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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

Authors

Matthias Schwaighofer

Freydis Vogel

Ingo Kollar

Stefan Ufer

Anselm Strohmaier

Ilka Terwedow

Sarah Ottinger

Kristina Reiss

Frank Fischer



Abstract

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.

Citation

Schwaighofer, M., Vogel, F., Kollar, I., Ufer, S., Strohmaier, A., Terwedow, I., …Fischer, F. (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), 281-305. https://doi.org/10.1007/s11412-017-9260-z

Journal Article Type Article
Acceptance Date Sep 1, 2017
Online Publication Date Sep 22, 2017
Publication Date Sep 22, 2017
Deposit Date Jun 28, 2018
Publicly Available Date Mar 28, 2024
Journal International Journal of Computer-Supported Collaborative Learning
Print ISSN 1556-1607
Electronic ISSN 1556-1615
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 12
Issue 3
Pages 281-305
DOI https://doi.org/10.1007/s11412-017-9260-z
Keywords Mathematical argumentation skills; Collaboration scripts; Heuristic worked examples; Working memory capacity
Public URL https://nottingham-repository.worktribe.com/output/884228
Publisher URL https://link.springer.com/article/10.1007%2Fs11412-017-9260-z

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