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To infinity and beyond

Descriptive

TypeOfResource
Text
TitleInfo
Title
To infinity and beyond
SubTitle
toward a local instruction theory for completed infinite iteration
Identifier
ETD_2077
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051893
Identifier (type = doi)
doi:10.7282/T3Z038BQ
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Genre (authority = marcgt)
theses
Subject (authority = RUETD)
Topic
Mathematics Education
Subject (authority = ETD-LCSH)
Topic
Infinite--Study and teaching
Subject (authority = ETD-LCSH)
Topic
Iterative methods (Mathematics)--Study and teaching
Subject (authority = ETD-LCSH)
Topic
Mathematics--Study and teaching
Abstract (type = abstract)
There is evidence that students’ and mathematicians’ images of and reasoning about concepts such as infinite unions and intersections of sets, limits, and convergent series often invoke the consideration of infinite iterative processes. Therefore, not reasoning normatively about infinite iteration may hinder students’ understanding of fundamental concepts in mathematics. Research suggests that the vast majority of college students are inclined to use non-normative reasoning when presented with tasks that challenge them to imagine an infinite iterative process as completed and define its outcome. However, there is almost no research on how students’ conceptions of completed infinite iteration can be refined in a normative direction.
Adopting a design research approach, the purpose of this thesis is to develop a local instruction theory for completed infinite iteration. This design entails multiple cycles through phases of development, implementation, and analysis. The study consisted of a sequence of two constructivist teaching experiments conducted with pairs of mathematics majors, during which the students worked collaboratively through a variety of infinite iteration tasks. Each cycle consisted of 6 or 7 sessions lasting approximately 2 hours, together with Pre-test and Post-Test sessions. The data analysis consisted of multiple phases of iterative analysis of the videotaped sessions and written work and was guided by situated learning transfer theories.
The participants in this study employed a variety of types of reasoning when solving completed infinite iteration tasks, some normative and some not. One way that the students refined their reasoning on infinite iteration was by making references to previously solved tasks (in the presence of a concern for consistent reasoning across tasks), although the refinement was not always in normative directions. The challenge that a researcher faces consists in helping students use such references to establish “anchors” in normatively solved tasks to which they can then contrast the solution paths proposed for other tasks. A variety of approaches to responding to this challenge are explored. The study culminates with the formulation of a local instruction theory for completed infinite iteration, containing among other things a sequence of instructional activities and a rationale for their appropriateness.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
xii, 476 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 469-473)
Note (type = statement of responsibility)
by Iuliana Radu
Name (type = personal)
NamePart (type = family)
Radu
NamePart (type = given)
Iuliana
NamePart (type = date)
1977-
Role
RoleTerm (authority = RULIB)
author
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Iuliana Radu
Name (type = personal)
NamePart (type = family)
Weber
NamePart (type = given)
Keith
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RoleTerm (authority = RULIB)
chair
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Advisory Committee
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Keith Weber
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn
Role
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internal member
Affiliation
Advisory Committee
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Carolyn Maher
Name (type = personal)
NamePart (type = family)
Cohen-Corwin
NamePart (type = given)
Amy
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internal member
Affiliation
Advisory Committee
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Amy Cohen-Corwin
Name (type = personal)
NamePart (type = family)
Tirosh
NamePart (type = given)
Dina
Role
RoleTerm (authority = RULIB)
outside member
Affiliation
Advisory Committee
DisplayForm
Dina Tirosh
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2009
DateOther (encoding = w3cdtf); (qualifier = exact); (type = degree)
2009-10
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 - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
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
Notice
Note
Availability
Status
Open
Reason
Permission or license
Note
RightsHolder (ID = PRH-1); (type = personal)
Name
FamilyName
Radu
GivenName
Iuliana
Role
Copyright holder
Telephone
Address
Email
ContactInformationDate
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
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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Role
Copyright holder
Name
Iuliana Radu
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

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ETD
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application/pdf
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application/x-tar
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2252800
Checksum (METHOD = SHA1)
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