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The development of mathematical reasoning in elementary school students' exploration of fraction ideas

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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
LanguageTerm (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.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
850 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note
Includes abstract
Note
Also available on CD
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Dina Yankelewitz
Note (type = degree)
Ed.D.
Name (type = personal)
NamePart (type = family)
Yankelewitz
NamePart (type = given)
Dina
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn A.
Role
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chair
Affiliation
Advisory Committee
DisplayForm
Carolyn A. Maher
Name (type = personal)
NamePart (type = family)
Steencken
NamePart (type = given)
Elena P
Role
RoleTerm (authority = RULIB)
internal member
DisplayForm
Elena P. Steencken
Name (type = personal)
NamePart (type = family)
Weber
NamePart (type = given)
Keith
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
Advisory Committee
DisplayForm
Keith Weber
Name (type = personal)
NamePart (type = family)
Mueller
NamePart (type = given)
Mary
Role
RoleTerm (authority = RULIB)
internal member
DisplayForm
Mary Mueller
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
Degree grantor
Name (type = corporate)
NamePart
Graduate School of Education
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009
Place
PlaceTerm (type = code)
xx
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Thesis and Dissertations
Identifier
etd
RelatedItem (type = host)
TitleInfo
Title
Graduate School of Education New Brunswick Electronic Theses and Dissertations
Identifier
rucore
RelatedItem (type = host)
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

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Yankelewitz
GivenName
Dina
Role
Copyright holder
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
DateTime
2010-09-26
AssociatedEntity (ID = AE-1); (AUTHORITY = rulib)
Role
Copyright holder
Name
Dina Yankelewitz
Affiliation
Rutgers University Graduate School -- New Brunswick
AssociatedObject (ID = AO-1); (AUTHORITY = rulib)
Type
License
Name
Author Agreement License
Detail
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

ContentModel
ETD
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
4710400
Checksum (METHOD = SHA1)
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