Many students persistently misinterpret histograms. This calls for closer inspection of students’ strategies when interpreting histograms and case-value plots (which look similar but are diferent). Using students’ gaze data, we ask: How and how well do upper secondary pre-university school students estimate and compare arithmetic means of histograms and case-value plots? We designed four item types: two requiring mean estimation and two requiring means comparison. Analysis of gaze data of 50 students (15–19 years old) solving these items was triangulated with data from cued recall. We found five strategies. Two hypothesized most common strategies for estimating means were confirmed: a strategy associated with horizontal gazes and a strategy associated with vertical gazes. A third, new, count-and-compute strategy was found. Two more strategies emerged for comparing means that take specific features of the distribution into account. In about half of the histogram tasks, students used correct strategies. Surprisingly, when comparing two case-value plots, some students used distribution features that are only relevant for histograms, such as symmetry. As several incorrect strategies related to how and where the data and the distribution of these data are depicted in histograms, future interventions should aim at supporting students in understanding these concepts in histograms. A methodological advantage of eye-tracking data collection is that it reveals more details about students’ problem-solving processes than thinking-aloud protocols. We speculate that spatial gaze data can be re-used to substantiate ideas about the sensorimotor origin of learning mathematics.
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Airports represent the major bottleneck in the air traffic management system with increasing traffic density. Enhanced levels of automation and coordination of surface operations are imperative to reduce congestion and to improve efficiency. This paper addresses the problem of comparing different control strategies on the airport surface to investigate their impacts and benefits. We propose an optimization approach to solve in a unified manner the coordinated surface operations problem on network models of an actual hub airport. Controlled pushback time, taxi reroutes and controlled holding time (waiting time at runway threshold for departures and time spent in runway crossing queues for arrivals) are considered as decisions to optimize the ground movement problem. Three major aspects are discussed:1) benefits of incorporating taxi reroutes on the airport performance metrics; 2) priority of arrivals and departures in runway crossings; 3) tradeoffs between controlled pushback and controlled holding time for departures. A preliminary study case is conducted in a model based on operations of Paris Charles De-Gaulle airport under the most frequently used configuration. Airport is modeled using a node-link network structure. Alternate taxi routes are constructed based on surface surveillance records with respect to current procedural factors. A representative peak-hour traffic scenario is generated using historical data. The effectiveness of the proposed optimization methods is investigated.
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