TY - JOUR

T1 - How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation - when working memory matters

AU - Schwaighofer, Matthias

AU - Vogel, Freydis

AU - Kollar, Ingo

AU - Ufer, Stefan

AU - Strohmaier, Anselm

AU - Terwedow, Ilka

AU - Ottinger, Sarah

AU - Reiss, Kristina M.

AU - Fischer, Frank

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Mathematical argumentation skills

KW - Collaboration scripts

KW - Heuristic worked examples

KW - Working memory capacity

KW - Educational science

UR - http://www.scopus.com/inward/record.url?scp=85029742597&partnerID=8YFLogxK

U2 - 10.1007/s11412-017-9260-z

DO - 10.1007/s11412-017-9260-z

M3 - Journal articles

VL - 12

SP - 281

EP - 305

JO - International Journal of Computer-Supported Collaborative Learning

JF - International Journal of Computer-Supported Collaborative Learning

SN - 1556-1607

IS - 3

ER -