Stahl Gerry

Drexel University | DU · The Math Forum

Cognition is no longer confined to the solitary musings of an armchair philosopher but takes place, for instance, in problem-solving efforts of teams of people distributed around the world and involving various artifacts. The study of such cognition can unfold at multiple units of analysis. In this investigation, three cases of problem-solving by v...

Studies of computer-supported collaborative learning have begun to explore processes of online group cognition—such as small-group methods of problem-solving—and how they can be mediated by various technological and interactional mechanisms to promote academically productive discourse. This investigation first presents (1) an analysis of co-presenc...

This is an invited keynote talk that opened the International Conference on Computers in Education (ICCE 2009) on November 30, 2009, in Hong Kong, China. The intent of the talk was to provide a personal view of the field of computer-supported collaborative learning (CSCL) and to relate it to the Asia-Pacific audience. To do this, I tried to describ...

Recent research on instructional technology has focused increasingly on the potential of computer support to promote collaborative learning, shared understanding, and collaborative knowledge building. Sociocultural theories have been imported from cognate fields to suggest that cognition and learning take place at the level of groups and communitie...

To develop a science of small-group interaction in collaboration software, we need a method for analyzing the structure of computer-mediated discourse that complements our theory of group cognition. We need an approach to understanding the structure of interaction during group sessions of mathematical problem-solving and similar group-cognitive act...

This essay poses the question: Can CSCL represent a new paradigm of educational research within the learning sciences? It begins by looking at the historical relationship of the two related research communities: computer-supported collaborative learning and the learning sciences. It presents them from the perspective of the author as a participant...

The digital age of computer support has transformed human cognition. Although thinking always had social origins in the small-group interaction of family units, tribes, work teams, and friendships, cognition is now enmeshed in networks of social media, technological infrastructure, online knowledge sources, and global production. Computer-supported...

The field of computer-supported collaborative learning (CSCL)—as a unity of educational practice and academic research—is characterized in this investigation by a specific vision of learning, illustrated by a prototypical research effort. A number of recent publications are reviewed to extend the scope of CSCL in response to contemporary theory and...

The ability of people to understand each other and to work together face-to-face is grounded in their sharing of our meaningful natural and cultural world. CSCL groups—such as virtual math teams—have to co-construct their online, shared world with extra effort. A case study of building shared understanding online illustrates several aspects of co-e...

Learning takes place over long periods of time that are hard to study directly. Even the learning experience involved in solving a single challenging math problem in a collaborative online setting can be spread across hundreds of brief postings during an hour or more. Such long-term interactions are constructed out of posting-level interactions, su...

The term “intersubjectivity” is ambiguous. It can refer to the problem of how two or more minds can interrelate: understand each other and work together from their individual cognitive positions. It can also refer to a form of joint cognition that is shared by a group and transcends, unifies, or even founds the cognition of the participating indivi...

In order to collaborate effectively in group discourse on a topic like mathematical patterns, group participants must organize their activities in ways that share the significance of their utterances, inscriptions, and behaviors. Here, we report the results of an ethnomethodological case study of collaborative math problem-solving activities mediat...

The Virtual Math Teams project is exploring how to create, structure, support, and assess an online chat-based collaborative community devoted to mathematics discourse. It is analyzing the forms of group cognition that emerge from the use of shared cognitive tools with specific functionalities. Centered on a case study of a synchronous online inter...

The analysis of group practices can make visible the work of novices learning how to inquire in science or mathematics. These ubiquitous practices are invisibly taken for granted by adults, but can be observed and rigorously studied in adequate traces of online collaborative learning. Such an approach contrasts with traditional pre-/post-comparison...

Sfard’s book, reviewed here, describes the discursive construction of math objects as a foundation for understanding how students learn mathematics. It defines a math object as a recursive tree of its manifold visual realizations and provides a set of concepts for analyzing its construction. By reconceptualizing thinking as communicating, Sfard sug...

The question of how it is possible for people to understand each other has been a controversial theme throughout the recent history of philosophy. It is a foundational issue for the social sciences, in which researchers try to understand the behaviors and statements of other people. It is of particular relevance to CSCW and CSCL, where participants...

