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Semantic contamination and mathematical proof: can a non-proof prove?
The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Hereweargue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learni...
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| Main Authors: | , |
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| Format: | Default Article |
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2011
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| Online Access: | https://hdl.handle.net/2134/8572 |
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| _version_ | 1818175556921851904 |
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| author | Juan P. Mejia-Ramos Matthew Inglis |
| author_facet | Juan P. Mejia-Ramos Matthew Inglis |
| author_sort | Juan P. Mejia-Ramos (7157663) |
| collection | Figshare |
| description | The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Hereweargue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove. |
| format | Default Article |
| id | rr-article-9368681 |
| institution | Loughborough University |
| publishDate | 2011 |
| record_format | Figshare |
| spelling | rr-article-93686812011-01-01T00:00:00Z Semantic contamination and mathematical proof: can a non-proof prove? Juan P. Mejia-Ramos (7157663) Matthew Inglis (1384290) Other education not elsewhere classified Language Mathematics Proof Reasoning Semantic contamination The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Hereweargue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to argument evaluation tasks suggest that students may hold two different and contradictory conceptions of proof: one related to conviction, and one to validity. We demonstrate that these two conceptions can be preferentially elicited by making apparently irrelevant linguistic changes to task instructions. After analyzing the occurrence of “proof” and “prove” in natural language, we report two experiments that suggest that the noun form privileges evaluations related to validity, and that the verb form privileges evaluations related to conviction. In short, we show that (what is judged to be) a non-proof can sometimes (be judged to) prove. 2011-01-01T00:00:00Z Text Journal contribution 2134/8572 https://figshare.com/articles/journal_contribution/Semantic_contamination_and_mathematical_proof_can_a_non-proof_prove_/9368681 CC BY-NC-ND 4.0 |
| spellingShingle | Other education not elsewhere classified Language Mathematics Proof Reasoning Semantic contamination Juan P. Mejia-Ramos Matthew Inglis Semantic contamination and mathematical proof: can a non-proof prove? |
| title | Semantic contamination and mathematical proof: can a non-proof prove? |
| title_full | Semantic contamination and mathematical proof: can a non-proof prove? |
| title_fullStr | Semantic contamination and mathematical proof: can a non-proof prove? |
| title_full_unstemmed | Semantic contamination and mathematical proof: can a non-proof prove? |
| title_short | Semantic contamination and mathematical proof: can a non-proof prove? |
| title_sort | semantic contamination and mathematical proof: can a non-proof prove? |
| topic | Other education not elsewhere classified Language Mathematics Proof Reasoning Semantic contamination |
| url | https://hdl.handle.net/2134/8572 |