Developing argumentation skills in mathematics through computer-supported collaborative learning: the role of transactivity

Collaboration scripts and heuristic worked examples are effective means to scaffold university freshmen’s mathematical argumentation skills. Yet, which collaborative learning processes are responsible for these effects has remained unclear. Learners presumably will gain the most out of collaboration if the collaborators refer to each other’s contributions in a dialectic way (dialectic transactivity). Learners also may refer to each other’s contributions in a dialogic way (dialogic transactivity). Alternatively, learners may not refer to each other’s contributions at all, but still construct knowledge (constructive activities). This article investigates the extent to which constructive activities, dialogic transactivity, and dialectic transactivity generated by either the learner or the learning partner can explain the positive effects of collaboration scripts and heuristic worked examples on the learners’ disposition to use argumentation skills. We conducted a 2 × 2 experiment with the factors collaboration script and heuristic worked examples with N = 101 math teacher students. Results showed that the learners’ engagement in self-generated dialectic transactivity (i.e., responding to the learning partner’s contribution in an argumentative way by critiquing and/or integrating their learning partner’s contributions) mediated the effects of both scaffolds on their disposition to use argumentation skills, whereas partner-generated dialectic transactivity or any other measured collaborative learning activity did not. To support the disposition to use argumentation skills in mathematics, learning environments should thus be designed in a way to help learners display dialectic transactivity. Future research should investigate how learners might better benefit from the dialectic transactivity generated by their learning partners

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 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

Group Random Call Can Positively Affect Student In-Class Clicker Discussions

Understanding how instructional techniques and classroom norms influence in-class student interactions has the potential to positively impact student learning. Many previous studies have shown that students benefit from discussing their ideas with one another in class. In this study of introductory biology students, we explored how using an in-class accountability system might affect the nature of clicker-question discussions. Clicker-question discussions in which student groups were asked to report their ideas voluntarily (volunteer call) were compared with discussions in which student groups were randomly selected to report their ideas (random call). We hypothesized that the higher-accountability condition (random call) would impress upon students the importance of their discussions and thus positively influence how they interacted. Our results suggest that a higher proportion of discussions in the random call condition contained exchanges of reasoning, some forms of questioning, and both on- and off-topic comments compared with discussion in the volunteer call condition. Although group random call does not impact student performance on clicker questions, the positive impact of this instructional approach on exchanges of reasoning and other features suggests it may encourage some types of student interactions that support learning

Students’ meaning making in classroom discussions: the importance of peer interaction

The aim is to investigate how encounters with peers affect an individual's meaning making in argumentation about socio-scientific issues, and how the individual's meaning making influences the argumentation at the collective level. The analysis is conducted using the analytical method ''transactional argumentation analysis'' (TAA) which enables in situ studies. TAA combines a transactional perspective on meaning making based on John Dewey's pragmatic philosophy with an argument analysis based on Toulmin's argument pattern. Here TAA is developed further to enable analysis that in detail clarifies the dynamic interplay between the individual and the collective-the intraand the inter-personal dimensions-and the result of this interplay in terms of meaning making and learning. The empirical material in this study consists of a video-recorded lesson in a Swedish upper secondary school. The results show that the analysed student is influenced by peers when construing arguments, and thereby acts on others' reasoning when making meaning. Further, the results show that most of the additions made by the analysed student are taken further by peers in the subsequent discussion. This study shows how an individual's earlier experiences, knowledge and thinking contribute to the collective meaning making in the classroom