How to combine collaboration scripts and heuristic worked examples to foster mathematical argumentation - when working memory matters
Research output: Journal contributions › Journal articles › Research › peer-review
Standard
In: International Journal of Computer-Supported Collaborative Learning, Vol. 12, No. 3, 01.09.2017, p. 281-305.
Research output: Journal contributions › Journal articles › Research › peer-review
Harvard
APA
Vancouver
Bibtex
}
RIS
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 -