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Beliefs teachers hold influence the judgments they make about their students, and opportunities they provide for engaging them in rigorous mathematics. While math-related beliefs have been widely studied, less is known about teachers’ attributional beliefs (i.e., beliefs about people’s actions or behaviors) for mathematical success. In this study we investigated in-service elementary teachers’ stated beliefs about mathematical success. Findings show that teachers attribute mathematical success to factors that are both internal and external to the student. Although teachers explicitly stated that race and gender were not factors, many used descriptors that served as proxies for students’ demographic markers. 

This paper presents a framework based on either iterative simulation or iterative experimentation for constructing an optimal, open-loop maneuver to regulate the aerodynamic force on a wing in the presence of a known flow disturbance. The authors refer to the method as iterative maneuver optimization and apply it in this paper to regulate lift on a pitching wing during a transverse gust encounter. A candidate maneuver is created by performing an optimal control calculation on a surrogate model of the wing–gust interaction. Execution of the proposed maneuver in a high-fidelity simulation or experiment provides an error signal based on the difference between the force predicted by the surrogate model and the measured force. The error signal provides an update to the reference signal used by the surrogate model for tracking. A new candidate maneuver is calculated such that the surrogate model tracks the reference force signal, and the process repeats until the maneuver adequately regulates the force. The framework for iterative maneuver optimization is tested on a discrete vortex model as well as in experiments in a water towing tank. Experimental results show that the proposed framework generates a maneuver that reduces the magnitude of lift overshoot by 92% for a trapezoidal gust with peak velocity equal to approximately 0.7 times the freestream flow speed. 

This paper experimentally investigates the flow field development and unsteady loading of three force-mitigating pitch manoeuvres during a transverse gust encounter. The manoeuvres are constructed using varying levels of theoretical and simulation fidelity and implemented as open-loop kinematics in a water towing tank. It is found that pitch actuation during a gust encounter results in two important changes in flow topology: (i) early detachment of the leading-edge vortex (LEV) and (ii) formation of an LEV on the pressure side of the wing upon gust exit. Each of the pitch manoeuvres is found to mitigate a significant portion of the circulatory contribution of the lift force while only manoeuvres with accurate modelling of the added-mass force are found to adequately mitigate the total lift force. The penalty of aerodynamic lift mitigation using pitch manoeuvres was a twofold increase in the pitching moment transients experienced by the wing for all cases. By quantifying changes in the vertical gust momentum before and after the encounter, lift-mitigating manoeuvres were found to reduce the disturbance to the gust's flow field, thereby reducing the momentum exchange between the gust and the wing.