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This paper proposes a low-cost interface and refined digital twin for the Raven-II surgical robot. Previous simulations of the Raven-II, e.g. via the Asynchronous Multibody Framework (AMBF), presented salient drawbacks, including control inputs inconsistent with Raven-II software, and lack of stable, high-fidelity physical contact simulations. This work bridges both of these gaps, both (1) enabling robust, simulated contact mechanics for dynamic physical interactions with the Raven-II, and (2) developing a universal input format for both simulated and physical platforms. The method furthermore proposes a low cost, commodity game-controller interface for controlling both virtual and real realizations of Raven-II, thus greatly reducing the barrier to access for Raven-II research and collaboration. Overall, this work aims to eliminate the inconsistencies between simulated and real representations of the Raven-II. Such a development can expand the reach of surgical robotics research. Namely, providing end-to-end transparency between the simulated AMBF and physical Raven-II platforms enables a software testbed previously unavailable, e.g. for training real surgeons, for creating digital synthetic datasets, or for prototyping novel architectures like shared control strategies. Experiments validate this transparency by comparing joint trajectories between digital twin and physical testbed given identical inputs. This work may be extended and incorporated into recent efforts in developing modular or common software infrastructures for both simulation and control of real robotic devices, such as the Collaborative Robotics Toolkit (CRTK). 

Who has mathematical authority in your classroom, and what does authority look like? Find out different ways you can help students gain authority. 

We investigate the beliefs that influence middle and high school algebra teachers’ appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical features, and connections to the real world. We recorded small-group discussions in which teachers shared their responses to this activity, and qualitatively analyzed their discussions for evidence of beliefs that influenced their appraisals of the tasks. The teachers’ beliefs about contextual problems attended to task authenticity, opportunities for mathematical activity, obligations of tasks, and pedagogy and access. Our preliminary findings can inform future efforts to equip teachers with contextual tasks that develop students’ algebraic reasoning and problem solving.