Dissertation/Thesis Abstract

Investigating conceptual, procedural, and intuitive aspects of area measurement with non-square area units
by Miller, Amanda L., Ph.D., Illinois State University, 2013, 267; 3572989
Abstract (Summary)

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.

Indexing (document details)
Advisor: Barrett, Jeffrey
Commitee: Critchfield, Thomas, El-Zanati, Saad, Ellerton, Nerida, Tobias, Jennifer
School: Illinois State University
Department: Mathematics
School Location: United States -- Illinois
Source: DAI-A 74/12(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics education, Developmental psychology
Keywords: Area measurement, Drawing development, Intuition, Jigsaw puzzles, Piaget, Jean, Spatial structuring
Publication Number: 3572989
ISBN: 9781303420184
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