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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
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
DisplayForm
Alice Alston
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Powell
NamePart (type = given)
Arthur B
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
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
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
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
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.
Status
Availability
Status
Open
Reason
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Schmeelk
GivenName
Suzanna
Role
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
DateTime
2009-12-20 20:13:03
AssociatedEntity (ID = AE-1); (AUTHORITY = rulib)
Role
Name
Suzanna Schmeelk
Affiliation
Rutgers University. Graduate School of Education
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Type