(Page 1 of 7) - A Taxonomy of Generative Activity Design Supported by Next-Generation Classroom Networks authored by Stroup, Walter., Ares, Nancy. and Hurford, Andrew.

A TAXONOMY OF GENERATIVE ACTIVITY DESIGN

SUPPORTED BY NEXT-GENERATION CLASSROOM NETWORKS

Walter M. Stroup, The University of Texas at Austin, ## email not listed ##

Nancy Ares, University of Rochester, Nancy.## email not listed ##

Andrew C. Hurford, The University of Texas at Austin, ## email not listed ##

Abstract: Previous work has examined how new theoretical, methodological, and design frameworks for engaging
classroom learning are provoked and supported by the highly interactive and group-centered capabilities of a new
generation of classroom–based networks. This network-supported interactivity, coupled with generative design,
allows the environment of the classroom itself to be thought of as a group-oriented “manipulative” or mediating tool
for teaching and learning. Given that this level of technologically-supported interactivity and group-oriented design
is new to classrooms, new challenges for teachers, researchers, and curriculum developers relative to how to think
about designing for and working in these types of environments need to be addressed. We present a taxonomy of
generative activity design that has emerged from our work in developing and then working with next generation
systems.

1.0 Introduction

Due to the group-focused interactivity and data collection capabilities of next-generation networking, we have a

new tool to explore the dynamics of – and designs for – classroom learning. A number of projects supported by the
National Science Foundation have responded to the challenge of advancing learning in these highly interactive
networks by using mathematical/scientific ideas to organize and analyze classroom activity. This use of domain-
related “big ideas” to study group learning has been discussed as “mathematics structuring the social sphere” [MS3]
(Stroup, et. al. 2002; Stroup, Ares & Hurford, in press). Many of the network-based projects began by focusing on
student learning (Kaput & Hegedus, 2002; Roschelle & Vahey, 2003; Wilensky & Stroup, 1999). Recently,
however, significant efforts have emerged that focus more directly on issues related to supporting, and learning
from, teachers’ developing understandings of how best to design for network supported classroom activity. We
suggest that there is a kind of “resonance” between technological affordance and generative forms of teaching and
learning. Generative design, as we use the term, develops from and supports the core commitments of the reform
movements in mathematics and science education and it is this resonance that we look to advance. Toward this end,
we present a new taxonomy of kinds of generative activity useful both in clarifying the relations between kinds of
generative activities and in clarifying internal aspects of generative design, especially as supported by next-
generation classroom networks.

2.0 Technology and Moving to Group-Oriented Generative Design

There is a significant literature related to generative approaches to teaching and learning. Generative teaching,

as discussed by Wittrock, is “a model of the teaching of comprehension and the learning of the types of relations that
learners must construct between stored knowledge, memories of experience, and new information for
comprehension to occur” (1991, p. 170). What Wittrock means by the learners’ active construction of new
“relations” is close to what might be called constructivist teaching pedagogy. Consequently, generative learning in
his framework involves students’ ability to create artifacts that embody their constructed understandings. In a
closely related way researchers from the Learning Technology Center at Vanderbilt emphasize aspects of creating
“shared environments that permit sustained exploration by students and teachers” in a manner that mirrors the kinds
of problems, opportunities, and tools engaged by experts (1992, p. 78). Teaching involves “anchoring or situating
instruction in meaningful, problem-solving contexts that allow one to simulate in the classroom some of the
advantages of apprenticeship learning” (1992, p. 78). Although many of these previous theories are generative at the
level of the individual learner or even at the level of a small group (Lesh, et al., 2000) there is not enough of a
picture of how to structure the cross individual or cross sub-group learning. Our efforts are directed at extending
and reconceptualizing these earlier analyses of generativity to engage the issue of how to design for the diversity and
multiplicity of learners’ ideas and insights in supporting the emergence and development of mathematical and
scientific reasoning in group contexts.

Generativity as we discuss it below and elsewhere (Stroup, 1997; Stroup, et. al. 2002; Stroup, Ares & Hurford,

in press) focuses on design for the group. The emphasis is on supporting the interactions of teacher and students
together in a classroom and natural subsets of this classroom-based grouping. Additionally, we are interested in how
mathematical and scientific content itself can frame the design of classroom activities and supportive technologies.
Content in this sense is an organized body of knowledge developed over time, which while enacted through activity,
still retains coherence and structures the group activity. The diversity of forms of student participation – including