SimCalc Classroom Connectivity Project
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Understanding Math Classroom
Affordances of Networked Hand-Held Devices
Project Abstract
Prior SimCalc work exploited the representational affordances of the
computational medium to democratize access to the core ideas leading to
and underlying Calculus. These important ideas had previously been
sequestered in a capstone course reached by at most 10-12% of the
population, but now can be successfully mastered by urban middle school
students if given the opportunity. Simulations, new graphical ways of
creating and editing functions (as well as derivatives and integrals of
functions), and dynamic visualization tools together enabled a
reconstituting of these ideas into core curriculum beginning in the
middle grades. We have now begun to study the profound potential of
combining the previously established representational innovations with
the new connectivity affordances of increasingly powerful, robust and
inexpensive hand-held devices in wireless networks. In combination with
the representational affordances, we see classroom connectivity as a
critical ingredient to unleash the long-unrealized potential of
computational media in education, because its potential impacts are
direct and at the communicative heart of everyday classroom instruction.
This will happen only if those impacts are sufficiently understood to
inform iterative improvement of technologies and classroom practices, as
well as design of teacher development and support structures, that
support and do not impede learning.
With the support of two major corporate partners, Texas Instruments and Palm, we work with teachers in Grade 7-12 classrooms equipped with
school-standard graphing calculators and newer devices wirelessly
networked to each other and to a teacher's workstation. We examine three
Opportunity Spaces generated by classroom connectivity. (1) Assessment:
Principled diagnostic assessment routinely embedded in instruction based
on students sending their responses to carefully designed
thought-revealing probes and problems to the teacher. (2) Learning: New
and highly engaging classroom activity structures exploiting
teacher-student and student-student interactions, through the
construction and use of publicly shared mathematical objects (e.g.,
students creating velocity functions on their hand-helds that, when
uploaded, control their character in a class marching parade or dance)
and by systematically varying student constructions in the public space
to reveal mathematical structure in new ways (e.g., by having students
create families of functions parametrized by student-indexed numbers).
(3) Teaching: Teacher classroom management support for distributing and
collecting student work, viewing & annotating student screens, and
generally managing the flow of information in the connected classroom.
We use design experiments to produce a series of classroom-grounded case
studies that embody theoretical frameworks and carefully structured
accounts of classroom phenomena. These are intended to help guide
further design and development as well as to support further research.
The work takes place primarily in ordinary Grade 7-10 classrooms taught
by typical teachers in MA and CA. We deliberately vary the experience of
the initial teachers, and, over time, vary the technology platforms. We
study affordances and constraints at three different time-scales and
levels of detail: (1) carefully-designed and closely observed 1-2 week
teaching experiments across sites; (2) semester-long observations of
teachers and classrooms based on occasional visits, teacher reflective
journals, and structured debriefing-interviews of teachers; and (3)
longitudinal change of the both the teachers and the technologies as
they mature together over the life of the project, including comparisons
with novice teachers introduced in YR 3.
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