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.
Recent perspectives on learning encourage educators interested in technology based learning environments to reconsider their basic assumptions about teaching as "transmitting correct information." Instead we view the teaching and learning enterprise as helping students construct knowledge from domain relevant experiences. In this paper we report on the Probability Inquiry Environment (PIE), which facilitates the development of probabilistic reasoning by making available collaborative inquiry activities and student-controlled simulations. These activities guide middle school students toward a deeper understanding of probability, a domain that is becoming increasingly important in the K-12 mathematics curricula of the United States but which is notoriously difficult to learn.
BackgroundTo help students construct knowledge in the domain of mathematics, we advocate student construction and appropriation of concepts by making available studentcontrolled interactive simulations, dynamicrepresentations, and contextualized learning activities. Our carefully crafted activities and student-controlled simulations are designed to focus students on particular intuitions, encourage them to articulate and refine these intuitions using the tools and practices of mathematics and probability, and guide them towards a normative conception of mathematics.In this paper we report on the Probability Inquiry Environment (PIE), which facilitates the development of probabilistic reasoning in middle school students. We first describe our theoretical underpinnings, and why we chose to use collaborative inquiry and simulations. We describe the specifics of PIE and the curriculum, and follow this with a description of a study in which PIE was implemented in two seventh grade classrooms. We then present detailed qualitative data from one pair of students as they investigate one of the computer activities, and show how the features of PIE contributed to student conversations and student understandings. We conclude with generalizations from our work, and recommendations for others creating collaborative environments for active knowledge construction.
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