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Tracing the building of Robert's connections in mathematical problem solving
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
Tracing the building of Robert's connections in mathematical problem solving
SubTitle
a sixteen-year study
Identifier
ETD_3005
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000057500
Language
LanguageTerm
(authority = ISO639-2);
(type = code)
eng
Genre
(authority = marcgt)
theses
Subject
(ID = SBJ-1);
(authority = RUETD)
Topic
Education
Subject
(ID = SBJ-2);
(authority = ETD-LCSH)
Topic
Mathematics--Research--Longitudinal studies
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
Problem solving in children--Problems, exercises, etc. --Case studies
Subject
(ID = SBJ-4);
(authority = ETD-LCSH)
Topic
Combinatory logic
Subject
(ID = SBJ-5);
(authority = ETD-LCSH)
Topic
Isomorphisms (Mathematics)
Abstract
(type = abstract)
This research analyzes how external representations created by a student, Robert, helped him in building mathematical understanding over a sixteen-year period. Robert (also known as Bobby), was an original participant of the Rutgers longitudinal study where students were encouraged to work on problem-solving tasks with minimum intervention (Maher, 2005). The research demonstrates how Robert built robust counting techniques by tracing the evolvement of his problem-solving heuristics, strategies, justifications and external representations. The study also examines how Robert made connections to his earlier problem solving. In addition, the origins of Robert’s ideas related to Pascal’s Triangle and Pascal’s Pyramid are investigated. Fifteen sessions were selected between Robert’s fifth grade (February 26, 1993) and post-graduate interviews (March 27, 2009) yielding more than twenty hours of video data. Powell, Francisco, and Maher (2003) model was used for analysis where by each session was viewed, transcribed and coded for critical events to create a comprehensive narrative. The study reveals that mature combinatorial techniques were a part of Robert’s counting strategies as early as middle school. Robert used binary notation to count two-colored candle arrangements and later to count the number of ways a team could win a World Series; modified exponential formulae to account for combinations for a garage door opener, arrangements for n-colored candles and n-toppings pizzas; discovered the combinations formula, C(n, 2), in his eleventh grade; and connected these solutions to Pascal’s identities. In general, Robert looked for patterns in his solutions; generalized the findings; and identified structural similarities in tasks presented to him as he connected three-position garage door opener to three-colored candles arrangements, pizza with four toppings to towers four high, and directions on Pascal’s Triangle to routes for a taxi on a two-dimensional grid. External representations created by Robert served as communication tools for him and provided insight into his problem solving heuristics and mathematical understanding. The research contributes to the growing body of case studies from Rutgers longitudinal study providing evidence that building of early mathematical ideas is the foundation of more advanced learning (Davis & Maher, 1997).
PhysicalDescription
Form
(authority = gmd)
electronic resource
Extent
xv, 609 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Anoop Ahluwalia
Name
(ID = NAME-1);
(type = personal)
NamePart
(type = family)
Ahluwalia
NamePart
(type = given)
Anoop
NamePart
(type = date)
1977-
Role
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author
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Anoop Ahluwalia
Name
(ID = NAME-2);
(type = personal)
NamePart
(type = family)
Maher
NamePart
(type = given)
Carolyn A.
Role
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chair
Affiliation
Advisory Committee
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Carolyn A. Maher
Name
(ID = NAME-3);
(type = personal)
NamePart
(type = family)
Goldin
NamePart
(type = given)
Gerald A.
Role
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(authority = RULIB)
internal member
Affiliation
Advisory Committee
DisplayForm
Gerald A. Goldin
Name
(ID = NAME-4);
(type = personal)
NamePart
(type = family)
Schorr
NamePart
(type = given)
Roberta G.
Role
RoleTerm
(authority = RULIB)
internal member
Affiliation
Advisory Committee
DisplayForm
Roberta G. Schorr
Name
(ID = NAME-5);
(type = personal)
NamePart
(type = family)
Uptegrove
NamePart
(type = given)
Elizabeth B.
Role
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(authority = RULIB)
outside member
Affiliation
Advisory Committee
DisplayForm
Elizabeth B. Uptegrove
Name
(ID = NAME-1);
(type = corporate)
NamePart
Rutgers University
Role
RoleTerm
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degree grantor
Name
(ID = NAME-2);
(type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm
(authority = RULIB)
school
OriginInfo
DateCreated
(qualifier = exact)
2011
DateOther
(qualifier = exact);
(type = degree)
2011-01
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 - New Brunswick Electronic Theses and Dissertations
Identifier
(type = local)
rucore19991600001
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3NP243N
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
Ahluwalia
GivenName
Anoop
Role
Copyright Holder
RightsEvent
(ID = RE-1);
(AUTHORITY = rulib)
Type
Permission or license
DateTime
2010-10-22 09:32:47
AssociatedEntity
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(AUTHORITY = rulib)
Role
Copyright holder
Name
Anoop Ahluwalia
Affiliation
Rutgers University. Graduate School - New Brunswick
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(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
MimeType
(TYPE = file)
application/pdf
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application/x-tar
FileSize
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4188160
Checksum
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