Supporting Online Collaborative Mathematical Exploration: Studying the Development of Collective Knowledge within Math-Towers

Supporting Online Collaborative Mathematical Exploration: Studying the Development of Collective Knowledge within Math-Towers

Geoffrey Roulet (Queen’s University, Canada)
DOI: 10.4018/978-1-4666-2053-7.ch019
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Math-Towers is a collaborative mathematics environment for pupils in grades 7 to 9. Using a fantasy adventure game context, students are presented with a mathematical challenge, given online tools for working on the problem, and provided with a messaging system by which they may exchange ideas and partial solutions. This paper presents the philosophy behind the design of Math-Towers and, using a complexity science framework, explores the extent to which it has been successful in meeting goals. The technical and social problems encountered and revisions made to address these are also described.
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Math-Towers Design

In Math-Towers, explorations, set within a medieval castle context, are initiated by challenges delivered to visitors by the Lord or Lady of the castle (Figure 1), thus using fantasy, a known motivator of student attention and work (Bergin, 1999). Each user is then sent off to a tower where they are provided with a laboratory containing virtual manipulatives (applets) that support investigation and tools and places to record their observations and conjectures (Figure 2). Student work is saved so that participants may visit the tower multiple times, climbing up the floors as they solve aspects of the problem, and finally emerge on the tower ramparts to be invited to now again meet the Lord or Lady and attempt to address the initial challenge. In the tower halls beside each laboratory door there is a scroll on which students can present their emerging understanding of the problem (Figure 3). In addition, users may, to illustrate their thoughts, append a copy of their manipulatives and tools in any state. After posting a message a user is free to explore the ideas shared by others, add comments, and if they wish, take any of the accompanying tools back to their laboratory for further exploration.

Figure 1.

Presenting the billiard challenge

Figure 2.

Tower laboratory

Figure 3.

Tower hall with scroll


Math-Towers may be described as an “empty technology” (Zucchermaglio, 1993). That is, the computer does not provide instruction, nor does it monitor student work and provide assessment or advice. The laboratory tools permit any user to test the accuracy of shared conjectures and support for or advice to participants comes from the community of explorers through their interactions via the scroll messaging system.

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