Rummel Scripted Collaborative Problem Solving

Collaborative Extensions to the Cognitive Tutor Algebra: Scripted Collaborative Problem Solving

Nikol Rummel, Dejana Diziol, Bruce McLaren, and Hans Spada

Abstract

In this study, the Algebra I Cognitive Tutor is extended to a collaborative learning environment: students learn to solve system of equations problems while working in dyads. As research has shown, collaborative problem solving and learning has the potential to increase elaboration on the learning content. However, students are not always able to effectively meet the challenges of a collaborative setting. To ensure that students capitalize on collaborative problem solving with the Tutor, a collaboration script was developed that guides their interaction and prompts fruitful collaboration. During the scripted problem solving, students alternate between individual and collaborative phases. Furthermore, they reflect on the quality of their interaction during a recapitulation phase that follows each problem they solve.

To assess the effectiveness of the script, we compared three instructional conditions: an individual condition, a collaborative condition without further instructional support, and a collaborative condition in which students’ dyadic problem solving was supported by a collaboration script. This experimental learning phase took place on two days of instruction. On the third day, during the test phase, students solved several post tests that assessed robust learning. Analyses on the collected measures are in progress.

Glossary

• Collaboration scripts: Collaboration scripts structure the collaboration process by guiding the interacting partners through a sequence of interaction phases with designated activities and roles. Scripts are expected to promote learning by prompting cognitive, meta-cognitive and social processes that might otherwise not occur – for example, the interacting partners are prompted to engage in activities like posing questions, providing explanations, and giving feedback.
• Collaborative Problem Solving Script (CPS): The script approach that is implemented in the experimental condition of the study. For each problem the dyad solves on the Cognitive Tutor, their interaction is structured in an individual problem solving phase, a collaborative problem solving phase, and a recapitulation phase. The script further provides guidance during the collaborative problem solving phase.
• Individual Problem Solving Phase: Both students solve a pre-task on their own as a preparation for the complex story problem they solve together during the following collaborative problem solving phase.
• Collaborative Problem Solving Phase: Students’ interaction is structured in several problem solving steps. For every step, students receive instructions prompting them to engage in collaborative behaviors that have been shown to increase learning. Furthermore, students receive adaptive instructional support when meeting impasses during the problem solving process.
• Recapitulation Phase: Students engage in a reflection of the group process: They evaluated (=rate) their collaboration on eight dimensions and set goals for how to improve it during the next joint problem solving.

Research question

Does collaboration – and in particular scripted collaboration – improve students’ robust learning in the domain of algebra?

Does the script approach improve students’ collaboration, and does this result in improved robust learning of the algebra content?

Independent variables

The independent variable was the mode of instruction. Three conditions were implemented in the learning phase that took place on two days of instruction:

• individual condition: Students solved problems with the Algebra I Cognitive Tutor in the regular fashion (i.e. computer program as additional agent).
• unscripted collaborative condition: Students solved problems on the Cognitive Tutor while working in dyads – thus, a second learning resource was added to the regular Tutor environment (i.e. both a peer and a computer program as additional agents).
• scripted collaboration condition: As in the unscripted collaborative condition, students solved problems on the Tutor while working in dyads; however, their dyadic problem solving was guided by the collaborative problem solving script (i.e. both a peer and a computer program as additional agents).

The Cognitive Tutor supported students’ problem solving by flagging their errors and by providing on-demand hints.

Communication between the collaborative partners in the collaborative conditions was face to face: they joined at one computer to solve the problems. In the scripted collaboration condition, the script structured the allocation of subtasks between the two students.

Hypothesis

The hypothesis can be separated in two parts: knowledge gains in the domain of algebra, and improvement of the dyads’ collaboration skills:

1. We expect the collaborative conditions – in particular the scripted collaboration condition – to outperform the individual conditions in measures of robust learning of the algebra content.
2. We expect that problem solving with the Collaborative Problem Solving Script yields a more effective interaction than unscripted collaboration in the learning phase. In addition, we expect that the newly gained collaborative skills will sustain during subsequent collaborations in the test phase when script support is no longer available.

Dependent variables & Results

Students solved several post tests during the test phase that took place two days after instruction:

• Near transfer, immediate: Student progress on training problems during the learning phase is analyzed. Their improvement in solving system of equations, i.e. their ability to transfer from one problem to an isomorphic problem with different content, can be assessed by looking at the learning curves.
• Near transfer, retention: Two post tests measured near transfer. As during the learning phase, students solved system of equations problems on the Cognitive Tutor. The problems were “isomorphic” to those in the instruction, but had a different content. One near transfer test was solved collaboratively to measure both students’ algebra skills and their collaboration skills, the other near transfer test was solved individually to assess if the students were able to transfer the gained knowledge to isomorphic problems when working on their own.
• Far transfer: Main concepts students were supposed to learn during instruction were slope, y-intercept and intersection point. The students’ understanding of these mathematical concepts was assessed in a far transfer paper and pencil test. The items of this test tapped the same knowledge components as the problems in instruction; however, the problems where non-isomorphic to those in the instruction, thus demanded students to flexibly apply their knowledge to problems with a new format.
• Accelerated future learning: To measure accelerated future learning, students learned how to solve problems in a new area of algebra – inequality problems – on the Cognitive Tutor. According to their condition during the experimental learning phase, they either worked individually or collaboratively on this post test. However, in contrast to the learning phase, they did not receive additional instructional support.

Explanation

This study is part of the Interactive Communication cluster, and its hypothesis is a specialization of the IC cluster’s central hypothesis. According to the IC cluster’s hypothesis, instruction that yields robust learning should be designed to have the right target paths. Furthermore, it should improve the students’ path choice, that means increasing the probability of students to take right paths and decreasing the probability of students to take alternative paths.

By enhancing the Cognitive Tutor with collaboration, the study tried to reach these two goals in two steps:

• individual condition: The existing Cognitive Tutor already offers right learning paths. However, individual learning on the Cognitive Tutor has several shortcomings. For example, students don’t have the opportunity to reflect on the underlying mathematical concepts in natural language interaction in order to gain deep understanding. In addition, students do not always use the offered learning paths (as the opportunity to reflect on on-demand hints and error feedback) effectively.
• unscripted collaboration condition (1st step): By enhancing the Algebra I Cognitive Tutor to be a collaborative learning environment, we added a second learning resource –the learning partner. This adds further right learning paths to the learning space, for instance, learning by giving explanations, the possibility to request help, and learning by knowledge co-construction. However, similarly to the learning paths in an individual setting, students do not always capitalize on these learning opportunities.
• scripted collaboration condition (2nd step): To increase the probability that students take right learning paths, students’ interaction in the scripted collaboration condition is guided by the Collaborative Problem Solving Script. By prompting collaborative skills that have shown to improve learning and by guiding students’ interaction when meeting impasses, we expect students to engage in a more fruitful collaboration that yields robust learning.

Annotated bibliography

• Rummel, N., Diziol, D., Spada, H., McLaren, B., Walker, E., & Koedinger, K. (2006, June). Flexible support for collaborative learning in the context of the Algebra I Cognitive Tutor. Workshop paper presented at the 7th International Conference of the Learning Sciences. Bloomington, IN, USA.
• Presentation to the NSF Site Visitors, June, 2006