(Page 5 of 7) - A Taxonomy of Generative Activity Design Supported by Next-Generation Classroom Networks authored by Stroup, Walter., Ares, Nancy. and Hurford, Andrew.

models

outcomes

modeling

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Figure 4. Modeling characterized as series of pathways, endpoints, and comparisons with data (experience).

How well the outcomes of the model fit with the data (whether real or anticipated) or experience (broadly
conceived). Unfortunately modeling in classrooms is often pursued as if it was nominally generative. Much of
current laboratory work in science classrooms has this collapsed structure. Students are to use a prescribed model
(single path) to create computed outcomes that are then mechanically compared to the actual data collected from
using tightly scripted “lab” procedures. A similarly collapsed notion of modeling is also what gets discussed when
the “application” of a particular mathematical idea is presented in textbooks or classroom presentations. Modeling
at its best however, would have a description closer to that represented in Figure 4. – learners would create a range
of models and use them to create model outcomes (implications or predictions). These outcomes would then be
discussed in terms of goodness of fit to data (real or anticipated). Structural conversations about the ways in which
various models might be similar or distinct can and should occur. In addition, issues related to deciding what it
means to fit data can be engaged. The double arrow over modeling indicates that models and outcomes interact
iteratively in the sense-making of learners.

As other researchers have noted in what can be seen as extending aspects of the pragmatists’ notion of “truth” to

modeling, “models consist of conceptual systems that are expressed using a variety of interacting media (concrete
materials, written symbols, spoken language)” and are used to organize our experiences and action in the world
(Lesh et.al. 2003, p. 214). While a generative sense of modeling can certainly be carried out without network
technology, next generation network capabilities allow the students and teachers to make visible and act on the
“interacting media” used to express a given set of models. Whether it is a drawing, a sketch in a network-enabled
geometry environment, a finite-difference equation, text, voice, or a Logo program, next generation networks offer
the potential for making the machine-based interacting media associated with mathematical ideas the coin of the
realm in pursuing generative approaches to modeling. Models can be made more visible and can be acted upon
directly in a network space. A perhaps more dramatic outcome in terms of student learning may be the ways in
which network mediated role-playing (discussed below) begins to make visible to students that useful and
informative modeling is often the negotiated product of groups of interacting modelers

4.4 Design Tasks – Multiple Path and Endpoints where Satisfaction of Goal is Central

Design tasks are similar to modeling above in that both are multiple path and multiple outcome tasks.

design paths

design outcomes

designing

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Figure 5. Generative design tasks are like modeling tasks except fit with a goal is central.

The difference is that fit with the goal or design specifications replaces the analysis of fit with data. As is true with
modeling, structural issues can be ignored in which case designing comes to be only about learners arriving at
particular designs. Unfortunately, when design tasks are pursued in classrooms it is often the case that no larger
discussions of the processes of design are engaged. Much of the richness and learning potential of design is lost.