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The development of mathematical reasoning in elementary school students' exploration of fraction ideas
Descriptive
TypeOfResource
Text
TitleInfo
Title
The development of mathematical reasoning in elementary school students' exploration of fraction ideas
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000054787
Identifier
etd_preRUETD
Identifier
(type = doi)
doi:10.7282/T3KW5G01
Language
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(authority = ISO 639-3:2007);
(type = text)
English
Genre
(authority = marcgt)
thesis
Genre
(authority = ExL-Esploro)
ETD doctoral
Subject
(authority = ETD-LCSH)
Topic
Mathematics--Study and teaching (Elementary)--New Jersey--Case studies
Subject
(authority = ETD-LCSH)
Topic
School children--New Jersey--Case studies
Subject
(authority = ETD-LCSH)
Topic
Critical thinking in children--New Jersey--Case studies
Subject
(authority = ETD-LCSH)
Topic
Mathematics--Research
Abstract
(type = abstract)
Reformers and educators across the U.S. and internationally have called for an increased emphasis on the learning and teaching of reasoning, justification, and proof in K-12 and post-secondary mathematics education. Numerous studies have established that students experience difficulty with these processes. Recently, however, analysis of videotape data of sixth grade student work in an informal mathematics program has identified the use of multiple forms of reasoning by middle school students. This qualitative study, drawing on data from seventeen sessions from a longitudinal study conducted by Rutgers University in a fourth grade class of twenty-five students in a suburban/rural school in New Jersey, identified and traced the development of the forms of reasoning and argumentation used by elementary school students as they were introduced to fraction as number concepts and as they used Cuisenaire® rods and other manipulative materials to make sense of number relationships.The following research questions guided this study: 1. What forms of reasoning and argumentation are elicited as students work on tasks involving the building of fraction ideas? 2. How does students’ reasoning change as they revisit tasks introduced previously in the study and as they progress in their development of mathematical understandings?
Data for the study included forty-six videotapes, students’ collected written work, and researcher field notes that were recorded during the seventeen 60-80 minute class sessions. The methodology of Francisco, Powell, and Maher (2003) was used for video data analysis. The video data was transcribed, verified, and coded for forms of reasoning, and a storyline and narrative was constructed to describe the results. Supplementary document analysis was used to verify and ensure validity of results. Analysis of the data showed that students used varied forms of reasoning and argumentation. Several tasks were flagged as supportive of the elicitation of varied forms of reasoning, and factors of those tasks and of the environment that encouraged the development of reasoning in the students were explored. The study has implications for effective strategies for the development of mathematical reasoning in the elementary school and ways that argumentation and proof can be introduced during the early school years.
Data for the study included forty-six videotapes, students’ collected written work, and researcher field notes that were recorded during the seventeen 60-80 minute class sessions. The methodology of Francisco, Powell, and Maher (2003) was used for video data analysis. The video data was transcribed, verified, and coded for forms of reasoning, and a storyline and narrative was constructed to describe the results. Supplementary document analysis was used to verify and ensure validity of results. Analysis of the data showed that students used varied forms of reasoning and argumentation. Several tasks were flagged as supportive of the elicitation of varied forms of reasoning, and factors of those tasks and of the environment that encouraged the development of reasoning in the students were explored. The study has implications for effective strategies for the development of mathematical reasoning in the elementary school and ways that argumentation and proof can be introduced during the early school years.
PhysicalDescription
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electronic resource
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850 p. : ill.
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Note
Includes abstract
Note
Also available on CD
Note
(type = bibliography)
Includes bibliographical references
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(type = statement of responsibility)
by Dina Yankelewitz
Note
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Ed.D.
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Yankelewitz
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Dina
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author
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Maher
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Carolyn A.
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chair
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Carolyn A. Maher
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Steencken
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Elena P
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Elena P. Steencken
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Weber
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Keith
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Keith Weber
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Mary
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Mary Mueller
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Rutgers University
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Graduate School of Education
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school
OriginInfo
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2009
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2009
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xx
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NjNbRU
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Title
Rutgers University Electronic Thesis and Dissertations
Identifier
etd
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TitleInfo
Title
Graduate School of Education New Brunswick Electronic Theses and Dissertations
Identifier
rucore
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TitleInfo
Title
Graduate School of Education Electronic Theses and Dissertations
Identifier
(type = local)
rucore10001500001
Subject
(authority = RUETD)
Topic
Mathematics Education
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Rights
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The author owns the copyright to this work
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsHolder
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Name
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Yankelewitz
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Dina
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Permission or license
DateTime
2010-09-26
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Dina Yankelewitz
Affiliation
Rutgers University Graduate School -- New Brunswick
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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Technical
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ETD
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application/pdf
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application/x-tar
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4710400
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