Computer-supported collaborative learning (CSCL) refers to collaborative learning that is facilitated or mediated by computers and networked devices. CSCL can occur synchronously, with learners interacting with each other in real time (e.g., a chat room), or asynchronously, with individual contributions stretched out over time (e.g., an e-mail exch...

This is an analysis of data from initial attempts to combine (a) technology from the Virtual Math Teams (VMT) Project, (b) helping agents, (c) collaborative small groups, and (d) accountable-talk prompting in order to scaffold biology student online chats about videotaped results of a biology experiment. Analysis of the response structure of the ch...

The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid’s organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in...

Both computer-supported collaborative learning (CSCL) and computer-supported cooperative work (CSCW) are centrally concerned with teamwork, learning, problem solving, knowledge building, task accomplishment, and other cognitive achievements by small groups of people. There are many theories useful for framing the cognitive work that groups undertak...

Dynamic mathematics software like GeoGebra provides new opportunities for mathematics education. With proper technological and pedagogical support for collaborative dynamic mathematics, it is possible to create a CSCL approach to foster significant math discourse. The demo of the Virtual Math Teams (VMT) online environment will focus on the recent...

Group cognition is analyzed at the small-group unit of analysis. It involves the semantics, syntactics and pragmatics of natural language, gestures, inscriptions, etc. The meaning-making processes involve inputs from individuals, based on their interpretation of the on-going context. They are also responses to the on-going social/historical/cultura...

In the new global world, it is time to recognize that knowledge is primarily produced socially and progressively, not just by spontaneous acts of isolated minds. Individuals participate in this as knowledge learners, knowledge users and knowledge builders, predominantly through their interactions in small groups. The cognitive work of small groups...

A sequence of inter-related proposals are made concerning how best to study collaborative information behavior. These proposals start by arguing for a clear distinction of three levels of description: individual, group and community. These should have three distinct sciences, theories and methodologies. The small-group level has a certain primacy,...

Understanding how a collaborative group as a whole constructs ­knowledge through joint activity in a CSCL setting is what sets the research field of CSCL apart from other approaches to the study of learning. Successful collaboration involves not only the incorporation of contributions of individuals into the group discourse, but also the effort to...

The field of Computer-Supported Collaborative Learning (CSCL) explores the design and use of collaboration technologies to support learning systems, such as school classrooms or small groups of people building knowledge together. I hope that CSCL environments can be designed that make possible and encourage groups to think and learn collaboratively...

There are many theories useful for framing CSCW research and they may in principle be irreducible to a single theory. CSCW research explores questions involving numerous distinct—though interacting—phenomena at multiple levels of description. The useful approach may be to clearly distinguish levels such as individual, small-group and community unit...

To understand how small groups use information to solve problems collaboratively within socio-technical environments, we need a method for analyzing the structure of computer-mediated discourse. Conversation analysis offers an analysis of conversational talk in terms of a fine structure of adjacency pairs and offers some suggestions about longer se...

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 collab...

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies t...

This commentary on the special issue suggests a focus on group cognition factors in investigations of teamwork involving sociotechnical systems. The author has conducted research in computer-supported collaborative learning and has found the need to rethink the theory and methodology of that field to take account of its defining characteristics of...

Two central principles of contemporary learning science theory (Stahl, Koschmann & Suthers, 2006) are: • Student learning involves construction of meaning by the learners (constructivism). • Learning often takes place originally inter-subjectively (socio-cultural theory). For learning in the discipline of mathematics, these principles imply: • Stud...

More than we realize it, knowledge is often constructed through interactions among people in small groups. The Internet, by allowing people to communicate globally in limitless combinations, has opened enormous opportunities for the creation of knowledge and understanding. However, a major barrier to taking advantage of this opportunity remains the...

Virtual math teams develop innovative methods of interacting within the synchronous text chat VMT environment. New competencies for communication, collaboration and mathematical reasoning emerge as the groups make sense of the complex features of their shared virtual worlds. KeywordsData session–expository discourse–explanatory discourse–adjacency...

