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ERIC Number: ED519702
Record Type: Non-Journal
Publication Date: 2010
Pages: 506
Abstractor: As Provided
Reference Count: N/A
ISBN: ISBN-978-1-1242-7556-7
ISSN: N/A
A Comparison of Middle School Students' Mathematical Arguments in Technological and Non-Technological Environments
Smith, Ryan Cummings
ProQuest LLC, Ph.D. Dissertation, North Carolina State University
Prior research on students' uses of technology has suggested it can be used to support students' development of formal justifications and proofs. The ways in which these technologies influence the construction of arguments and proofs remain uncertain. Furthermore, research has not been conducted that compares the arguments students develop while working in a technological environment to those created by students working in a non-technological environment. This study characterized and compared the arguments eighth grade mathematics students created while working in technological and non-technological environments as the students worked through a unit in which they investigated and developed definitions, properties, theorems, and classification systems related to triangles. A teaching experiment methodology was utilized with two eighth grade mathematics classes in an urban middle school in the southeast United States. For one class, technology played an integral role using a dynamic geometry environment, Geometer's Sketchpad (Jackiw, 2001) to explore and investigate geometric concepts. For the other class, the students used non-technological mathematical tools such as snap-cubes, rulers, and protractors. The arguments created by three pairs of students in each class were documented, analyzed, and compared. Toulmin's (1958) argumentation model was used to analyze the content and structure of the arguments, including the ways in which the students used the tools (technological and non-technological). Findings from this study indicate that students in the technology class created more arguments than their counterparts in the non-technology class, which may be related to the dynamic abilities of the tools rather than merely the use of the technology. In addition, students in both classes were less likely to make their reasoning explicit when using tools, technological or non-technological, which may be related to the task on which the students were working. When students were working on generalization or conjecturing tasks, the students were rarely actively using the tools and the warrants tended to be explicit. However, when the students were prompted to make their reasoning explicit while using the technology, the students obliged. The results from this study suggest that teachers need to design tasks and activities that utilize tools with dynamic abilities, capitalize on the dynamic affordance of the tools, and ask students to make their reasoning explicit when using these tools. [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: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Grade 8; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A