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To symbols from meaning

Descriptive

TypeOfResource
Text
TitleInfo
Title
To symbols from meaning
SubTitle
students' investigations in counting
Identifier
etd_preRUETD
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000055263
Identifier (type = doi)
doi:10.7282/T3TD9X8V
Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Genre (authority = marcgt)
theses
Subject (authority = ETD-LCSH)
Topic
Mathematics--Study and teaching--Psychological aspects
Subject (authority = RUETD)
Topic
Education
Subject (authority = ETD-LCSH)
Topic
Students--New Jersey
Abstract (type = abstract)
This research provides an analysis of how a cohort group of five students learned standard notation for combinatorics over an I8-month period. The students were among the participants in a long-term study of the development of mathematical ideas and reasoning. Over the years, the students worked on open-ended and challenging mathematical problems from a combinatorics strand, such as building-towers of different heights from different colored cubes, counting pizzas with different toppings, and counting taxicab routes. The group was videotaped doing mathematics during their sophomore and junior years of high school, when they revisited combinatorics tasks that they had worked on during middle and elementary school. During these reinvestigations, they were introduced to the standard notation for combinatorics and to Pascal's Triangle and they explored the addition rule for Pascal's Triangle (Pascal's Identity). Three years later, three of the students were videotaped during task-based interviews in which they again revisited the combinatorics problems and the notation. Analysis of their work shows that the students used the combinatorial tasks with
which they were already familiar to give meaning to the standard notation and to entries
of Pascal's Triangle. They used the understanding of the combinatorics problems that they developed and refined over the years, including their recognition of the isomorphic relationships among the pizza, towers, and taxicab problems (structurally similar problem with different surface features), to build Pascal's Identity. A major contributing factor for the representation of Pascal's Identity in standard notation was their retrieval of earlier images of pizzas and towers that had meaning for them. Other important factors for their success included working together in collaborative investigations and having sufficient time for revisiting and rethinking ideas related to the problems. Follow-up
interviews, in which individual students were asked again about Pascal's Triangle, provided evidence that students, independently, were able to rebuild or reconstruct what they had built together earlier as a group. This research provides evidence of the power of giving meaning to symbols. It suggests that students who build meaning first and then develop the symbolic vocabulary can acquire lasting understanding.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
xvi, 532 p. : ill.
InternetMediaType
text/xml
InternetMediaType
application/pdf
Note (type = degree)
Ed.D.
Note
Includes abstract
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Elizabeth B. Uptegrove
Name (type = personal)
NamePart (type = family)
Uptegrove
NamePart (type = given)
Elizabeth B.
Role
RoleTerm (authority = RULIB); (type = code)
author
Name (type = personal)
NamePart (type = family)
Maher
NamePart (type = given)
Carolyn A.
Role
RoleTerm (authority = RULIB); (type = code)
chair
Name (type = personal)
NamePart (type = family)
Alcock
NamePart (type = given)
Lara J.
Role
RoleTerm (authority = RULIB); (type = code)
internal member
Name (type = personal)
NamePart (type = family)
Barnhart
NamePart (type = given)
Steven M.
Role
RoleTerm (authority = RULIB); (type = code)
internal member
Name (type = personal)
NamePart (type = family)
Powell
NamePart (type = given)
Arthur B.
Role
RoleTerm (authority = RULIB); (type = code)
internal member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB); (type = text)
degree grantor
Name (type = corporate)
NamePart
Graduate School of Education-New Brunswick
Role
RoleTerm (authority = RULIB); (type = text)
school
OriginInfo
DateCreated (qualifier = exact)
2005
DateOther (qualifier = exact); (type = degree)
2005-01
Place
PlaceTerm (type = code)
xx
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
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
Uptegrove
GivenName
Elizabeth
Role
Copyright holder
RightsEvent (ID = RE-1); (AUTHORITY = rulib)
Type
Permission or license
DateTime
2005-01-30
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Technical

ContentModel
ETD
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
43745280
Checksum (METHOD = SHA1)
faa6649e17660a129ddcf0647f49a101895f470e
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