This is an informal discussion from my personal perspective on computer-supported collaborative learning (CSCL). I envision an epical opportunity for promising new media to enable interpersonal interaction with today’s network technologies. While asynchronous media have often been tried in classroom settings, I have found that synchronous text chat...

The approach of the VMT Project has usually been described as design-based research in the learning sciences. However, it can also be understood as ethnography, using a micro-ethnographic style of interaction analysis to study the construction of social order in the exotic culture of virtual math teams. This chapter reviews the history of critical...

Online text chat has great potential for allowing small groups of people in school or at work to build knowledge and understanding together. However, chat participants often post in parallel, making it difficult to follow the conversational flow and to identify who is talking to whom about what. The loosely ordered succession of turns contributes t...

This chapter reviews Anna Sfard’s book, Thinking as communicating: Human development, the growth of discourses and mathematizing (Sfard, 2008). It highlights insights of the book that are relevant to studying virtual math teams as well as calling for further analysis to situate Sfard’s theory within the discourses of CSCL and socio-cultural theory....

The concept of scripts has considerable appeal as addressing or at least naming an urgent issue in CSCL: how to use the promise of networked computers to guide groups of students to engage in desirable and successful collaborative learning. However, the concept of scripts is often applied inconsistently or founded on problematic theoretical grounds...

Studying virtual math teams involves explorations along multiple dimensions: (a) designing a testbed to support interaction within teams, (b) analyzing how math is discussed within this setting and (c) describing how the teams achieve their cognitive tasks. Previous chapters have shown in various ways how virtual math teams co-construct their share...

In this chapter, we trace collaborative problem solving as an interactive, layered building of meaning among learners working as a small group. Our analytic aim is to investigate how students through their inscriptive signs collaboratively build mathematical ideas, heuristics and lines of reasoning in the VMT environment. KeywordsDiscourse–heurist...

Theories of collaborative learning have identified the central role of the joint problem space in coordinating work and establishing intersubjective understanding. The concept of problem space had its inception within the information-processing perspective as a characterization of individual problem-solving activity. It was then reformulated and ex...

This work describes a methodology for analyzing the social construction of mathematical knowledge within a chat environment like VMT. It proposes a model for representing the flow of discourse by linking contributions based on information uptake. A framework for analysis using the model is designed to represent: (1) the co-construction and manipula...

Centered on a case study of a synchronous online interchange, this chapter discusses the use of the VMT graphical referencing tool in coordination with text chat to achieve a group orientation to a particular mathematical object in a shared whiteboard. Deictic referencing is seen to be a critical foundation of intersubjective cognitive processes th...

In this chapter we describe ongoing work towards enabling dynamic support for collaborative learning in the Virtual Math Teams (VMT) environment using state-of-the-art language technologies such as text classification and dialogue agents. The key research goal of our long-term partnership is to experimentally learn broadly applicable principles for...

Meaning making is central to the interactions that take place in CSCL settings. The collaborative construction of shared meaning is a complex process that has not previously been analyzed in detail despite the fact that it is often acknowledged as being the distinguishing element in CSCL. Here, a three-minute excerpt from a discussion among three s...

The aim of the Virtual Math Teams (VMT) Project is to catalyze and nurture networks of people discussing mathematics online. It does this by providing chat rooms for small groups of K-12 students and others to meet on the Web to communicate about math. The vision is that people from all over the world will be able to converse with others at their c...

The challenges of designing computer support for education have shifted considerably in recent years, with, e.g., the rapid growth of the Web, online learning and social networking. New human–computer interaction (HCI) design approaches, methods, tools and theories are now required to analyze and understand interactions and learning of online group...

Studying Virtual Math Teams centers on detailed empirical studies of how students in small online groups make sense of math issues and how they solve problems by making meaning together. These studies are woven together with materials that describe the online environment and pedagogical orientation, as well as reflections on the theoretical implica...

As a foundation for the design of groupware, we need a new science of group interaction, a systematic description of the processes at the group level of description that may contribute to problem solving, knowledge building and other cognitive tasks undertaken by small groups collaborating synchronously over networked computers. A scientific invest...

