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Abstract. In this paper we describe how a statistical test on a hypothesis regarding collaborative math problem solving using online chats showed an unexpected result, whose understanding required the use of qualitative methods. The phenomenon behind the result is identified using Conversation Analysis. This paper demonstrates the importance of using qualitative methods to describe the perspective of participants as a way of interpreting statistical results, revising hypotheses and developing alternative coding schemes and procedures. The combined approach of quantitative and qualitative methods is applied on real data coming from Virtual Math Teams research project (Drexel University) and is identifying issues not addressed so far in the analysis of online collaborative group activity. 1

www.library.drexel.edu The following item is made available as a courtesy to scholars by the author(s) and Drexel University Library and may contain materials and content, including computer code and tags, artwork, text, graphics, images, and illustrations (Material) which may be protected by copyright law. Unless otherwise noted, the Material is made available for non profit and educational purposes, such as research, teaching and private study. For these limited purposes, you may reproduce (print, download or make copies) the Material without prior permission. All copies must include any copyright notice originally included with the Material. You must seek permission from the authors or copyright owners for all uses that are not allowed by fair use and other provisions of the U.S. Copyright Law. The responsibility for making an independent legal assessment and securing any necessary permission rests with persons desiring to reproduce or use the Material.

Abstract not found

The Virtual Math Teams (VMT) project investigates the innovative use of online collaborative environments to support effective mathematical problem-solving by small groups of learners in an online community. A key research issue for us is to understand how team interactions evolve over time and how to support them effectively. As designers, we expect the persistent records of the teams ’ interactions provided in the VMT environment to contribute to the sustainability of the teams ’ knowledge work. Our analysis of data collected from distributed virtual teams working on open-ended mathematical tasks across multiple sessions shows the situated usage of such persistent artifacts. In particular, we observe a series of “bridging ” methods used to co-construct mathematical knowledge over time, evolve a sense of collectivity, and interlink the online environment with other interaction spaces. We propose that bridging, the purposeful crossing of interactional boundaries, is a consequential and often unsupported aspect of the collaborative user experience. 1.

This is a case study of online collaboration on an algebra problem. It adapts the methodology of conversation analysis to quasi-synchronous, text-based chat room technology. The analysis is conducted within the context of a design-based research effort, so a primary goal is to identify technological barriers caused by standard chat technology with an eye to designing a more appropriate and supportive online collaborative learning environment. “Group cognition ” is a theoretical framework in which cognitive processes are identified as resulting from the dynamic interaction of multiple personal interpretive perspectives within contexts of group discourse and collaboration. The analysis is conducted within a theoretical framework that focuses attention on the small group unit of analysis as the site of problem-solving agency, rather than on cognitive processes of the individual participants. The analysis results in the identification of interactive methods of “doing mathematics ” as a group. This, in turn, reflects back on the theoretical framework and refines the notion of group cognition. The analysis aims to motivate the following theoretical, methodological and design-based claims: • The discourse displays elements of mathematical understanding, problem-solving strategies and logical rationality by the group that parallel those of individual students. • Interaction among the student participants can be conceptualized as an instance of “group cognition.” • Excerpts of online collaborative math problem solving can productively be analyzed at the small group unit of analysis. • The methodology of conversation analysis can effectively be adapted to interpret text-based online interaction. • Group cognition displays the potential to achieve more than the individual participants seem capable of accomplishing on their own, but also displays interactional problems that prevent the group from achieving its full problemsolving potential. • Conclusions can be drawn from such an analysis that are relevant to the design of improved computer-supported collaborative learning environments.

this paper we depart from this view to investigate instead the publicly available activities which take place in the use of maps

Understanding collective creativity is crucial for advancing the general study of human creativity as well as for guiding the design of creativity support tools for small teams and larger collectivities. In this article, a qualitative case study of collective creativity online, derived from an analysis of collaborative interactions of virtual teams of students working in the field of mathematics, is presented. Group creative activity is examined broadly, ranging from the microlevel coconstruction of novel resources for team problem solving to the evolutionary reuse of ideas and solution strategies across teams. The analysis focuses on describing the relationship between the dynamics of creative work present in a single collaborative episode of an online group and their evolution across time and across collectivities. The analysis indicates that the synergy between these two types of interactions and the resulting creative engagement of the teams relies on three fundamental processes: (a) indexical referencing, (b) group remembering, and (c) bridging across discontinuities.

In this text, I insist on the difference between lived mathematical experience and accounts of mathematical experience. Almost all research, both quantitative and qualitative, is concerned with accounts of mathematical experience rather than with the lived work of mathematics. In this text, I articulate the difference between the two and provide some guidance with respect to the ways of going about researching the lived work rather than accounts thereof. In this, I counter the false belief that our experiences are “constructed, ” and insist that the real work that makes mathematics an objective science is actually lived and the result of our living/lived bodies rather than that of the constructivist mind. In this manner, I state an approach that is an incommensurable, asymmetrical alternate form to formal analyses of living/lived mathematical experience. 1. The Living/Lived Work of Mathematics I begin this investigation with two practical examples, which, when readers engage with these, allows them to live the mathematical experiences of seeing a geometrical object as a specific object (cube) and doing the proof of the angle sum of a triangle.

Abstract not found