Abstract:

The paper presents mathematical approaches for implementing methods for synchronizing human actions and virtual avatar movements, using inverse kinematics. To create a complete system for synchronizing the player's behavior and VR-avatar, the implementation of the necessary functionality is described: hand positioning, calibration of their size, bending of hands into anatomically acceptable sides, anatomical flexion of the spine, squatting and moving in space. The implementation of tilt and squat significantly extends the functionality of synchronization of the player's behavior and avatar, which allows creating a complete set of visual sensations of the user in a virtual environment, which is deprived of most of the applications of virtual reality at the moment.

Abstract: The productive status of errors is discussed in Mexico and the US mathematics education reforms. However, teachers’ positionings toward mistakes may or may not converge with this productive status. For that reason, reflecting on teachers’ positioning during the teaching and learning process is crucial (Stooksberry et al., 2009). This study examines teachers’ positional framing during teacher and students’ moment-to-moment interaction in the context of errors occurring in the classroom. Findings reveled two opposite error frames that teachers used to address errors in their classrooms. One of these frames provided student support for using errors as tools for their learning. On the contrary, the other provided an idea of student incapacity to cope with errors.