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Percents are not natural numbers
Descriptive
TitleInfo
Title
Percents are not natural numbers
Name
(type = personal)
NamePart
(type = family)
Jacobs
NamePart
(type = given)
Jennifer A.
NamePart
(type = date)
1983-
DisplayForm
Jennifer Jacobs
Role
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author
Name
(type = personal)
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Gelman
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Rochel
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Rochel Gelman
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Advisory Committee
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chair
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Chapman
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Gretchen
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Gretchen Chapman
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Advisory Committee
Role
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internal member
Name
(type = personal)
NamePart
(type = family)
Epstein
NamePart
(type = given)
Yakov
DisplayForm
Yakov Epstein
Affiliation
Advisory Committee
Role
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(authority = RULIB)
internal member
Name
(type = personal)
NamePart
(type = family)
Schorr
NamePart
(type = given)
Roberta
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Roberta Schorr
Affiliation
Advisory Committee
Role
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outside member
Name
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NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
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NamePart
Graduate School - New Brunswick
Role
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school
TypeOfResource
Text
Genre
(authority = marcgt)
theses
OriginInfo
DateCreated
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2013
DateOther
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(type = degree)
2013-05
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated with rational numbers all around them, from the “% Daily Values” on nutrition labels to sales and discounts in stores to the constant ups and downs of gas prices. From an early age, humans have a rather robust concept of natural number, but this earlier knowledge seems to act as a barrier to future learning of rational number. While participants performed better on one-statement problems with a single percent, they ignored the principles of rational number when presented with two-statement percent problems. For example, using rational numbers involves dropping the successor principle, a principle that applies to the natural numbers. Problems presented algebraically gave participants great difficulty, though performance improved when subjects were able to replace the variable y with a natural number (100). When using a numerical hint (substituting in a value during a training phase), participants still did not improve their performance on algebra problems in posttest. Error analyses revealed a strong tendency for students to interpret the problems as novel examples of natural number problems. This research discusses the failure to understand percents in light of overuse or failure to apply the natural number successor principle, division, false cognates, and the absence of knowledge that relates multiple rational number representations to a common underlying knowledge structure. The amount of previous math experience is also correlated with the ease of moving between natural number and rational number concepts.
Subject
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Topic
Psychology
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
Identifier
ETD_4793
PhysicalDescription
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electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
viii, 106 p. : ill.
Note
(type = degree)
Ph.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by Jennifer A. Jacobs
Subject
(authority = ETD-LCSH)
Topic
Percentage
Subject
(authority = ETD-LCSH)
Topic
Numbers, Rational
Subject
(authority = ETD-LCSH)
Topic
Numbers, Natural
Subject
(authority = ETD-LCSH)
Topic
Mathematics--Philosophy
Identifier
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000068885
RelatedItem
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier
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rucore19991600001
Location
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3TX3CZ3
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Jacobs
GivenName
Jennifer
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2013-05-01 14:22:53
AssociatedEntity
Name
Jennifer Jacobs
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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
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ContentModel
ETD
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windows xp
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