# Some students interpret the box as representing the

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Some students interpret the box as representing the “majority” of the data although it contains only 50%. The quantiles of the box plot are used for quantile by quantile comparisons but students do not understand why only this quantile selection. The quantile comparison of distributions was introduced by Galton and we consider this use as different from the use intended in EDA. Other students can see the varying data density in a box plot and can relate this to the different density representation in a histogram. It seems however to be difficult to see the box plot as a center ± spread display at the same time. Generally, group comparisons need much more conceptual underpinnings than usual courses seem to offer (including our own). Different uses and interpretations of box plots have to be developed with adequate contexts. The presentation showed some tasks and data sets we used in order to achieve this goal. One of the formats was to ask the students to sketch the distribution in group 2 when a graph of the distribution in group 1 was given. This task opened an instructive window on students’ thinking in terms of distributions and the interplay between representation and contextual knowledge. ROLF BIEHLER Universität Kassel FB17-Mathematik/Informatik Hienrich-Plett-Str. 40, 34132 Kassel Germany
42 12. STATISTICAL REASONING USED BY ELEMENTARY AND MIDDLE SCHOOL STUDENTS WHEN THEY ANALYZE AND INTERPRET DATA GRAHAM A. JONES, CAROL A. THORNTON, CYNTHIA W. LANGRALL, EDWARD MOONEY (1) , BOB PERRY (2) and IAN PUTT (3) (1) Illinois State University, USA (2) University of Western Sydney, Australia (3) James Cook University, Australia The session focused on elementary and middle school students’ statistical reasoning when they faced tasks that engage them in analysis and interpretation. Analysis and interpretation incorporates recognizing patterns, trends, and exceptions in the data and making inferences and predictions from the data. It includes what Curcio (1987) refers to as reading the data , reading between the data , and reading beyond the dat a. Hence, when observing students analyzing and interpreting data, we were interested in the following processes: (a) how they extracted and described information explicitly stated in the data (reading the data), (b) how they compared and combined data (reading beyond the data), and (c) how they made predictions from the data (reading beyond the data). Consistent with these processes, we generated clusters of tasks like the following to assess children’s statistical reasoning when they analyzed and interpreted data: (a) What does the picture tell you? (describe the data) (b) Which day had the lowest number of visitors? (compare) (c) How many friends came to visit during the week? (combine) (d) About how many friends would you expect to visit during the next 4-week month? (predict).

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