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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 freydis.vogel@nottingham.ac.uk

Ingo Kollar ingo.kollar@phil.uni-augsburg.de

Stefan Ufer ufer@math.lmu.de

Anselm Strohmaier anselm.strohmaier@tum.de

Ilka Terwedow

Sarah Ottinger ottinger@math.lmu.de

Kristina Reiss kristina.reiss@tum.de

Frank Fischer frank.fischer@psy.lmu.de



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.

Journal Article Type Article
Publication Date Sep 22, 2017
Journal International Journal of Computer-Supported Collaborative Learning
Print ISSN 1556-1607
Electronic ISSN 1556-1615
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 12
Issue 3
APA6 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), doi:10.1007/s11412-017-9260-z
DOI https://doi.org/10.1007/s11412-017-9260-z
Keywords Mathematical argumentation skills; Collaboration scripts; Heuristic worked examples; Working memory capacity
Publisher URL https://link.springer.com/article/10.1007%2Fs11412-017-9260-z
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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