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ERIC Number: ED532691
Record Type: Non-Journal
Publication Date: 2009
Pages: 89
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1095-2700-1
ISSN: N/A
The Role of Structure in Learning Non-Euclidean Geometry
Asmuth, Jennifer A.
ProQuest LLC, Ph.D. Dissertation, Northwestern University
How do people learn novel mathematical information that contradicts prior knowledge? The focus of this thesis is the role of structure in the acquisition of knowledge about hyperbolic geometry, a non-Euclidean geometry. In a series of three experiments, I contrast a more holistic structure--training based on closed figures--with a mathematically equivalent elemental structure. Study 1 shows that differences in relational structure lead to differences in generalization to the geometry as a whole. Study 2 explores whether type of relational structure affects resistance to interference from conflicting geometry information. Study 3 demonstrates that making relevant training information more salient improves the performance of line-trained participants. Protocols provide insight into participant reasoning and are drawn upon in interpreting the results. Taken together, these studies suggest that the structure by which novel, unintuitive information is conveyed plays a central role in facilitating generalization of that knowledge. [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.]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A