This CAREER grant funds the study of teaching practices in a year long high school algebra course that integrates hand-held and other electronic devices throughout the year. Of particular interest is how these technologies can support learners' capacity to efficiently and effectively draw on the distributed intelligences that technical and social networks make available. The investigation focuses on collaborative learning tasks that are centered on collective mathematical objects, such as functions, expressions, coordinates, shapes or sets that participants in a group must jointly manipulate through networked computers. The study addresses two research questions: 1) What novel forms of student learning do collaborative designs for classroom networks support? 2) What kinds of teaching practices are made possible by classroom networks and made necessary by collaborative designs?
One line of investigation is to use a series of design experiments in which new technology designs provide a context for exploring student learning through collaborative problem-solving activities and investigations. A second line involves alternating between two different settings for conducting four successive year-long cycles of those design experiments: a set of high school algebra classrooms taught by teachers who serve as collaborative partners in the development and implementation of new activity designs, and another high school algebra classroom in which the principal investigator will serve as the teacher.
This research project focused on designing and studying a novel form of technology for middle and high school mathematics classrooms. The research team developed specialized software to create a "classroom network" that allows students to use personal computing devices such as graphing calculators or iPads to participate in collaborative learning activities with their classmates. While experimental and commercial systems that facilitate instructional activity—such as real-time polling—through classroom communication between student and teacher computing devices via wireless networking have become increasingly common in recent years, few of these systems directly support peer collaboration among small groups of students, and even fewer support the critical area of secondary mathematics teaching. Given that collaborative learning has been demonstrated in other research studies to be an effective approach to supporting student learning, but also that the collaboration needs to be carefully structured in order to achieve that effectiveness for all members of a small group, we hypothesized that appropriately designed classroom networking tools could provide scaffolds for successful group collaboration. The purpose of this project was to develop and study the educational potential of a prototype system along these lines. Over the course of the five-year project, several math teachers in schools in Northern California used these tools and activities with their Algebra classes. While they did so, members of the research team observed and recorded the ways students used the technology and the kinds of mathematical reasoning and problem-solving conversations they participated in with their peers and their teacher. Through these investigations, the team learned about several aspects of mathematics teaching and collaborative learning supported by these tools. Foremost among these lessons was that different topics in the mathematics curriculum require different design solutions to create successful learning activities—so in other words, our design for graphing linear functions needed different technology and a different way of organizing peer collaboration than our design for solving equations. A second lesson learned followed closely from the first: different curricular topics enable different forms and degrees of collaboration in mathematics tasks. In other words, some topics, and the collaborative activities we developed to teach them, were more likely to lead, for example, to having students talk about and reason through their ideas about a mathematical rule or relationship, while others more often found students dividing up parts of a problem and working on them separately. A third set of lessons from the project centered on the ways that the classroom network system provided teachers with a tremendous amount of real-time information about student work, which they were able to use in unexpected and pedagogically powerful ways, both for monitoring the progress of individual students and groups through a task and for fostering productive discussions about mathematical concepts with the whole class. Each of these key lessons and related research findings has been reported to appropriate research and practitioner audiences through journal publications, book chapters, and conference presentations over the course of the grant. Another primary outcome of this project is the technology developed. The collaborative networking tools and learning activity designs were iteratively refined and expanded based on the successive cycles of classroom implementation and data analysis over the five years of the project. The first and most extensively developed collaborative activity platform, an environment called Graphing in Groups, is now freely available—the student software can be downloaded from Apple’s iOS app store, and the teacher software that runs the classroom network is available on the project website. Additional learning activity designs are in the final stages of refinement and will soon be available for free distribution through the same mechanisms. A final project outcome involves the significant research mentorship, training, and professional development opportunities it provided for a number of UC Davis students and Sacramento-area math teachers who participated in the project. Seven graduate and three undergraduate students served as members of the research team over the course of the project, including two PhD students who completed dissertation research directly related to project activities and data. Six high school math teachers in the region implemented project technology and activities with hundreds of their students over the lifetime of the grant. And dozens of other middle and high school mathematics teachers and teaching credential candidates had opportunities to work with and learn from the tools and materials developed throughout the project in the context of professional development workshops and teacher education courses.
