Pictorial models in math4/20/2023 ![]() 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. 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.Ī pictorial chart is based on a similarity transformation. 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. Material of the National Assessment of Educational Progress is public domain.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. Explain why” ( National Assessment of Educational Progress NAEP, 1992). Stimulus for a standardized test item in a task: “The picture above is misleading. Do individuals base their interpretation on the real-life volume of the garbage can? Do they consider the covered area on the paper? Or do they only compare the height of the garbage cans? ![]() To evaluate whether a pictorial chart is misleading, it is worth knowing how people interpret this form of data visualization. Consequently, standardized testing includes the evaluation of pictorial charts (cf. Therefore, various countries’ curricula and standards in mathematics require students to have the ability to judge statistical data visualizations and to be able to identify misleading data displays (e.g., National Council of Teachers of Mathematics, 2000). However, graphical features can create a distorting visual impression and mislead the reader. Reprinted with permission (Grenzwert Euro: threshold value Euro norm, realer Ausstoβ: actual emission).Īn appealing graphical design for a chart can make data more accessible. ![]() Copyright 2017 by Allgemeiner Deutscher Automobil-Club. Pictorial chart of the nitrogen oxide emission of cars in a German magazine ( Allgemeiner Deutscher Automobil-Club, 2017, p. 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. 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.
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