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Referential and syntactic approaches to proving: case studies from a transition-to-proof course
The goal of this paper is to increase our understanding of different approaches to proving in advanced mathematics. We present two case studies from an interview-based investigation in which students were asked to complete proof-related tasks. The first student consistently took what we call a refer...
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| Main Authors: | , |
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| Format: | Default Book chapter |
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2010
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| Online Access: | https://hdl.handle.net/2134/8945 |
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| _version_ | 1818174831870345216 |
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| author | Lara Alcock Keith Weber |
| author_facet | Lara Alcock Keith Weber |
| author_sort | Lara Alcock (1384308) |
| collection | Figshare |
| description | The goal of this paper is to increase our understanding of different approaches to proving in advanced mathematics. We present two case studies from an interview-based investigation in which students were asked to complete proof-related tasks. The first student consistently took what we call a referential approach toward these tasks, examining examples of the objects to which the mathematical statements referred, and using these to guide reasoning. The second consistently took what we call a syntactic approach toward these tasks, working logically with definitions and proof structures without reference to examples. Both students made substantial progress on each of the tasks, but they exhibited different strengths and experienced different difficulties. In this paper we: demonstrate consistency in these students' approaches across a range of tasks, examine the different strengths and difficulties associated with their approaches to proving, and consider the pedagogical issues raised by these apparent student preferences for reasoning in certain ways. |
| format | Default Book chapter |
| id | rr-article-9371975 |
| institution | Loughborough University |
| publishDate | 2010 |
| record_format | Figshare |
| spelling | rr-article-93719752010-01-01T00:00:00Z Referential and syntactic approaches to proving: case studies from a transition-to-proof course Lara Alcock (1384308) Keith Weber (7157651) untagged The goal of this paper is to increase our understanding of different approaches to proving in advanced mathematics. We present two case studies from an interview-based investigation in which students were asked to complete proof-related tasks. The first student consistently took what we call a referential approach toward these tasks, examining examples of the objects to which the mathematical statements referred, and using these to guide reasoning. The second consistently took what we call a syntactic approach toward these tasks, working logically with definitions and proof structures without reference to examples. Both students made substantial progress on each of the tasks, but they exhibited different strengths and experienced different difficulties. In this paper we: demonstrate consistency in these students' approaches across a range of tasks, examine the different strengths and difficulties associated with their approaches to proving, and consider the pedagogical issues raised by these apparent student preferences for reasoning in certain ways. 2010-01-01T00:00:00Z Text Chapter 2134/8945 https://figshare.com/articles/chapter/Referential_and_syntactic_approaches_to_proving_case_studies_from_a_transition-to-proof_course/9371975 CC BY-NC-ND 4.0 |
| spellingShingle | untagged Lara Alcock Keith Weber Referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| title | Referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| title_full | Referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| title_fullStr | Referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| title_full_unstemmed | Referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| title_short | Referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| title_sort | referential and syntactic approaches to proving: case studies from a transition-to-proof course |
| topic | untagged |
| url | https://hdl.handle.net/2134/8945 |