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This study is part of a larger project exploring students' thinking of Dynamic Measurement (DYME), an approach to area measurement that engages students in dynamic digital experiences of measuring rectangular surfaces through sweeping lengths. The goal of this study was to evaluate the extent to which students could bridge the mathematical knowledge they gained from these dynamic experiences to other activities that are more static in nature. A classroom of 19 third grade students participated in an 8-period design experiment (DE) centered on DYME. Data to evaluate the bridging were obtained from pre- and post-assessments administered before and after students' participation in the DE. The results suggest that by working with the DYME tasks, students were able develop a conceptual connection between multiplicative reasoning and area measurement that were able to apply to solve static tasks. [ABSTRACT FROM AUTHOR]

Mathematics teacher educators are faced with designing teacher in-service professional development experiences for developing and transforming Technological Pedagogical Content Knowledge (TPACK) towards integrating digital technologies as mathematics learning tools. Online environments provide opportunities to a broad range of teachers, yet, the asynchronous nature presents communication and collaboration challenges. A researcher-conjectured, empirically-supported learning trajectory guides this online TPACK program for engaging teachers in knowledge-building communities. Three online technology education courses provide teachers with experiences as students, learning about the technologies while confronting challenges to their thinking about teaching with the technologies. The fourth course provides the teachers with key experiences through blended instruction. Through online explorations and discourses in their communities, they examine reform-based instructional strategies for teaching with technologies. Concurrently, they design, implement, analyze and reflect on their teaching experiences through their designed five-day unit in their mathematics classrooms. Four TPACK components reveal how this experience in knowledge-building communities transforms their TPACK. [ABSTRACT FROM AUTHOR]

Software developers need to develop technical and social skills to be successful in large projects. We model the relative sociality of developer as a ratio between the size of her communication network and the number of tasks she participates in. We obtain both measures from the problem tracking systems. We use her workflow peer network to represent her social learning, and the issues she has worked on to represent her technical learning. Using three open source and three traditional projects we investigate how the project environment reflected by the sociality measure at the time a developer joins, affects her future participation. We find: a) the probability that a new developer will become one of long-term and productive developers is highest when the project sociality is low; b) times of high sociality are associated with a higher intensity of new contributors joining the project; c) there are significant differences between the social learning trajectories of the developers who join in low and in high sociality environments; d) the open source and commercial projects exhibit different nature in the relationship between developer's tenure and the project's environment at the time she joins. These findings point out the importance of the initial environment in determining the future of the developers and may lead to better training and learning strategies in software organizations. [ABSTRACT FROM AUTHOR]