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Tracing Milin's development of inductive reasoning

Descriptive

TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Tracing Milin's development of inductive reasoning
SubTitle
a case study
Identifier
ETD_2540
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052900
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
Heuristic
Subject (ID = SBJ-3); (authority = ETD-LCSH)
Topic
Reasoning in children
Subject (ID = SBJ-4); (authority = ETD-LCSH)
Topic
Induction (Mathematics)
Abstract
This study examined how Milin, a nine-year old student, justified his solutions to towers of a variety of heights over a 13 month period. Specifically, it sought to identify heuristics, strategies, and forms of reasoning and argumentation used by Milin in building and supporting his reasoning by partial cases, cases, and then an inductive argument. The research also traced how Milin's ideas traveled to other students. Videotape recordings of Milin's work on towers task and its extensions were analyzed along with his written work, written assessments and the researcher's field notes. The video data consisted of two problem-solving sessions, three individual task-based interviews, a small group assessment, and a whole class discussion. As Milin searched for and sought to justify a global solution for the towers problem, he constructed mathematical ideas by continuously evolving the heuristics and strategies employed. He started by making random towers using a "guess and check" method, where he would randomly create a tower and then compared it with existing towers to identify duplicates. He then proceeded to use local organization strategies to create pairs of towers. This included opposites by color, opposites by inverting and a hybrid strategy. Later, Milin moved towards more refined local organizations such as staircase patterns. When these schemes also proved inadequate to justify a complete solution, Milin developed a family strategy, based on a doubling pattern he had uncovered. This strategy gave him a global organization method. The progression to the global solution was an iterative process in which Milin revisited earlier strategies. Milin also used various forms of reasoning to account for all towers. These included amount of time elapsed between building towers, the concept of "partner" towers, justification by contradiction, cases, doubling rule, and the family strategy. Milin shared his inductive argument with three other students during a small group assessment session. Almost one year later, he re-explained his inductive argument to his partner, Michelle, while working on another task. In turn she shared this argument with other class mates, culminating with one student presenting it to the entire class. The students appeared to understand and retain Milin's strategy better when involved in solving the problem themselves. This case study contributes the body of research in several ways. It documents strategies used by young students to build models of reasoning and argumentation. It also provides support for Davis and Maher's idea that building understanding is not a linear process in that new ideas are built from previous ideas. Finally, this study contributes to the broader collection of case studies from the longitudinal study at Rutgers University.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
xi, 455 p. : ill.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note (type = degree)
Ed.D.
Note
Includes abstract
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Manjit Kaur Sran
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Sran
NamePart (type = given)
Manjit Kaur
NamePart (type = date)
1966-
Role
RoleTerm (authority = RULIB)
author
DisplayForm
Manjit Sran
Name (ID = NAME-2); (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn A.
Role
RoleTerm (authority = RULIB)
chair
Affiliation
Advisory Committee
DisplayForm
Carolyn A. Maher
Name (ID = NAME-3); (type = personal)
NamePart (type = family)
Alston
NamePart (type = given)
Alice S.
Role
RoleTerm (authority = RULIB)
internal member
Affiliation
Advisory Committee
DisplayForm
Alice S. Alston
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Uptegrove
NamePart (type = given)
Elizabeth B.
Role
RoleTerm (authority = RULIB)
outside member
Affiliation
Advisory Committee
DisplayForm
Elizabeth B. Uptegrove
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School of Education
Role
RoleTerm (authority = RULIB)
school
OriginInfo
DateCreated (qualifier = exact)
2010
DateOther (qualifier = exact); (type = degree)
2010-05
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/T34Q7V2G
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
Sran
GivenName
Manjit
Role
Copyright Holder
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
DateTime
2010-04-07 11:42:57
AssociatedEntity (ID = AE-1); (AUTHORITY = rulib)
Role
Copyright holder
Name
Manjit Sran
Affiliation
Rutgers University. Graduate School of Education
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

ContentModel
ETD
MimeType (TYPE = file)
application/pdf
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application/x-tar
FileSize (UNIT = bytes)
5539840
Checksum (METHOD = SHA1)
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