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A longitudinal case study tracing growth in mathematical understanding through the lens of the Pirie-Kieren theory

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TitleInfo
Title
A longitudinal case study tracing growth in mathematical understanding through the lens of the Pirie-Kieren theory
Name (type = personal)
NamePart (type = family)
Teehan
NamePart (type = given)
Kara
NamePart (type = date)
1993-
DisplayForm
Kara Teehan
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn
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Carolyn Maher
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Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Morrow
NamePart (type = given)
Lesley
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Lesley Morrow
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Zhang
NamePart (type = given)
Dake
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Dake Zhang
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Uptegrove
NamePart (type = given)
Elizabeth
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Elizabeth Uptegrove
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
School of Graduate Studies
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RoleTerm (authority = RULIB)
school
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Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2019
DateOther (encoding = w3cdtf); (qualifier = exact); (type = degree)
2019-05
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Abstract (type = abstract)
How mathematical ideas and ways of reasoning are built, over time, is an important aspect of the concept development for a student in his or her learning process. Using a qualitative, phenomenological approach that is backed by newly constructed video narratives (VMCAnalytics) to illustrate Stephanie’s growth in understanding over time, this study analyzes archived data from a ten-year longitudinal study to trace the growth of mathematical understanding of a participant in the longitudinal study from the lens of the Pirie-Kieren model for studying growth in mathematical understanding. Using archived video data, published VMCAnalytics, transcripts, student work, and publications, the study traces growth in mathematical understanding of one student, Stephanie, as she engages in non-routine mathematics problems in formal and informal learning environments. A learning progression was created, attentive to Stephanie’s movement in mathematical understanding through various layers of the Pirie-Kieren Model, starting from primitive knowing to formalizing, structuring, and inventising. Attention was given to following Stephanie’s folding back in tracking her growth in understanding, particularly as she makes connections and recognizes the structural relationships between and among task solutions. The VMCAnalytics created to trace Stephanie’s growth illustrate how she revisits inner layers of understanding to rebuild and extend that understanding. This study contributes to addressing gaps in the literature by focusing on Stephanie’s reasoning as she works with a partner, small group, and in whole class settings. It extends the Pirie-Kieren work by attending to Stephanie’s growth in collaborative settings. Also, analyses of response to researcher moves and interactions with others, and the influence of these on Stephanie’s growth extend earlier work using the Pirie-Kieren framework. This study demonstrates growth in and among layers of understanding though video narratives, with a learning progression showing visual evidence of mathematical growth in understanding. A major finding includes a proposal for an addendum to the Pirie-Kieren model for studying growth in mathematical understanding that encompasses collaboration’s effect on individual learners’ growth. Another finding highlights the significance of folding back on growth in mathematical understanding. A third finding indicates that interaction with researchers were instrumental in advancing Stephanie’s growth in understanding and development of mathematical ideas.
Subject (authority = local)
Topic
Growth progression
Subject (authority = RUETD)
Topic
Education
Subject (authority = LCSH)
Topic
Mathematics -- Study and teaching -- Longitudinal studies
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_9880
PhysicalDescription
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application/pdf
InternetMediaType
text/xml
Extent
1 online resource (viii, 391 pages) : illustrations
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
RelatedItem (type = host)
TitleInfo
Title
School of Graduate Studies Electronic Theses and Dissertations
Identifier (type = local)
rucore10001600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/t3-6w2c-qm85
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Teehan
GivenName
Kara
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2019-04-16 20:59:24
AssociatedEntity
Name
Kara Teehan
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
Type
License
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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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2019-04-23T01:21:34
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2019-04-23T01:21:34
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