Calculus using proximities: a mathematical approach in which students can actually prove theorems
Teaching and learning calculus are notoriously difficult and the didactic solutions may involve resorting to intuitive but vague definitions or informal gestures offered as proofs. The teaching literature is rife with examples of metaphors, adverb manipulations and descriptions of what happens “just...
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-02-01
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| Series: | Open Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0007/math-2017-0007.xml?format=INT |
| _version_ | 1818260672420511744 |
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| author | O’Donovan Richard |
| author_facet | O’Donovan Richard |
| author_sort | O’Donovan Richard |
| collection | DOAJ |
| description | Teaching and learning calculus are notoriously difficult and the didactic solutions may involve resorting to intuitive but vague definitions or informal gestures offered as proofs. The teaching literature is rife with examples of metaphors, adverb manipulations and descriptions of what happens “just before” the limit. It is then difficult to leave the domain of the mental image, thus losing the training in rigour. The author (with Karel Hrbacek and Olivier Lessmann) has endeavoured a radically different approach with the objective of training students to prove theorems while preserving both intuition and mathematical rigour. Hence we change the mathematical setting rather than the didactic setting. The result (which is a by-product of nonstandard analysis) has been used in several high schools in Geneva – Switzerland – for over ten years. |
| first_indexed | 2024-12-12T18:35:03Z |
| format | Article |
| id | doaj.art-2b4a9ad0ccb7432f967b6822c4e7356f |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-12T18:35:03Z |
| publishDate | 2017-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-2b4a9ad0ccb7432f967b6822c4e7356f2022-12-22T00:15:48ZengDe GruyterOpen Mathematics2391-54552017-02-01151303610.1515/math-2017-0007math-2017-0007Calculus using proximities: a mathematical approach in which students can actually prove theoremsO’Donovan Richard0Collège André-Chavanne, Geneva, SwitzerlandTeaching and learning calculus are notoriously difficult and the didactic solutions may involve resorting to intuitive but vague definitions or informal gestures offered as proofs. The teaching literature is rife with examples of metaphors, adverb manipulations and descriptions of what happens “just before” the limit. It is then difficult to leave the domain of the mental image, thus losing the training in rigour. The author (with Karel Hrbacek and Olivier Lessmann) has endeavoured a radically different approach with the objective of training students to prove theorems while preserving both intuition and mathematical rigour. Hence we change the mathematical setting rather than the didactic setting. The result (which is a by-product of nonstandard analysis) has been used in several high schools in Geneva – Switzerland – for over ten years.http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0007/math-2017-0007.xml?format=INTdidacticsanalysisnonstandard analysisultrasmall numbers03c9903e7003h0526a0326a0697i1097i40 |
| spellingShingle | O’Donovan Richard Calculus using proximities: a mathematical approach in which students can actually prove theorems Open Mathematics didactics analysis nonstandard analysis ultrasmall numbers 03c99 03e70 03h05 26a03 26a06 97i10 97i40 |
| title | Calculus using proximities: a mathematical approach in which students can actually prove theorems |
| title_full | Calculus using proximities: a mathematical approach in which students can actually prove theorems |
| title_fullStr | Calculus using proximities: a mathematical approach in which students can actually prove theorems |
| title_full_unstemmed | Calculus using proximities: a mathematical approach in which students can actually prove theorems |
| title_short | Calculus using proximities: a mathematical approach in which students can actually prove theorems |
| title_sort | calculus using proximities a mathematical approach in which students can actually prove theorems |
| topic | didactics analysis nonstandard analysis ultrasmall numbers 03c99 03e70 03h05 26a03 26a06 97i10 97i40 |
| url | http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0007/math-2017-0007.xml?format=INT |
| work_keys_str_mv | AT odonovanrichard calculususingproximitiesamathematicalapproachinwhichstudentscanactuallyprovetheorems |