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The purpose of this study was to investigate fourth-grade students’ sensemaking of a word problem. Sensemaking occurs when students connect their understanding of situations with existing knowledge. We investigated students’ sensemaking through inductive task analysis of their strategies and solutions to a problem that involved determining the difference between two quantities and number of groups within the task. This analysis provided useful themes about students’ strategy use across the sensemaking domains. Students exhibited three levels of sensemaking and many different strategies for solving the problem. Some strategies were more helpful to students in achieving a correct result to the problem. Findings suggest that sensemaking about problems involving differences and number of groups is difficult for many fourth-grade students. Among students who did make sense of the problem, those who used efficient strategies with more familiar operations tended to do better than those who used less efficient strategies or algorithms. 

Designing air-water systems for industrial applications requires a fundamental understanding of mass accommodation at the liquid-vapor interface, which depends on many factors, including temperature, vapor concentration, and impurities that vary with time. Hence, understanding how mass accommodation changes over a droplet’s lifespan is critical for predicting the performance of applications leveraging evaporation. In this study, experimental data of water droplets on a gold-coated surface evaporating into dry nitrogen is coupled with a computational model to measure the accommodation coefficient at the liquid-vapor interface. We conduct this measurement by combining macroscopic observations with the microscopic kinetic theory of gasses. The experiments utilize a sensitive piezoelectric device to determine the droplet radius with high accuracy and imaging to measure the droplet contact angle. This setup also quantifies the trace amounts of non-volatile impurities in the droplet. For water droplets evaporating in a pure nitrogen stream, the accommodation coefficient directly relates to vapor flux over the droplet’s surface and is affected by the presence of impurities. We obtained a surface-averaged accommodation coefficient close to 0.001 across multiple water droplets evaporating close to room temperature. This quantification can aid in conducting a more accurate analysis of evaporation, which can assist in the improved design of evaporation-based applications. We believe the modeling approach presented in this work, which integrates the kinetic theory of gases to the macroscale flow behavior, can provide a basis for predicting evaporation kinetics in the presence of extremely dry non-condensable gas streams. 

The purpose of this study was to investigate fourth-grade students’ sensemaking of a word problem. Sensemaking occurs when students connect their understanding of a situation with existing knowledge. We investigated students’ sensemaking about a word problem by comparing students’ strategy use. Inductive analysis was used to find themes about student sensemaking. Students exhibited one of three levels of sensemaking. Some problem-solving strategies, as a result of students’ sensemaking, led to a greater frequency of correct results. 

Abstract Habits are inflexible behaviors that develop after extensive repetition, and overreliance on habits is a hallmark of many pathological states. The striatum is involved in the transition from flexible to inflexible responding, and interspersed throughout the striatum are patches, or striosomes, which make up ~15% of the volume of the striatum relative to the surrounding matrix compartment. Previous studies have suggested that patches are necessary for normal habit formation, but it remains unknown exactly how patches contribute to habit formation and expression. Here, using optogenetics, we stimulated striatal patches in Sepw1-NP67 mice during variable interval training (VI60), which is used to establish habitual responding. We found that activation of patches at reward retrieval resulted in elevated responding during VI60 training by modifying the pattern of head entry and pressing. Further, this optogenetic manipulation reduced subsequent responding following reinforcer devaluation, suggesting modified habit formation. However, patch stimulation did not generally increase extinction rates during a subsequent extinction probe, but did result in a small ‘extinction burst’, further suggesting goal-directed behavior. On the other hand, this manipulation had no effect in omission trials, where mice had to withhold responses to obtain rewards. Finally, we utilized fast-scan cyclic voltammetry to investigate how patch activation modifies evoked striatal dopamine release and found that optogenetic activation of patch projections to the substantia nigra pars compacta (SNc) is sufficient to suppress dopamine release in the dorsal striatum. Overall, this work provides novel insight into the role of the patch compartment in habit formation, and provides a potential mechanism for how patches modify habitual behavior by exerting control over dopamine signaling. 

The purpose of this study was to investigate fourth-grade students’ sensemaking of a word problem. Sensemaking occurs when students connect their understanding of a situation with existing knowledge. We investigated students’ sensemaking about a word problem by comparing students’ strategy use. Inductive analysis was used to find themes about student sensemaking. Students exhibited one of three levels of sensemaking. Some problem-solving strategies, as a result of students’ sensemaking, led to a greater frequency of correct results.