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Designing a learning environment for promoting math discourse. Paper for presentation at
 the the 12th International Conference on Mathematical Education
, 2012
"... Designing a software environment for online learning of mathematics in small collaborative groups requires innovation in multiple dimensions. There has to be generic support for collaborative learning at a distance and also special functionality for mathematical work and communication. We combine th ..."
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Designing a software environment for online learning of mathematics in small collaborative groups requires innovation in multiple dimensions. There has to be generic support for collaborative learning at a distance and also special functionality for mathematical work and communication. We combine the Virtual Math Teams environment with a multiuser version of GeoGebra. We also develop curricular activities through an iterative process of evaluating the discourse that is stimulated by drafts of the activities in prototypes of the technology. Significant mathematical discourse, virtual math teams, group cognition, learning environment.
Interaction Analysis of DualInteraction CSCL Environments
, 2009
"... In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities so that they have a shared understanding of the significance of their utterances, inscriptions and behaviors—adequate for sustaining productive interaction. ..."
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In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities so that they have a shared understanding of the significance of their utterances, inscriptions and behaviors—adequate for sustaining productive interaction. The need for participants to coordinate their actions becomes particularly salient in dualinteraction environments, where, e.g., chat postings and graphical drawings must work together; analysts of such interactions must identify the subtle and complex ways in which meaning making proceeds. This paper considers the methodological requirements on analyzing interaction in dualinteraction environments by reviewing several exemplary CSCL studies. It reflects on the nature of social organization, grounding and indexicality that frame the interaction to be analyzed.
Collaborative learning through practices of group cognition
"... Abstract: While there is evidence that collaborative learning consists largely of grouplevel practices, there has been little analysis and description of these processes as such; learning has generally been studied at the individual unit of analysis. Our research, in contrast, focuses on describing ..."
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Abstract: While there is evidence that collaborative learning consists largely of grouplevel practices, there has been little analysis and description of these processes as such; learning has generally been studied at the individual unit of analysis. Our research, in contrast, focuses on describing the interactional smallgroup practices that take place in learning contexts. This paper considers these practices and how they work together to form the foundation for effective collaborative learning activities. It analyzes collaborative learning activities in a paradigmatic CSCL setting to discuss such smallgroup practices as: resolving cognitive conflict, pursuing inquiry, maintaining a group problem space and coordinating multiple modes of reasoning. These have broad implications for foundational issues of temporality, indexicality and group cognition. Individual and Group Learning Learning has traditionally been considered a change in the knowledge of individual minds. More recently, it has been conceptualized at the opposite extreme in terms of participation in communities of practice (Lave & Wenger, 1991). In general, learning is conceptualized at the individual level and group knowledge building at the community level, despite evidence of the centrality of the small group, particularly in CSCL settings. An
ENHANCING MATHEMATICAL COMMUNICATION FOR VIRTUAL MATH TEAMS
"... Abstract: The Math Forum is an online resource center for prealgebra, algebra, geometry and precalculus. Its Virtual Math Teams (VMT) service provides an integrated webbased environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting m ..."
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Abstract: The Math Forum is an online resource center for prealgebra, algebra, geometry and precalculus. Its Virtual Math Teams (VMT) service provides an integrated webbased environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical microworlds together. The VMT Project studies the online math discourse that takes place during sessions of virtual math teams working on openended problemsolving tasks. In particular, it investigates methods of group cognition that are employed by teams in this setting. The VMT environment currently integrates social networking, synchronous text chat, a shared whiteboard for drawing, web browsers and an asynchronous wiki for exchanging findings within the larger community. A simple version of MathML is supported in the whiteboard, chat and wiki for displaying mathematical expressions. The VMT Project is currently integrating the dynamic mathematics application, GeoGebra, into its collaboration environment. This will create a multiuser version of GeoGebra, which can be used in concert with the chat, web browsers, curricular topics and wiki repository.
A chapter by Gerry Stahl for the International Handbook of Collaborative Learning Chapter 29 of Section IV. Technology and Collaborative Learning Group Cognition in Synchronous Chat
"... Underlying deeply successful collaborative learning are processes of group cognition. Where collaborative learning is more than a group of individuals supporting each other’s individual learning, there are group processes in which contributions from participants build on each other. The group achiev ..."
