Jim Kaput, UMass Dartmouth
Jeremy Roschelle, SRI International (Co-PI)
National Science Foundation
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.