Effects of collaboration scripts and heuristic worked examples on the acquisition of mathematical argumentation skills of teacher students with different levels of prior achievement

A challenging demand for mathematics teacher students is to produce acceptable scientific mathematical argumentations. We investigated to what extent mathematics teacher students with different levels of prior achievement who collaborated in dyads can be supported in their development of mathematical argumentation skills by two different instructional approaches that were systematically varied in a 2 × 2-factorial design: collaboration scripts (with vs. without) and heuristic worked examples vs. problem solving. An experimental study was run in the context of a two-weeks preparatory course for beginning mathematics teacher students (N = 101). Mathematical argumentation skills were conceptualized as consisting of an individual-mathematical and a social-discursive component. Results indicated positive effects of both scaffolds on the social-discursive component. Moreover, the effects of both scaffolds on both components were dependent on learners' prior achievement (high-school GPA). Heuristic worked examples and collaboration scripts were particularly effective in the facilitation of mathematical argumentation skills for teacher students with higher general learning prerequisites. Possible process-based explanations for this pattern of results as well as ways to more specifically address the needs of teacher students with lower prior achievement are discussed

Learning to argue in mathematics: effects of heuristic worked examples and CSCL scripts on transactive argumentation

A previous study has shown that both CSCL scripts and heuristic worked examples implemented in a CSCL environment were effective to fostering students' acquisition of argumentation skills in the context of mathematical proof tasks (Kollar, et al. 2012). This paper investigates the extent to which transactive argumentation during the collaborative learning process can be evoked by both means of instructional support and to what extent transactive argumentation mediates their effects on students' knowledge about argumentation. We present process measures from a 2x2-factorial experiment with the factors CSCL script and heuristic worked examples conducted with N=101 prospective math teacher students. Results show that both means of instructional support induced transactive argumentation in the collaborative learning process. The self-generated transactive argumentation, but not the partner-generated transactive argumentation mediated the effects of both types of instructional support on students' development of argumentation knowledge. Nevertheless, the learning partners mutually influenced their transactive argumentation

Fostering argumentation skills in mathematics with adaptable collaboration scripts: only viable for good self-segulators?

Argumentation scripts have been proposed as an effective means to structure students’ argumentation and to support their acquisition of argumentation skills. Yet, argumentation scripts run the danger of overscripting students’ argumentation. A possible solution might be to offer adaptable argumentation scripts that allow students to adjust the script to their own needs. This study compares the effects of three argumentation scripts (high structured vs. low structured vs. adaptable) on students’ argumentation skills. Furthermore, we investigate to what extent students’ self-regulation skills influence the acquisition of argumentation skills in the three conditions. N = 109 math students were randomized to the three treatment conditions and worked in dyads on mathematical proof tasks in a CSCL environment. Students’ argumentation skills increased between pre- and post-tests with comparable gains in all three conditions. Only for students learning with the adaptable argumentation script, self-regulation skills were a significant positive predictor for argumentation skills

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