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ERIC Number: ED559942
Record Type: Non-Journal
Publication Date: 2013
Pages: 332
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-3033-3459-7
Students' Reasoning about Invariance of Volume as a Quantity
Kara, Melike
ProQuest LLC, Ph.D. Dissertation, Illinois State University
The aims of this study were to investigate how upper-elementary-grade students compare the volume of rectangular prisms of equal volume (specifically, students' noticing and reasoning for invariance of volume and coordination of the three linear dimensions of rectangular prisms) and how students' levels of sophistication in volume measurement relate to their comparisons of volume of rectangular prisms with equal volumes. A qualitative research methodology was used in conducting the study. The study was designed in an exploratory nature and cross-sectional data were collected from participants at two different age groups: Grades 4 and 6 (ages 10 to 12). In each grade group, seven students were selected from two classes per grade within a Midwestern, suburban, public school, providing a total of 14 participants. Structured task-based clinical interviews (Goldin, 2000) were conducted. The interview tasks required participants to compare 3-dimensional objects (i.e. rectangular prisms or containers) by various aspects of volume. The tasks, which involved the pairs of objects with equal or nearly equal volume, were prepared to explore students' reasoning about volume invariance. The tasks, which involved the pairs of objects, which had overtly different volume, were prepared to explore students' reasoning in volume measurement as well as to place their reasoning into the levels of learning trajectory for volume measurement (Sarama & Clements, 2009). All interviews were videotaped and transcribed. A constant comparative method (Merriam, 1998) was used to develop codes regarding students' strategies and correctness for exploring volume invariance tasks. The frequency of each strategy and correctness for each task were determined per task, per aspect of volume, per grade level. Students' responses to learning trajectory placement tasks were analyzed according to the levels of sophistication stated in the learning trajectory for volume measurement. According to the results, while reasoning in volume invariance tasks, three main categories, highly effective, effective, and ineffective, were observed in students' strategies in volume invariance tasks. Students exhibiting specific levels of the learning trajectory also applied similar strategies for the volume invariance tasks. These patterns suggest additions to the existing learning trajectory for volume measurement developed by Sarama and Clements (2009). The findings of the study contributed to the literature about upper elementary grade students' reasoning about volume invariance for rectangular prisms of equal volume and its relationship with their levels of sophistication in volume measurement. 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:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Elementary Education; Grade 4; Intermediate Grades; Grade 6; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A