![]() ![]() In Figure 2, one could argue that the garbage cans are just replacing the bars of a bar chart to make the chart more appealing to the reader. ![]() There is also a third manner in which people could interpret the pictorial chart. Generally speaking, the area of a shape quadruples if the shape’s length and width are doubled, due to a quadratic relationship between the scale factor and the area. If readers perceptually evaluate pictures based on the area covered by ink, the garbage can of 1980 extends over four times as much area as the garbage can of 1960. While the mathematics of volume is clear, this might not be the way people interpret the pictures of the garbage cans. In other words, the relationship between the scale factor and the volume is cubic. If the length, width, and height of a three-dimensional object are doubled, the volume increases eightfold. The expected answer was based on mathematical considerations concerning the displayed objects’ volume in the real world. The students had to explain why the chart was misleading. This item ( National Assessment of Educational Progress NAEP, 1992) represents two quantities (the number of tons of trash produced in the United States in the years 19) using two perspective drawings of a garbage can. Therefore, one can try to generate assumptions about how people interpret pictorial charts by exemplarily analyzing an item ( Figure 2) from a standardized test of the National Assessment of Educational Progress (NAEP). For pictorial charts, Tufte’s claim raises the question of how people interpret visual representations and whether people’s interpretation is consistent with the intended numerical representation. Tufte (2001) pointed out that in data visualization, the visual representation should be consistent with the numerical representation. A graphic designer uniformly scales a picture A by a factor to generate a mathematically similar picture B. Theoretical BackgroundĪ pictorial chart is based on a similarity transformation. Furthermore, it is argued that given the increasing variety and importance of data visualization in public life, mathematics education should pay more attention to popular or novel forms of data visualizations. Finally, in the “Discussion” section, the paper tries to explain the different research results by suggesting that whether people have to assess pictures analytically or perceptually might have a substantial effect. Subsequently, the paper presents an empirical study investigating how students interpret pictorially displayed quantities in pictorial charts. It may be that the routines for the interpretation of pictures differ considerably depending on whether a person must calculate a quantity arithmetically or is prompted to estimate the quantity based on visual perception.įirst, this brief research report reflects from a theoretical perspective upon how people interpret pictorial charts and reviews empirical results from mathematics education and psychology that could substantiate different assumptions. This result deviates from research that found an overgeneralization of linearity when students compare the areas of two mathematically similar shapes. The experiment showed that, on average, a model assuming a quadratic relationship fitted best. Instead, it was analyzed which functional relationship between scale factor and estimated quantity best described people’s interpretation of pictorial charts. Therefore, the students’ answers were not rated as correct or incorrect. The study aimed to evaluate how individuals perceive the quantities in the pictorial charts intuitively. In the present study, 63 university students answered a 12-item questionnaire containing three different pictorial charts. They represent different quantities with differently scaled pictures. Pictorial charts are a popular form of data visualization in media. This brief research report presents an experiment investigating how people interpret quantities displayed in pictorial charts. IPN – Leibniz Institute for Science and Mathematics Education, Kiel, Germany. ![]()
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