Scripting Collaborative Problem Solving with the Cognitive Tutor Algebra: A Way to Promote Learning in Mathematics

Interest in developing improved instructional methods for mathematics has increased since TIMSS and PISA. In our project, we introduce a new way to promote knowledge acquisition in mathematics: we enhanced the Cognitive Tutor Algebra, an intelligent tutoring system for learning mathematics in high school that only has been used for individual learning so far, to a collaborative learning setting. Although the Tutor has shown to increase learning, there also are several shortcomings. For instance, learning with the Tutor places emphasis on improving students' problem solving skills, yet a deep understanding of underlying mathematical concepts is not necessarily achieved. To reduce these shortcomings, we extended the learning environment to a dyadic setting, adding new learning opportunities such as the possibility to mutually elaborate on the learning content. A script was developed to guide students' interaction and to ensure that students profit from these new learning opportunities. The script structured students' collaboration in an individual and a collaborative phase and prompted students to engage in fruitful interaction. An adaptive script component provided hints when the dyad encountered difficulties in their problem solving. Finally, dyads engaged in a reflection activity following each problem to improve their collaboration over subsequent interactions. The scripts' effect on students' collaborative learning was tested in a classroom study that took place over the course of one week. We compared the learning of dyads collaborating at the Tutor without script support to the learning of dyads scaffolded by the script. To measure different aspects of learning, students solved several post-tests on the Tutor and with paper and pencil. The results of the paper and pencil test assessing improvement of students' conceptual understanding show significantly better performances of the script condition. The Tutor log data are still being analyzed and the results will be presented at the conference. The Cognitive Tutor Algebra is a tutor for mathematics instruction at the high school level. Its main features are immediate error feedback, the possibility to ask for a hint when encountering impasses, and knowledge tracing, i.e. the Tutor creates and updates a model of the student's knowledge and selects new problems tailored to the student's knowledge level. As several studies have shown, this Tutor improves learning by about one standard deviation compared to traditional classroom instruction (Koedinger, Anderson, Hadley, & Mark, 1997). However, students do not always benefit as much as they might from learning with the Tutor. First, a deep understanding of underlying mathematical concepts is not necessarily achieved since the Tutor emphasizes learning of procedural skills (Anderson, Corbett, Koedinger, & Pelletier, 1995). Second, students do not always make good use of the learning opportunities provided by the Cognitive Tutor. The collaborative extension we introduced to the Tutor environment aims at reducing these shortcomings. As research has shown, collaborative problem solving and learning have the potential to promote deep elaboration of the learning content (Teasley, 1995) and can yield improved conceptual understanding. However, students do often not show beneficial collaborative behaviours spontaneously (Rummel & Spada, 2005). Collaboration scripts have proven effective in helping people meet the challenges encountered when learning or working collaboratively (Kollar, Fischer, & Hesse, in press), thus we developed a script to prompt fruitful interaction on the Tutor. For the present study we focused on "systems of equations", a content novel to participating students. Our script consisted of three components that aimed at facilitating students to capitalize on learning opportunities offered in the collaborative Tutor environment. The fixed script component structured the problem solving process in two phases. During the individual problem solving phase, each student solved a problem with one equation in the Cognitive Tutor. In the collaborative phase, students joined on a single computer to solve a more complex system of equations problem that combined the two individual equations. They received instructions from the enhanced Tutor, e.g. prompting them on collaborative skills like explanation giving. The division in individual and collaborative phases served to increase the individual's accountability for the joined problem solving and set up the preconditions