approaches to content

["Ares, Nancy" <nancy.ares@rochester.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