The small-gain theorem,the passivity theorem and their equivalence

Two small-gain theorems and a passivity theorem yielding stability results for general feedback systems are shown to be equivalent.     

Kinecting Physics: Conceptualization of Motion Through Visualization and Embodiment

The purpose of this work was to share our findings in using the Kinect technology to facilitate the understanding of basic kinematics with middle school science classrooms. This study marks the first three iterations of this design-based research that examines the pedagogical potential of using the Kinect technology. To this end, we explored the impact of using the Kinect in conjunction with an SDK Physical Virtual Graphing program on students’ understanding of displacement, velocity and acceleration compared to students who conducted more traditional inquiry of the same concepts. Results of this study show that, while there may be some affordances to be gained from integrating this technology, there is a need for a scaffolded approach that helps students to understand the “messiness” of the data collected. Further, meta-cognitive activities, such as reflective opportunities, should be integrated into the inquiry experiences in order to scaffold student learning and reinforce concepts being presented. While the Kinect did work to generate large-scale visualization and embodied interactions that served as a mechanism for student understanding, this study also suggests that a complementary approach that includes both the use of hands-on inquiry and the use of the Kinect sensor, with each activity informing the other, could be a powerful technique for supporting students’ learning of kinematics.