Noel Enyedy, Phil Vahey, and Bernard R. Gifford
Education of Mathematics, Science and Technology Graduate School of Education, University of California at Berkeley
Communication is a central aspect of human learning. Using the Probability Inquiry Environment (PIE) as an example, we examine how external representations (both textual and iconic) mediate face- to-face conversations among students, and support productive mathematical discourse. We provide quantitative data that suggests that seventh grade students who used PIE learned some of the basic principles of probability. Two cases studies are that illustrate how communication supported by computer-mediated representations contributed to this success. The first case study demonstrates how the computer can actively prompt student conversations that lead to learning. The second case study examines how an animated graphical representation supported these productive conversations.
Computer Supported Collaborative Learning (CSCL) as a field of inquiry sets out to understand, support and change the learning practices of students and teachers working together in groups. This paper explores the theme of collaboration as a design principle and illustrates how to use the rich media of the computer to support students as they collaborate. Using the Probability Inquiry Environment (PIE) as an example, we look at the computer-mediated representational resources designed to help support productive mathematical conversations.
There is a synergetic relationship between the practices and artifacts of a community and an individual's thinking and activity. Clifford Geertz stated, "culture, rather than being added on, so to speak, to a finished or virtually finished animal, was ingredient, and centrally ingredient, in the production of the animal itself" ( 1973, p.47). Cognitive artifacts, those cultural artifacts used to aid the process of thinking and communication, quickly become inseparable from the knowledge and established practices of a community. While this relationship makes describing human activity increasingly difficult to analyze, it provides a leverage point to promote change. One way to conceptualize instructional design, then, is as a type of anthropological activism ( diSessapersonal communication) in which we leverage the relationship between tools and practice in an attempt to redefine the practices of the teaching and learning community through the introduction of new technologies.
Re-conceptualizing the issues of instructional design as anthropological activism encourages designers of educational software to seriously consider that a critical dimension of the design space is the practices and activities that surround and influence how the software will be used in a classroom. The purpose of this paper is to illustrate a genre of educational software that recognizes discourse practices as a central component of human learning and uses technology to support this key classroom practice and improve learning.
In this paper we will try to answer the question, "How can the computer be effectively used to start and support mathematical conversations?" Specifically, in the domain of probability, how can computer-mediated textual and graphical representations help students to articulate their naive intuitions about probability, and scaffold them in the process of constructing arguments that reflect a more standard understanding of probabilistic reasoning?
By examining the design of PIE and its implementation in a seventh grade classroom, we hope to refine both our theoretical understanding of collaboration and learning, and how to better support the emerging collaborative practices of the classroom. In this paper we first discuss the aspects of CSCL that influenced our initial design and then illustrate, through two case studies, how we refined the representational resources to make them better support collaborative learning. In the first example, we show how making the computer an active agent that prompted and structured student conversations created the opportunity for students to productively build on their existing ideas. In the second example, we explore how the students used a dynamic,