NotesFAQContact Us
Search Tips
ERIC Number: ED555346
Record Type: Non-Journal
Publication Date: 2013
Pages: 284
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-3034-2018-4
Investigating Conceptual, Procedural, and Intuitive Aspects of Area Measurement with Non-Square Area Units
Miller, Amanda L.
ProQuest LLC, Ph.D. Dissertation, Illinois State University
This dissertation reports the results of a qualitative research project on area measurement. The study utilized structured, task-based interviews with students to (a) investigate the ways students enumerate and structure two-dimensional space with a variety of area units; (b) identify conceptual, procedural, and intuitive aspects of area measurement; and (c) compare and contrast the ways students resolve square unit area tasks with the ways they resolve non-square unit area tasks. The major design was that of a cross-sectional study, with students from four different grade groups: Grades 1, 3, 5, and 7 (ages 7, 9, 11, and 13). In each grade group, five students were selected from two classes per grade within a Midwestern, suburban, public school, providing a total of 20 participants. Participant selection was based on a seven item initial survey, verbal for first graders and written for third, fifth, and seventh graders. Ten tasks were posed within two one-on-one interviews. For each interview task, a student was presented with a rectilinear region and a rectilinear unit. Dimensions were displayed in a variety of ways (e.g., tick marks, dots, grids). The student was then asked to operate on conceptual, figural, and physical area units. All interviews were video recorded and transcribed. A constant comparative method (Merriam, 1998) was used to develop codes regarding covering, enumerating, subdividing, and spatial structuring schemes through an iterative process. These codes were then compared per student, per task, and per unit type. By comparing the development of covering, enumerating, subdividing, and spatial structuring schemes across tier groups, I observed four distinct strategies used across tasks, regardless of unit type and dimension display type. This then led to the identification of levels of sophistication in the ways students operated on physical, figural, and conceptual area units, regardless of unit shape. The results presented here not only extend the existing literature on the ways students resolve area measurement tasks with non-standard area units, but also link area measurement developmental progressions to drawing development research. Implications for instruction and research are discussed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site:
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Elementary Secondary Education; Grade 1; Elementary Education; Grade 3; Grade 5; Intermediate Grades; Middle Schools; Grade 7; Junior High Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A