My research focuses on children's mathematical and scientific reasoning in the context of schooling, with a special emphasis on tools and notations for developing thought. There are two major strands to this program. The first focuses on the design of learning environments that foster the growth and development of model-based reasoning about mathematics and science. This research, conducted with Leona Schauble, involves collaboration with teachers in local schools to reform mathematics and science so that students can invent and revise models as forms of mathematical and scientific explanation. We work with teachers to design a cumulative science education centered about modeling practices. In a related reform effort, I collaborate with teachers to redesign elementary-grade mathematics to include systematic investigation of space and geometry. We investigate children's understanding of the mathematics of space when mathematics education is grounded in children's everyday experiences. I also examine the inscriptions and notations children invent as tools for mathematical exploration and argument. My research in mathematics education includes work with teachers and children in urban schools (Phoenix, AZ) and with Yup'ik children and their teachers in Alaska.
A second strand of research, connected in principle to the first by its focus on student inquiry and the semiotics of inscription, considers students as software authors and designers. This research has included examination of Logo, Lego Logo, and hypermedia as design tools for students in the elementary and secondary grades. I've been especially interested in the growth of critical standards about design when students are provided prolonged opportunities to author in electronic environments. Current research focuses on design and development of case-based hypermedia tools for teachers, with attention to the role that dynamic tools like these can play in fostering community and continued professional development.