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*To*: "'xmca@weber.ucsd.edu'" <xmca@weber.ucsd.edu>*Subject*: approaches to content*From*: "Ares, Nancy" <nancy.ares@rochester.edu>*Date*: Wed, 10 Nov 2004 16:27:08 -0500*Delivered-to*: xmca@weber.ucsd.edu*Old-return-path*: <owner-xmca@weber.ucsd.edu>*Reply-to*: xmca@weber.ucsd.edu*Resent-date*: Wed, 10 Nov 2004 13:27:10 -0800 (PST)*Resent-from*: xmca@weber.ucsd.edu*Resent-message-id*: <nN2LKB.A.6YB.teokBB@weber>*Resent-sender*: xmca-request@weber.ucsd.edu

Hello, I, too, am enjoying the discussion of education, technology and math, and appreciate the use of data to foster dialogue. My colleague Walter Stroup and I have been working on notions of generativity in technology design and use for math and science classrooms. We ground our work in the notion of a dialectic of math and science as both socially structured and socially structuring. The idea is that we can design technologies and activities in ways that both use 'big ideas' in math or science (e.g., dynamic systems, proof, parametric space, statistics) to structure the social space of learning and highlight social interaction as structuring the math or science that emerges from activity. Space-creating play (as in mathematical space) and dynamic structure are central features of the ways we attend to 'content,' while agency and participation are central features of social interactions that structure the 'content'. An example of math structuring social space: Participatory simulations are networked activities where learners act out the roles of individual system elements and observe how the behavior of the system as a whole emerges from their individual behaviors. These emergent results then become the focus of discussions and analyses. Using network technology with a public visual display, students can, for example, become agents in a population where a disease is introduced and be part of the system as the disease spreads. In another simulation they each can control a stoplight in a simulated city's traffic grid and together work toward improving the traffic flow. Not only is dynamic-systems modeling the content being introduced into the curriculum, the learning itself is organized in terms of the classroom becoming the dynamic system. By assuming iconic roles in a system, mathematical ideas like emergence, feedback, and complexity are literally embodied by the network-supported learning activity. An example of social interaction structuring the math: in one participatory simulation used by a teacher to explore positive/negative integers, students also recognized and explored concepts of slope and rate, as well as their representation in graphs. Here, students used the mathematics of the network-mediated activity itself to expand the content and representations involved. Their agency and participation involved making contributions to critical aspects of practice, as in students' expansion of the activity to include concepts of rate, slope, and representation. The space of mathematical objects was enlarged through their play-full engagement in the generative activity. One of the critical things, we think, is that we must attend to the structuring relationship between content and activity to both understand learning and to develop powerful use and design of classroom technologies. I know this is a bit long-winded... Nancy Ares

**Follow-Ups**:**Re: approaches to content***From:*"Peg Griffin" <Peg.Griffin@worldnet.att.net>

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