Some students interpret the box as representing the

  • No School
  • AA 1
  • 72

This preview shows page 43 - 45 out of 72 pages.

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
Image of page 43
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 [email protected], [email protected], [email protected], [email protected] (2) University of Western Sydney, Australia [email protected] (3) James Cook University, Australia [email protected] 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).
Image of page 44
Image of page 45

You've reached the end of your free preview.

Want to read all 72 pages?

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors