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Exploring and justifying ideas in an undergraduate mathematics course

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TitleInfo
Title
Exploring and justifying ideas in an undergraduate mathematics course
SubTitle
a case study
Name (type = personal)
NamePart (type = family)
Brophy
NamePart (type = given)
Anna
NamePart (type = date)
1973-
DisplayForm
Anna Brophy
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn A
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Carolyn A Maher
Affiliation
Advisory Committee
Role
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chair
Name (type = personal)
NamePart (type = family)
Hmelo-Silver
NamePart (type = given)
Cindy E
DisplayForm
Cindy E Hmelo-Silver
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Uptegrove
NamePart (type = given)
Elizabeth B
DisplayForm
Elizabeth B 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
Graduate School of Education
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2013
DateOther (qualifier = exact); (type = degree)
2013-10
CopyrightDate (encoding = marc); (point = start); (qualifier = exact)
2013
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
The improvement of mathematics education relies very heavily on the improvement of undergraduate mathematics education for future teachers (National Research Council, 1989). It is important that undergraduate mathematics instruction for prospective teachers demonstrates techniques to be used in their future classrooms (Blair, 2006; Senk, Keller, & Ferrini-Mundy, 2004). Specifically, pre-service teachers should develop an understanding of the mathematical processes of exploration and proof (Senk, Keller, & Ferrini-Mundy, 2004). If problems that encourage mathematical exploration and justification are to be brought into the undergraduate classroom, understanding how students build and justify their solutions will be of importance. The purpose of this research was to (1) investigate how undergraduate students enrolled in a mathematics course solve and justify their solution to a series of combinatorics tasks, (2) analyze the moves employed by the instructor and (3) investigate how their solutions compare to the solutions of other students involved in the same problem-solving tasks. This case study was conducted in a mathematics class at a liberal arts college. The six students in this class were all mathematics majors studying to be teachers. Using videotaped data and students’ written work, a careful analysis of how the students built their solutions and justified their answers to three combinatoric problems was conducted. It was found that the strategies and justifications used by the students in this study were similar to those used by participants in earlier studies. Furthermore, in investigating how the college math students built their solutions to the problems, it was found that the instructor played a critical role in the learning process. Findings from this study verify that mathematical learning can take place in a college mathematics class that fosters mathematical exploration and justification with well-chosen tasks, collaboration with peers, and student-centered instruction. This study also has implications for implementation in other settings by providing examples of students’ solutions to specific tasks as well as examples of how instructors can effectively interact with students in a mathematical classroom that nurtures the mathematical processes of conjecturing, generalizing, and justifying solutions to problems.
Subject (authority = RUETD)
Topic
Mathematics Education
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_4954
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
xi, 414 p. : ill.
Note (type = degree)
Ed.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Anna Brophy
Subject (authority = ETD-LCSH)
Topic
Mathematics--Study and teaching
Subject (authority = ETD-LCSH)
Topic
Mathematics teachers--Training of
Subject (authority = ETD-LCSH)
Topic
Student teachers--Training of
RelatedItem (type = host)
TitleInfo
Title
Graduate School of Education Electronic Theses and Dissertations
Identifier (type = local)
rucore10001500001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3BC3WHM
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
Brophy
GivenName
Anna
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2013-08-24 10:50:18
AssociatedEntity
Name
Anna Brophy
Role
Copyright holder
Affiliation
Rutgers University. Graduate School of Education
AssociatedObject
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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

RULTechMD (ID = TECHNICAL1)
ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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