This study investigated fourteen Grade 4 teachers' understandings of graphical representations of categorical data. The study examined what the teachers knew about: (a) categorical data and graphical representations of categorical data, (b) their students' knowledge of graphical representations of categorical data, and (c) how to work in class with student errors and misunderstandings. A list of common errors was developed from a review of the literature and used to create written assessments for students and teachers. Teachers completed the Categorical Data Graph Knowledge instrument, Curriculum Implementation Survey , and participated in an interview. Interviews probed the understanding teachers had of student errors and instructional strategies to assist student learning.
The group of teachers revealed some basic knowledge of graphical representations of categorical data. These teachers could: (a) name common types of graphs, (b) name components of graphs, (c) identify title and labels on all graphs, (d) understand horizontal and vertical bar graphs, and (e) compare bar graphs and circle graphs. The teachers were also successful in identifying many errors the students made. Issues uncovered that are of primary interest to teachers and teacher educators include: (a) confusion between histograms and bar graphs; (b) interpretation of data within context; (c) putting labels for the frequency in the spaces, not at the end of line; (d) use of a template, or bars in a bar graph touching; (e) keeping a category with a zero value and how to explain a zero category value; and (f) creating the scale. The difficulty revealed in this study regarding the teachers' knowledge was not that the teachers couldn't make a bar graph, but that these teachers did not have a depth of understanding of graphical representations of categorical data, which is needed to assist students.
University of Minnesota Ph.D. dissertation. December 2007. Major: Education, Curriculum and Instruction. Advisors: Cramer, Kathleen A., Garfield, Joan B. 1 computer file (PDF); xi, 253 pages.
Tiefenbruck, Brenda Fay.
Elementary teachers conceptions of graphical representations of categorical data.
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