary curriculum around which students can be engaged in authentic argumentation, one of them is whether 0.999… = 1.", "publicationTitle": "Mathematics Teacher Educator", "publisher": "", "place": "", "date": "March 1, 2013", "volume": "1", "issue": "2", "section": "", "partNumber": "", "partTitle": "", "pages": "172-180", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Mathematics Teacher Educator", "DOI": "10.5951/mathteaceduc.1.2.0172", "citationKey": "", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/10.5951/mathteaceduc.1.2.0172", "accessDate": "2015-09-30T21:07:08Z", "PMID": "", "PMCID": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "Authentic Argumentation With Prospective Secondary Teachers", "language": "", "libraryCatalog": "JSTOR", "callNumber": "", "rights": "Copyright © 2013 National Council of Teachers of Mathematics", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2015-09-30T21:07:08Z", "dateModified": "2015-09-30T21:07:08Z" } }, { "key": "KQEGW2B4", "version": 32, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/KQEGW2B4", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/KQEGW2B4", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Ely", "parsedDate": "2010-03-01", "numChildren": 1 }, "data": { "key": "KQEGW2B4", "version": 32, "itemType": "journalArticle", "title": "Nonstandard Student Conceptions About Infinitesimals", "creators": [ { "creatorType": "author", "firstName": "Robert", "lastName": "Ely" } ], "abstractNote": "This is a case study of an undergraduate calculus student's nonstandard conceptions of the real number line. Interviews with the student reveal robust conceptions of the real number line that include infinitesimal and infinite quantities and distances. Similarities between these conceptions and those of G. W. Leibniz are discussed and illuminated by the formalization of infinitesimals in A. Robinson's nonstandard analysis. These similarities suggest that these student conceptions are not mere misconceptions, but are nonstandard conceptions, pieces of knowledge that could be built into a system of real numbers proven to be as mathematically consistent and powerful as the standard system. This provides a new perspective on students' \"struggles\" with the real numbers, and adds to the discussion about the relationship between student conceptions and historical conceptions by focusing on mechanisms for maintaining cognitive and mathematical consistency.", "publicationTitle": "Journal for Research in Mathematics Education", "publisher": "", "place": "", "date": "March 1, 2010", "volume": "41", "issue": "2", "section": "", "partNumber": "", "partTitle": "", "pages": "117-146", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Journal for Research in Mathematics Education", "DOI": "", "citationKey": "", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/20720128", "accessDate": "2015-09-30T21:03:33Z", "PMID": "", "PMCID": "", "ISSN": "0021-8251", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "JSTOR", "callNumber": "", "rights": "Copyright © 2010 National Council of Teachers of Mathematics", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2015-09-30T21:03:33Z", "dateModified": "2015-09-30T21:03:33Z" } }, { "key": "3S8CDE9D", "version": 31, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/3S8CDE9D", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/3S8CDE9D", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/S6GS3MVW", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "3S8CDE9D", "version": 31, "parentItem": "S6GS3MVW", "itemType": "attachment", "linkMode": "imported_url", "title": "JSTOR Full Text PDF", "accessDate": "2015-09-30T21:00:21Z", "url": "http://www.jstor.org.ezproxy2.library.arizona.edu/stable/pdfplus/10.2307/3481802.pdf?acceptTC=true", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Tall - 1980 - The Notion of Infinite Measuring Number and Its Re.pdf", "md5": "609fa45c51adc53ce247d106aa377109", "mtime": 1443646825000, "tags": [], "relations": {}, "dateAdded": "2015-09-30T21:00:21Z", "dateModified": "2015-09-30T21:00:25Z" } }, { "key": "S6GS3MVW", "version": 30, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/S6GS3MVW", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/S6GS3MVW", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Tall", "parsedDate": "1980-08-01", "numChildren": 1 }, "data": { "key": "S6GS3MVW", "version": 30, "itemType": "journalArticle", "title": "The Notion of Infinite Measuring Number and Its Relevance in the Intuition of Infinity", "creators": [ { "creatorType": "author", "firstName": "David", "lastName": "Tall" } ], "abstractNote": "In this paper a concept of infinity is described which extrapolates the measuring properties of number rather than counting aspects (which lead to cardinal number theory). Infinite measuring numbers are part of a coherent number system extending the real numbers, including both infinitely large and infinitely small quantities. A suitable extension is the superreal number system described here; an alternative extension is the hyperreal number field used in non-standard analysis which is also mentioned. Various theorems are proved in careful detail to illustrate that certain properties of infinity which might be considered 'false' in a cardinal sense are 'true' in a measuring sense. Thus cardinal infinity is now only one of a choice of possible extensions of the number concept to the infinite case. It is therefore inappropriate to judge the 'correctness' of intuitions of infinity within a cardinal framework alone, especially those intuitions which relate to measurement rather than one-one correspondence. The same comments apply in general to the analysis of naive intuitions within an extrapolated formal framework.", "publicationTitle": "Educational Studies in Mathematics", "publisher": "", "place": "", "date": "August 1, 1980", "volume": "11", "issue": "3", "section": "", "partNumber": "", "partTitle": "", "pages": "271-284", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Educational Studies in Mathematics", "DOI": "", "citationKey": "", "url": "http://www.jstor.org.ezproxy2.library.arizona.edu/stable/3481802", "accessDate": "2015-09-30T21:00:21Z", "PMID": "", "PMCID": "", "ISSN": "0013-1954", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "JSTOR", "callNumber": "", "rights": "Copyright © 1980 Springer", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2015-09-30T21:00:21Z", "dateModified": "2015-09-30T21:00:21Z" } }, { "key": "MH2H284E", "version": 29, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/MH2H284E", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/MH2H284E", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/K6ZN6AQP", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "MH2H284E", "version": 29, "parentItem": "K6ZN6AQP", "itemType": "attachment", "linkMode": "imported_url", "title": "JSTOR Full Text PDF", "accessDate": "2015-09-30T20:56:09Z", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/pdfplus/10.2307/41485943.pdf?acceptTC=true", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Kidron - 2011 - Tacit models, treasured intuitions and the discret.pdf", "md5": "0fb032c8f7295eb19b9ca4ed73c0e1a6", "mtime": 1443646595000, "tags": [], "relations": {}, "dateAdded": "2015-09-30T20:56:09Z", "dateModified": "2015-09-30T20:56:36Z" } }, { "key": "K6ZN6AQP", "version": 28, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/K6ZN6AQP", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/K6ZN6AQP", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Kidron", "parsedDate": "2011-09-01", "numChildren": 1 }, "data": { "key": "K6ZN6AQP", "version": 28, "itemType": "journalArticle", "title": "Tacit models, treasured intuitions and the discrete—continuous interplay", "creators": [ { "creatorType": "author", "firstName": "Ivy", "lastName": "Kidron" } ], "abstractNote": "We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students' understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit models that coexist with students' logical reasoning. The students are highly trained in mathematics. We encounter expressions of the persistence and impact of intuitions and tacit pictorial models as described by Fischbein. But we also observe some new characterization of persistence of tacit models in which the tacit pictorial model continues to interfere in the student's reasoning process, coexists with a logical reasoning but does not prevent the student from reaching a feeling of logical consistency. The empirical analysis and the theoretical discussion offered in the present paper permit us to highlight this very special integration of the formal and the intuitive components of the reasoning process.", "publicationTitle": "Educational Studies in Mathematics", "publisher": "", "place": "", "date": "September 1, 2011", "volume": "78", "issue": "1", "section": "", "partNumber": "", "partTitle": "", "pages": "109-126", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Educational Studies in Mathematics", "DOI": "", "citationKey": "", "url": "http://www.jstor.org.ezproxy1.library.arizona.edu/stable/41485943", "accessDate": "2015-09-30T20:56:09Z", "PMID": "", "PMCID": "", "ISSN": "0013-1954", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "JSTOR", "callNumber": "", "rights": "Copyright © 2011 