Generating and using examples in the proving process
We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulatio...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2013
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| _version_ | 1797104923214610432 |
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| author | Sandefur, J Mason, J Stylianides, G Watson, A |
| author_facet | Sandefur, J Mason, J Stylianides, G Watson, A |
| author_sort | Sandefur, J |
| collection | OXFORD |
| description | We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: experience of utility of examples in proving, personal example spaces and technical tools, formulation of the problem, and relational necessity. Our analysis led to integrating two theoretical ideas: the alignment of conceptual insight and technical handle when trying to prove; and manipulating, getting-a-sense-of, and articulating as phases of work associated with example construction. © 2012 Springer Science+Business Media Dordrecht. |
| first_indexed | 2024-03-07T06:40:19Z |
| format | Journal article |
| id | oxford-uuid:f91002d3-4d76-443d-986d-f444a1ae645f |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:40:19Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:f91002d3-4d76-443d-986d-f444a1ae645f2022-03-27T12:55:04ZGenerating and using examples in the proving processJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f91002d3-4d76-443d-986d-f444a1ae645fEnglishSymplectic Elements at Oxford2013Sandefur, JMason, JStylianides, GWatson, AWe report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of situations in which example generation seems to play a positive role in proving. These aspects integrate qualities of students and of problems: experience of utility of examples in proving, personal example spaces and technical tools, formulation of the problem, and relational necessity. Our analysis led to integrating two theoretical ideas: the alignment of conceptual insight and technical handle when trying to prove; and manipulating, getting-a-sense-of, and articulating as phases of work associated with example construction. © 2012 Springer Science+Business Media Dordrecht. |
| spellingShingle | Sandefur, J Mason, J Stylianides, G Watson, A Generating and using examples in the proving process |
| title | Generating and using examples in the proving process |
| title_full | Generating and using examples in the proving process |
| title_fullStr | Generating and using examples in the proving process |
| title_full_unstemmed | Generating and using examples in the proving process |
| title_short | Generating and using examples in the proving process |
| title_sort | generating and using examples in the proving process |
| work_keys_str_mv | AT sandefurj generatingandusingexamplesintheprovingprocess AT masonj generatingandusingexamplesintheprovingprocess AT stylianidesg generatingandusingexamplesintheprovingprocess AT watsona generatingandusingexamplesintheprovingprocess |