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Fifth Graders’ Reasoning on the Enumeration of Cube-Packages in Rectangular Boxes in an Inquiry-Based Classroom

WIner, Michael Loyd
http://rave.ohiolink.edu/etdc/view?acc_num=osu1281978828

Abstract Details

2010, Master of Arts, Ohio State University, EDU Teaching and Learning.
In this study, I am taking what Cobb and Yackel (1996) called an “emergent” perspective, which is a blend of psychological and socio-cultural perspectives from the constructivist paradigm, to investigate how fifth graders construct and modify their mental models and processes for understanding volume measurement in terms of cube-package enumeration problems. In particular, this study is an extension of the Battista’s 1999 study, in which he investigated how fifth grade students predicted and enumerated the number of cubes in a rectangular box in an inquiry-based classroom. I describe the work and reasoning of two pairs of fifth grade boys as they predicted the number of cube-packages that fit into graphically represented boxes in an inquiry-based classroom. This study extends on the essential mental processes that previous research has already defined for cube enumeration problems (Battista, 1999; Battista & Clements, 1996), and describes three additional essential mental processes (locating, positioning, and orienting) that students need to do for cube-package enumeration problems. The results of this study indicate that there are three types of mental models used by the students when dealing with package problems: layer based, non-layer composite-unit based, and non-composite-unit based. Finally, I describe some of the cognitive obstacles and errors that occur when students attempt to solve cube-package problems.
Michael Battista, PhD (Advisor)
Douglas Owens, PhD (Committee Member)
196 p.
Education; Elementary Education; Mathematics Education
Student reasoning; Volume measurement; Elementary students; Visualization/spatial structuring; Mental processes.

Recommended Citations

Citations

  • WIner, M. L. (2010). Fifth Graders’ Reasoning on the Enumeration of Cube-Packages in Rectangular Boxes in an Inquiry-Based Classroom [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281978828

    APA Style (7th edition)

  • WIner, Michael. Fifth Graders’ Reasoning on the Enumeration of Cube-Packages in Rectangular Boxes in an Inquiry-Based Classroom. 2010. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1281978828.

    MLA Style (8th edition)

  • WIner, Michael. "Fifth Graders’ Reasoning on the Enumeration of Cube-Packages in Rectangular Boxes in an Inquiry-Based Classroom." Master's thesis, Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1281978828

    Chicago Manual of Style (17th edition)

osu1281978828
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© 2010, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.