How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters
Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different sca...
| Main Authors: | , , , , , , , , |
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/52660/ |
| _version_ | 1848798779392655360 |
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| author | Schwaighofer, Matthias Vogel, Freydis Kollar, Ingo Ufer, Stefan Strohmaier, Anselm Terwedow, Ilka Ottinger, Sarah Reiss, Kristina Fischer, Frank |
| author_facet | Schwaighofer, Matthias Vogel, Freydis Kollar, Ingo Ufer, Stefan Strohmaier, Anselm Terwedow, Ilka Ottinger, Sarah Reiss, Kristina Fischer, Frank |
| author_sort | Schwaighofer, Matthias |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners with more than one scaffold may be overwhelming, especially when these scaffolds are presented at the same time in the learning process and when learners’ individual learning prerequisites are suboptimal. The present study therefore investigated the effects of the presentation sequence of introducing two scaffolds (collaboration script first vs. heuristic worked examples first) and the fading of the primarily presented scaffold (fading vs. no fading) on the acquisition of dialogic and dialectic MAS of participants of a preparatory mathematics course at university. In addition, we explored how prior knowledge and working memory capacity moderated the effects. Overall, 108 university freshmen worked in dyads on mathematical proof tasks in four treatment sessions. Results showed no effects of the presentation sequence of the collaboration script and heuristic worked examples on dialogic and dialectic MAS. Yet, fading of the initially introduced scaffold had a positive main effect on dialogic MAS. Concerning dialectic MAS, fading the collaboration script when it was presented first was most effective for learners with low working memory capacity. The collaboration script might be appropriate to initially support dialectic MAS, but might be overwhelming for learners with lower working memory capacity when combined with heuristic worked examples later on. |
| first_indexed | 2025-11-14T20:25:12Z |
| format | Article |
| id | nottingham-52660 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:25:12Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-526602020-05-04T19:08:20Z https://eprints.nottingham.ac.uk/52660/ How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters Schwaighofer, Matthias Vogel, Freydis Kollar, Ingo Ufer, Stefan Strohmaier, Anselm Terwedow, Ilka Ottinger, Sarah Reiss, Kristina Fischer, Frank Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners with more than one scaffold may be overwhelming, especially when these scaffolds are presented at the same time in the learning process and when learners’ individual learning prerequisites are suboptimal. The present study therefore investigated the effects of the presentation sequence of introducing two scaffolds (collaboration script first vs. heuristic worked examples first) and the fading of the primarily presented scaffold (fading vs. no fading) on the acquisition of dialogic and dialectic MAS of participants of a preparatory mathematics course at university. In addition, we explored how prior knowledge and working memory capacity moderated the effects. Overall, 108 university freshmen worked in dyads on mathematical proof tasks in four treatment sessions. Results showed no effects of the presentation sequence of the collaboration script and heuristic worked examples on dialogic and dialectic MAS. Yet, fading of the initially introduced scaffold had a positive main effect on dialogic MAS. Concerning dialectic MAS, fading the collaboration script when it was presented first was most effective for learners with low working memory capacity. The collaboration script might be appropriate to initially support dialectic MAS, but might be overwhelming for learners with lower working memory capacity when combined with heuristic worked examples later on. Springer 2017-09-22 Article PeerReviewed Schwaighofer, Matthias, Vogel, Freydis, Kollar, Ingo, Ufer, Stefan, Strohmaier, Anselm, Terwedow, Ilka, Ottinger, Sarah, Reiss, Kristina and Fischer, Frank (2017) How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters. International Journal of Computer-Supported Collaborative Learning, 12 (3). pp. 281-305. ISSN 1556-1615 Mathematical argumentation skills; Collaboration scripts; Heuristic worked examples; Working memory capacity https://link.springer.com/article/10.1007%2Fs11412-017-9260-z doi:10.1007/s11412-017-9260-z doi:10.1007/s11412-017-9260-z |
| spellingShingle | Mathematical argumentation skills; Collaboration scripts; Heuristic worked examples; Working memory capacity Schwaighofer, Matthias Vogel, Freydis Kollar, Ingo Ufer, Stefan Strohmaier, Anselm Terwedow, Ilka Ottinger, Sarah Reiss, Kristina Fischer, Frank How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| title | How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| title_full | How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| title_fullStr | How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| title_full_unstemmed | How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| title_short | How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| title_sort | how to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation – when working memory matters |
| topic | Mathematical argumentation skills; Collaboration scripts; Heuristic worked examples; Working memory capacity |
| url | https://eprints.nottingham.ac.uk/52660/ https://eprints.nottingham.ac.uk/52660/ https://eprints.nottingham.ac.uk/52660/ |