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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Educational innovations often tend to fail, mainly because teachers and school principals do not feel involved or are not allowed to have a say. Angela de Jong's dissertation shows the importance of school principals and teachers leading 'collaborative innovation' together. Collaborative innovation requires a collaborative, distributed approach involving both horizontal and vertical working relationships in a school. Her research shows that teams with more distributed leadership have a more collaborative 'spirit' to improve education. Team members move beyond formal (leadership) roles, and work more collectively on school-wide educational improvement from intrinsic motivation. De Jong further shows that school principals seek a balance in steering and providing space. She distinguished three leadership patterns: Team Player, Key Player, Facilitator. Team players in particular are important for more collaborative innovation in a school. They balance between providing professional space to teachers (who look beyond their own classroom) and steering for strategy, frameworks, boundaries, and vision. This research took place in schools working with the program of Foundation leerKRACHT, a program implemented by more than a thousand schools (primary, secondary, and vocational education). The study recommends, towards school principals and teachers, and also towards trainers, policymakers, and school board members, to reflect more explicitly on their roles in collaborative innovation and talk about those roles.
In Sicht von oben, ‘Powers of Ten’ und Bildpolitiken der Vertikalität (Spector Books, Leipzig, 2022) German media theorist and curator Vera Tollmann analyses the power aspects of the technical view from above. The context here is not so much the first manned flight with a balloon in 1783 in Paris but the iconic 1968/77 short film Powers of Ten by Charles and Ray Eames, which can be considered the first virtual camera trip. Her study can be seen as material image analysis along the lines of Friedrich Kittler’s optical media and is strongly informed by the work of Hito Steyerl. Part one deals with the verticality of the image regime, while part two focuses on the vertical aspect and part three theorizes scale and scalability.
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