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Underlying deeply successful collaborative learning are processes of group cognition. Where collaborative learning is more than a group of individuals supporting each other’s individual learning, there are group processes in which contributions from participants build on each other. The group achieves cognitive tasks such as problem solving in ways that no individual could have on their own. Researchers have often looked for signs of such group cognition in asynchronous online settings like discussion forums. However, the Virtual Math Teams (VMT) Project has produced considerable data of small groups of students using synchronous chat to achieve group cognitive results. While there have been claims that collaborative learning is a “social ” phenomenon— i.e., consists largely of grouplevel practices—there has been little analysis and description of these processes as such; learning has generally been studied at the individual unit of analysis. The VMT research, in contrast, focuses on describing the interactional smallgroup practices that take place in synchronous chat learning
The Organization of Graphical, Narrative and Symbolic Interactions
"... In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities so that they have a shared understanding of the significance of their utterances, inscriptions and behaviors—adequate for sustaining productive interaction. ..."
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In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities so that they have a shared understanding of the significance of their utterances, inscriptions and behaviors—adequate for sustaining productive interaction. Some methodologies applied in CSCL research—such as the widespread codingandcounting quantitative analysis genre—systematically ignore the sequentiality of actions and thereby miss the implicit referencing, which is essential to shared understanding. The VMT Project attempts to capture and analyze the sequential organization of references and interrelationships among whiteboard inscriptions, chat postings, mathematical expressions and other elements of virtual math team activities in order to understand the mechanisms of group cognition. Here, we report the results of a microethnographic case study of collaborative math problemsolving activities mediated by the VMT multimodal online environment. We employ ethnomethodological
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PROGRAM ANNOUNCEMENT/SOLICITATION NO./CLOSING DATE/if not in response to a program announcement/solicitation enter NSF 101
Improving GeoGebra SUPPORTING GROUP MATH COGNITION IN VIRTUAL MATH TEAMS WITH SOFTWARE CONVERSATIONAL AGENTS
"... Abstract. This is a research paper on a new tool to support dynamic mathematics in education. The research explores the use of software agents to engage in synchronous interaction with a small group of students working online in the Virtual Math Teams environment. The purpose of the agents is to fac ..."
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Abstract. This is a research paper on a new tool to support dynamic mathematics in education. The research explores the use of software agents to engage in synchronous interaction with a small group of students working online in the Virtual Math Teams environment. The purpose of the agents is to facilitate discourse by the students that promotes their collaborative learning. In particular, the conversational agents try to encourage academically productive talk, in which students work together in ways that are accountable to each other and to their task. The agents are currently being tested in student groups working on problems in combinatorics. This research will soon be extended to student groups using a multiuser version of GeoGebra. 1. THE VISION OF SOFTWARE AGENTS USED TO SUPPORT COLLABORATIVE ONLINE
ComputerSupported Math Discourse Among Teachers and Students
"... This full researchanddevelopment project designs, develops and tests an interrelated system of technological, pedagogical and analytic components to provide a range of opportunities for middle and highschool students to engage in significant mathematical discourse (DR K12 challenge 2); it catal ..."
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This full researchanddevelopment project designs, develops and tests an interrelated system of technological, pedagogical and analytic components to provide a range of opportunities for middle and highschool students to engage in significant mathematical discourse (DR K12 challenge 2); it catalyzes and supports these opportunities by enhancing the ability of inservice teachers to engage in, appreciate and foster mathproblemexploration and mathdiscourse skills in their students (DR K12 challenge 3). The project addresses the core STEM discipline of mathematics by motivating the identification, comprehension and enjoyment of mathematical discourse skills through socially interactive, collaborative learning experiences involving pedagogically organized series of stimulating, skillappropriate problems using computerbased visualization/exploration and smallgroup mathproblem discussion. The project’s designbasedresearch approach crafts a sociotechnical educational model to provide a comprehensive, practical package of tools and techniques for classroom teachers and students, which integrates and refines a number of mutually supportive components: (a) Innovative technology: A custom, opensource virtual learning environment that integrates synchronous and asynchronous media with the first multiuser dynamicmathvisualization application. (b) Curricular resources: Problembased learning topics in specific areas of mathematics designed to help teachers tune rich math problems to local