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Tracing students' growing understanding of rational numbers

Descriptive

TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Tracing students' growing understanding of rational numbers
Identifier
ETD_2320
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052898
Language
LanguageTerm (authority = ISO639-2); (type = code)
English
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics Education
Subject (ID = SBJ-2); (authority = ETD-LCSH)
Topic
Mathematics--Study and teaching
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Numbers, Rational
Subject (ID = SBJ-4); (authority = ETD-LCSH)
Topic
Fractions
Subject (ID = SBJ-5); (authority = ETD-LCSH)
Topic
Learning--Mathematical models
Abstract
This research, a component of a year long National Science Foundation funded study, traces and documents how rational number ideas are built by students as they move from placing fractions on a line segment (finite concept) to placing fractions on an infinite number line (infinite concept). The evidence is supported by representations used by students to express their ideas, explanations given by students and student justifications about their reasoning. The study was guided by the following research questions: 1. What evidence, if any, is there of the students' understanding of the idea of fraction as number? 2. How do students extend their understanding of fraction ideas to rational numbers? 3. What representations do students use to express their fraction ideas and extend these ideas to rational numbers? The subjects consisted of a heterogeneous class of twenty-five, fourth grade (nine and early ten year old) students. Digitized videos, transcripts, student work, observation notes, and student overhead transparencies comprised the data from extended classroom sessions, videotaped with three cameras. The study gives evidence that the students built understanding of fraction ideas such as equivalence and extended these ideas to negative fractions and improper fractions. It also showed that students successfully ordered fractions on line segments, then number lines, after working out distinctions between operator and number ideas. Student ideas revealed in these sessions showed that they were comfortable and successful with basic fraction operations. Lively classroom discussions and arguments worked out obstacles in the placement of fractions on a number line. Engagement in discussions about fraction ideas and negative fractions extended to rational numbers to include improper fractions as students identified equivalent number names for fractions. In the active student-centered environment the students worked together on tasks and shared their personal representations of rational number ideas and density of the rationals. This study provides detailed evidence that students can build understanding of fraction as number and successfully make connections to extend their understanding of number, generating and interest and understanding of fraction ideas that generally are not made accessible to students of this age.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
1 v. (various pagings) : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note
Supplementary File: Dissertation Body
Note
Supplementary File: Dissertation Appendix A
Note
Supplementary File: Dissertation Appendix B
Note
Supplementary File: Dissertation Appendix C
Note
Supplementary File: Dissertation Appendix D
Note (type = degree)
Ed.D.
Note
Includes abstract
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Suzanna E. Schmeelk
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Schmeelk
NamePart (type = given)
Suzanna E.
NamePart (type = date)
1979-
Role
RoleTerm (authority = RULIB)
author
DisplayForm
Suzanna Schmeelk
Name (ID = NAME-2); (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn A.
Role
RoleTerm (authority = RULIB)
chair
Affiliation
Advisory Committee
DisplayForm
Carolyn A. Maher
Name (ID = NAME-3); (type = personal)
NamePart (type = family)
Alston
NamePart (type = given)
Alice
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
Advisory Committee
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Alice Alston
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Powell
NamePart (type = given)
Arthur B
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
Advisory Committee
DisplayForm
Arthur B Powell
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Steencken
NamePart (type = given)
Elena P
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
Advisory Committee
DisplayForm
Elena P Steencken
Name (ID = NAME-6); (type = personal)
NamePart (type = family)
Gjone
NamePart (type = given)
Gunnar
Role
RoleTerm (authority = RULIB)
outside member
Affiliation
Advisory Committee
DisplayForm
Gunnar Gjone
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School of Education
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (qualifier = exact)
2010
DateOther (qualifier = exact); (type = degree)
2010-01
Place
PlaceTerm (type = code)
xx
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
Graduate School of Education Electronic Theses and Dissertations
Identifier (type = local)
rucore10001500001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3W66KVR
Genre (authority = ExL-Esploro)
ETD doctoral
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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
Schmeelk
GivenName
Suzanna
Role
Copyright Holder
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
DateTime
2009-12-20 20:13:03
AssociatedEntity (ID = AE-1); (AUTHORITY = rulib)
Role
Copyright holder
Name
Suzanna Schmeelk
Affiliation
Rutgers University. Graduate School of Education
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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