Negotiation in online, synchronous, collaborative mathematics problem solving

The Virtual Math Teams (VMT) project is an NSF-funded research program through which researchers at the College of Information Science and Technology (IST) and the Math Forum investigate the innovative use of online collaborative environments to support effective K-12 mathematics learning. Negotiation, provisionally defined as action to achieve agreement, takes place in the constitution of a shared conception from multiple perspectives, as evidenced by the agreement which takes place, in many cases, after contentious debate. We hypothesize that negotiation is the guiding mechanism of collaboration, especially in the resolution of situations whose complexity is such that understanding them is enhanced by multiple perspectives made possible through collaboration. A research methodology based on conversation analysis is used to identify how negotiation is conducted in online mathematics problem solving, by locating its methods as negotiation is initiated, processed and concluded in different computer mediated environments ranging from an all-text environment such as AIM® to a webbased collaboration environment with dual-interaction spaces such as VMTChat. Initial findings show artful ways through which participants use both text and whiteboard postings to initiate, process and conclude negotiation, and how participants allocate participation in the choice of approaches to a problem, the sequence in which different approaches are used and contribution to the execution of an approach. Findings from this research can be consequential for the design of negotiation support for CSCL environments; early results show how participants invent new uses for tools introduced into iterations of the design of the VMTChat collaborative environment

The virtual math teams project: A global math discourse community

Paper presented at the International Conference on Computers and Education (ICCE '06), Beijing, China.The Virtual Math Teams Project is an on-going research effort conducted within the Math Forum online suite of educational services related to school mathematics. It is an iterative effort to evolve an online math discourse community and to design effective software support for collaborative learning within this community. A central research aim is to develop a systematic understanding of how math discourse takes place in an online chat environment. This is part of a larger research agenda of analyzing group cognition, the ability of small groups to engage in high-level intellectual processes like argumentation, problem-solving and inquiry

Methods of negotiation in online collaborative mathematics problem-solving

The Virtual Math Teams (VMT) project is an NSF-funded research program through which researchers at the College of Information Science and Technology (IST) and the Math Forum investigate the innovative use of online collaborative environments to support effective K-12 mathematics learning. Negotiation is an indispensable element in collaboration, especially in the resolution of situations whose complexity is such that understanding them is enhanced by multiple perspectives made possible through collaboration. Some mathematics problems which are described as ‘ill-structured’ because they admit of several possible interpretations and multiple solutions, are candidates for collaborative problem-solving. Negotiation is necessary to make this collaborative approach possible, inasmuch as sense- and meaning-making associated with this particular approach to problem-solving has for its distinctive characteristic, the dynamics of a group rather than the jig-saw style of cooperating individuals. A research methodology based on conversation analysis is used to identify how negotiation is conducted in online mathematics problem-solving by locating its methods as negotiation is initiated, processed and concluded. Initial findings show: - how changes in the tempo of turn-taking indicate shifts in the conduct of problem-solving, - how repetition and ‘forced conclusions’ are used to negotiate a choice among several problems at hand, - how intervals and transitions are used by participants to indicate preferred responses and responders, - how referencing tools impact negotiation. Findings from this research can assist in the design of CSCL environments, especially in the transformation of generic communication applications to collaborative technology

Virtual math teams (VMT): Continuity and sustainability of collaborative knowledge building

How can we support online groups to better sustain their collaborative learning activity over time? In this poster, we present a qualitative case study of group creativity online in the domain of mathematics. We define collaborative learning work broadly, ranging from the micro-level co-construction of novel resources for collective problem solving to the innovative reuse and expansion of ideas across multiple virtual teams. Based on our analysis of the collaborative interactions of five virtual math teams we characterize the relationship between "synchronic" aspects of collaborative knowledge building (i.e. single episode interactions) and their "diachronic" evolution across time and across collectivities. Our analysis indicates that the synergy between these two types of interactions and the resulting creative engagement of the teams relies on three fundamental processes: (1) referencing and the “configuration of indexicals”, (2) collective remembering, and (3) bridging across discontinuities. In addition we also reflect on the aspects of the online environment used by these virtual teams which promote, support or hinder diachronic and synchronic interactions leading to successful knowledge building

Virtual math teams project: using conversation analysis for collaborative math problem-solving chats

The Virtual Math Teams (VMT) project is an NSF-funded research program aimed at investigating the innovative use of online collaborative environments to support effective K-12 mathematics learning. Among the methods it uses is Conversation Analysis (CA) -- to identify and investigate the methods by which these students collaboratively solve math problems when using computer chat programs such as AOL® Instant Messenger™. Using CA, we treat problem-solving as an interactional achievement of participation rather than as an internal and private process of the individual. We examine chat logs and seek to describe, in detail, the publicly available and observable procedures by which these problem-solving collaborations are achieved. In these online, problem-solving chats, the production and distribution of text messages and – on occasion -- other artifacts such as drawings, diagrams, etc., constitute the principal resources for sense making for both participants and researchers. Interaction conducted through textually mediated technologies like AOL® Instant Messenger™ is both similar to and significantly different from speech-based conversational interaction in important ways. As a text-based method of conducting interaction, chat offers different affordances for problem solving. In analyzing chats, we have begun to identify and describe: - how multiple threading of chat interaction is used as a resource in problem solving, - ways that participants put forward and take up proposed problemsolving strategies, - how understanding and misunderstandings are done as interactional achievements in chat, - different ways that collaboration and cooperation are organized as participation frameworks

Virtual math teams: virtual teams, real math

A 2004 report from the Pew Internet & American Life project indicates that 53 million American adults use instant messaging (IM), and its appeal is especially strong among younger Internet users. At the same time, according to the results of the 2003 Program for International Student Assessment (PISA), the performance in mathematics and problem solving of 15-year-old American students is lower than that of the average student in most of the 30 countries examined. Could these two trends be made to intersect? The Virtual Math Teams (VMT) project is an NSF-funded research program that investigates the innovative use of online collaborative environments to support effective K-12 mathematics learning. VMT implements a multidisciplinary approach to research and development that integrates (a) the quantitative modeling of students’ interactions online, (b) ethnographic and conversation analytical studies of collaborative problemsolving, and (c) an iterative process of software design (see related VMT posters). Key research issues addressed include: how to group students for effective online collaboration; how to design rich mathematical problems that foster collaboration and deep mathematical reasoning; how to structure the online collaborative experience; and how to study the forms of collaboration and reasoning that take place. Preliminary findings point to unique features of collaborative interactions such as the multidimensional aspects of interaction; the use of expository and exploratory talk; and also to challenges of coordinating the participants’ perspectives, resources, and strategies

Virtual math teams: Can the collaborative power of the Internet be used to help students learn mathematics?

Poster presented at the international conference on Computer Support for Collaborative Learning, CSCL 2005, Taipei, Taiwan. Retrieved July 19, 2007 from http://www.cis.drexel.edu/faculty/gerry/pub/csclp1.pdf