While there is evidence that collaborative learning consists largely of group-level 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 small-group practices that take place in...

The ijCSCL Board of Editors presents a day-long introduction to CSCL. This tutorial will be a dialog among oldtimers and newcomers to the CSCL community. The day will be divided into four sessions, focusing on CSCL visions, CSCL practices, CSCL technologies and CSCL theories. During each session, several members of the ijCSCL Board will discuss wit...

Using as data videotapes of archaeologists working to see and map structure in the dirt they are excavating, meaning-making in the home of a man with severe aphasia, and sequences of actual talk-in-interaction, this talk will investigate action, cognition, ...

This symposium explores central themes related to the design of specific wiki features to support collective cognition, and presents analyses of wiki use in authentic educational settings. Through the presentation of four different projects, the symposium will take up issues related to the significance of iterative design approaches for aligning so...

The Virtual Math Teams (VMT) knowledge building environment has been used in Singapore and in the United States. It includes support for synchronous, quasi-synchronous and asynchronous online interaction using text chat, whiteboard drawing and wiki summarization. It has been used for groups of students to collaborate on challenge problems in mathem...

Collaborative learning environments require carefully crafted designs -both technical and social. This paper presents a model describing how to design socio-technical environments that will promote collaboration in group activities. A game was developed based on this model. This tool was used to conduct experiments for studying the collaborative le...

This paper provides elements of a transformational conceptual framework for CSCL by focusing on how learning takes place when the answer is not known (this being the case for complex design problems in numerous domains encountered in lifelong learning ...

Meaning making ,is central to the interactions that take place in CSCL settings. The collaborative construction of shared ,meaning ,is a complex ,process that has not previously been analyzed,in detail despite the fact that it is often acknowledged ,as being ,the distinguishing element in CSCL. Here, a three-minute excerpt from a discussion among t...

The development of high functioning healthcare teams is advanced through facilitative leadership, the development of socialization strategies that embrace the importance of tacit as well as explicit knowledge, and relational environments that promote transparency and trust. This report is a summary of reflections on collaborative practice from an i...

Learning takes place over long periods of time that are hard to study directly. Even the learning experience involved in solving a challenging math problem in a collaborative online setting can be spread across hundreds of brief postings during an hour or more. Such long-term interactions are constructed out of posting-level interactions, such as t...

More than we realize it, knowledge is often constructed through interactions among people in small groups. The Internet, by allowing people to communicate globally in limitless combinations, has opened enormous opportunities for the creation of knowledge and understanding. A major barrier today is the poverty of adequate groupware. To design more p...

Exploring the software design, social practices, and collaboration theory that would be needed to support group cognition; collective knowledge that is constructed by small groups online. Innovative uses of global and local networks of linked computers make new ways of collaborative working, learning, and acting possible. In Group Cognition Gerry S...

Computer-supported collaborative learning (CSCL) is an emerging branch of the learning sciences concerned with studying how people can learn together with the help of computers. As we will see in this essay, such a simple statement conceals considerable complexity. The interplay of learning with technology turns out to be quite intricate. The inclu...

Collaborative learning environments require carefully crafted designs – both technical and social. This paper presents a model describing how to design socio-technical environments that will promote collaboration in group activities. A game was developed based on this model. This tool was used to conduct experiments for studying the collaborative l...

More than we realize it, knowledge is often constructed through interactions among people in small groups. The Internet, by allowing people to communicate globally in limitless combinations, has opened enormous opportunities for the creation of knowledge and understanding. A major barrier today is the poverty of adequate groupware. To design more p...

Recent research on instructional technology has focused increasingly on the potential of computer support to promote collaborative learning. Socio-cultural theories have been imported from cognate fields to suggest that cognition and learning take place at the level of groups and communities as well as individuals. Various positions on this issue h...

CSCL faces the challenge of not only designing educational technologies and interventions, but of inventing analytic methodologies and theoretical frameworks appropriate to the unique character of collaborative learning as an interactional group accomplishment. This paper argues that thinking in CSCL settings should be primarily analyzed at the sma...