Springer", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2015-09-30T20:56:09Z", "dateModified": "2015-09-30T20:56:09Z" } }, { "key": "F92HHQQN", "version": 27, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/F92HHQQN", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/F92HHQQN", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/K2UKPRXH", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "F92HHQQN", "version": 27, "parentItem": "K2UKPRXH", "itemType": "attachment", "linkMode": "imported_url", "title": "JSTOR Full Text PDF", "accessDate": "2015-09-30T20:54:10Z", "url": "http://www.jstor.org.ezproxy2.library.arizona.edu/stable/pdfplus/10.2307/3483137.pdf?acceptTC=true", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Tsamir - 1999 - The Transition from Comparison of Finite to the Co.pdf", "md5": "29e030150c4a35cec054ca15f51f9a11", "mtime": 1443646460000, "tags": [], "relations": {}, "dateAdded": "2015-09-30T20:54:10Z", "dateModified": "2015-09-30T20:54:20Z" } }, { "key": "K2UKPRXH", "version": 26, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/K2UKPRXH", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/K2UKPRXH", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "creatorSummary": "Tsamir", "parsedDate": "1999-01-01", "numChildren": 1 }, "data": { "key": "K2UKPRXH", "version": 26, "itemType": "journalArticle", "title": "The Transition from Comparison of Finite to the Comparison of Infinite Sets: Teaching Prospective Teachers", "creators": [ { "creatorType": "author", "firstName": "Pessia", "lastName": "Tsamir" } ], "abstractNote": "Research in mathematics education indicates that in the transition from given systems to wider ones prospective teachers tend to attribute all the properties that hold for the former also to the latter. In particular, it has been found that, in the context of Cantorian Set Theory, prospective teachers have been found to erroneously attribute properties of finite sets to infinite ones - using different methods to compare the number of elements in infinite sets. These methods which are acceptable for finite sets, lead to contradictions with infinite ones. This paper describes a course in Cantorian Set Theory that relates to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. The findings clearly indicate that when comparing the number of elements in infinite sets the prospective teachers who took the course were more successful and were also more consistent in their use of a single method than those who studied the traditional, formally-based Cantorian Set Theory course.", "publicationTitle": "Educational Studies in Mathematics", "publisher": "", "place": "", "date": "January 1, 1999", "volume": "38", "issue": "1/3", "section": "", "partNumber": "", "partTitle": "", "pages": "209-234", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Educational Studies in Mathematics", "DOI": "", "citationKey": "", "url": "http://www.jstor.org.ezproxy2.library.arizona.edu/stable/3483137", "accessDate": "2015-09-30T20:54:10Z", "PMID": "", "PMCID": "", "ISSN": "0013-1954", "archive": "", "archiveLocation": "", "shortTitle": "The Transition from Comparison of Finite to the Comparison of Infinite Sets", "language": "", "libraryCatalog": "JSTOR", "callNumber": "", "rights": "Copyright © 1999 Springer", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2015-09-30T20:54:10Z", "dateModified": "2015-09-30T20:54:10Z" } }, { "key": "CJWPEB7N", "version": 25, "library": { "type": "group", "id": 399961, "name": "Teaching and Learning of Infinity", "links": { "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/399961/items/CJWPEB7N", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/teaching_and_learning_of_infinity/items/CJWPEB7N", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/399961/items/RKG5VTNE", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1583373, "username": "queerpedagogue", "name": "James Sheldon", "links": { "alternate": { "href": "https://www.zotero.org/queerpedagogue", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "CJWPEB7N", "version": 25, "parentItem": "RKG5VTNE", "itemType": "attachment", "linkMode": "imported_url", "title": "JSTOR Full Text PDF", "accessDate": "2015-09-30T20:52:44Z", "url": "http://www.jstor.org.ezproxy2.library.arizona.edu/stable/pdfplus/10.2307/3482297.pdf?acceptTC=true", "note": "", "contentType": "application/pdf", "charset": "", "filename": "A. and Waldegg - 1991 - The Conceptual Evolution of Actual Mathematical In.pdf", "md5": "4bcc18aa2368e15b163e0976275f6ffd", "mtime": 1443646383000, "tags": [], "relations": {}, "dateAdded": "2015-09-30T20:52:44Z", "dateModified": "2015-09-30T20:53:03Z" } } ]