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A case study
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
A case study
SubTitle
the development of Stephanie's algebraic reasoning
Identifier
ETD_3064
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Language
LanguageTerm
(authority = ISO639-2);
(type = code)
eng
Genre
(authority = marcgt)
theses
Subject
(ID = SBJ-1);
(authority = RUETD)
Topic
Mathematics Education
Subject
(ID = SBJ-2);
(authority = ETD-LCSH)
Topic
Algebra--Study and teaching (Middle school)--United States--Case studies
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
Algebra--Study and teaching (Middle school)--United States--Longitudinal studies
Abstract
(type = abstract)
This research provides an analysis of the mathematical growth and development of one student, Stephanie, as she worked on early algebra tasks during her eighth-grade year as part of a teaching experiment. Stephanie was among the original participants in a longitudinal study which investigated how students develop mathematical ideas under conditions that fostered independent exploration, reasoning, and justification of ideas (Maher, 2005). A qualitative approach based on the analytical model described by Powell, Francisco, and Maher (2003), was taken in analyzing videotape data from the Robert B. Davis Institute of Learning archive, along with student work. Seven task-based interview sessions were analyzed, spanning a six month period, beginning from November 8, 1995 to April 17, 1996. The research focused on Stephanie’s algebraic reasoning; in particular, how she built an understanding of the binomial theorem and related it to Pascal’s triangle. Stephanie’s representations, her explanations and justifications, and her methods of dealing with obstacles to understanding, were all examined and provided the basis for this research. The analysis shows that Stephanie built her mathematical understanding through the development of multiple representations of concepts and moved fluidly between and among the representations that she organized into ‘symbolic’ and ‘visual’ representations. Symbolic representations included algebraic expressions, combinatorics notation, and Pascal’s triangle while visual representations included drawings, tables, models formed by algebra blocks and other manipulatives, and towers built with unifix cubes. Furthermore, through Stephanie’s explanations and justification of her representations and reasoning in general, she invented strategies to convince herself as well as the researchers that she had fulfilled the requirements of the problem task. When dealing with obstacles to her understanding such as lack of information, or calculating obstacles, Stephanie acquired the use of several heuristic methods in order to overcome them. These included the use of substituting in numbers in order to test a conjecture; returning to basic meaning; drawing diagrams; building models; and considering a simpler problem. Throughout the task-based interviews, Stephanie retrieved knowledge from her earlier problem solving and extended this knowledge to build new ideas, while tackling more challenging problems. In particular, Stephanie mapped the coefficients in the binomial expansion to particular rows in Pascal’s Triangle; she connected these ideas to her problem solving from earlier work in the elementary grades. The findings are relevant to the timing and method of early algebraic instruction in schools.
PhysicalDescription
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electronic resource
Extent
xiii, 558 p. : ill.
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application/pdf
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text/xml
Note
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Ed.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Eman Y. Aboelnaga
Name
(ID = NAME-1);
(type = personal)
NamePart
(type = family)
Aboelnaga
NamePart
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Eman Y. (Eman Yousry)
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1973-
Role
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author
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Eman Aboelnaga
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Maher
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Carolyn A.
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chair
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Advisory Committee
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Carolyn A. Maher
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Alston
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Alice S.
Role
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internal member
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Advisory Committee
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Alice S. Alston
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Uptegrove
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Elizabeth B.
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outside member
Affiliation
Advisory Committee
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Elizabeth B. Uptegrove
Name
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NamePart
Rutgers University
Role
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degree grantor
Name
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NamePart
Graduate School of Education
Role
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school
OriginInfo
DateCreated
(qualifier = exact)
2011
DateOther
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(type = degree)
2011-01
Place
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(type = code)
xx
RelatedItem
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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
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rucore10001500001
Location
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T33R0SKR
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
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(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
Aboelnaga
GivenName
Eman
Role
Copyright Holder
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(ID = RE-1);
(AUTHORITY = rulib)
Type
Permission or license
DateTime
2010-12-21 09:36:56
AssociatedEntity
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Role
Copyright holder
Name
Eman Aboelnaga
Affiliation
Rutgers University. Graduate School of Education
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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.
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Technical
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ETD
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(TYPE = file)
application/pdf
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application/x-tar
FileSize
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3205120
Checksum
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