CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks
This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics te...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hipatia Press
2019-10-01
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| Series: | REDIMAT |
| Online Access: | https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3315 |
| _version_ | 1811165655527849984 |
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| author | Uffe Thomas Jankvist Morten Misfeldt |
| author_facet | Uffe Thomas Jankvist Morten Misfeldt |
| author_sort | Uffe Thomas Jankvist |
| collection | DOAJ |
| description | This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are identified in ten different textbooks. The CAS based proofs in these textbooks are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses draw on theoretical constructs related to both proofs and proving (e.g. proof schemes) and to use of digital technologies in mathematics education (lever potential, blackboxing, instrumental genesis). In particular, the analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning. |
| first_indexed | 2024-04-10T15:40:13Z |
| format | Article |
| id | doaj.art-c108339461d24ab782cf8124d910ea5a |
| institution | Directory Open Access Journal |
| issn | 2014-3621 |
| language | English |
| last_indexed | 2024-04-10T15:40:13Z |
| publishDate | 2019-10-01 |
| publisher | Hipatia Press |
| record_format | Article |
| series | REDIMAT |
| spelling | doaj.art-c108339461d24ab782cf8124d910ea5a2023-02-12T12:54:50ZengHipatia PressREDIMAT2014-36212019-10-018310.17583/redimat.2019.3315CAS Assisted Proofs in Upper Secondary School Mathematics TextbooksUffe Thomas Jankvist0Morten Misfeldt1Aarhus UniversityAalborg UniversityThis article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are identified in ten different textbooks. The CAS based proofs in these textbooks are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses draw on theoretical constructs related to both proofs and proving (e.g. proof schemes) and to use of digital technologies in mathematics education (lever potential, blackboxing, instrumental genesis). In particular, the analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning.https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3315 |
| spellingShingle | Uffe Thomas Jankvist Morten Misfeldt CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks REDIMAT |
| title | CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks |
| title_full | CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks |
| title_fullStr | CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks |
| title_full_unstemmed | CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks |
| title_short | CAS Assisted Proofs in Upper Secondary School Mathematics Textbooks |
| title_sort | cas assisted proofs in upper secondary school mathematics textbooks |
| url | https://hipatiapress.com/hpjournals/index.php/redimat/article/view/3315 |
| work_keys_str_mv | AT uffethomasjankvist casassistedproofsinuppersecondaryschoolmathematicstextbooks AT mortenmisfeldt casassistedproofsinuppersecondaryschoolmathematicstextbooks |