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Task analysis
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
Task analysis
SubTitle
the inherent mathematical structures in students' problem-solving processes
Identifier
ETD_3149
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000058837
Language
LanguageTerm
(authority = ISO639-2);
(type = code)
eng
Genre
(authority = marcgt)
theses
Subject
(ID = SBJ-1);
(authority = RUETD)
Topic
Mathematics Education
Subject
(ID = SBJ-2);
(authority = ETD-LCSH)
Topic
Task analysis in education
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
Mathematical analysis
Subject
(ID = SBJ-4);
(authority = ETD-LCSH)
Topic
Mathematics--Study and teaching
Subject
(ID = SBJ-5);
(authority = ETD-LCSH)
Topic
Problem solving
Abstract
(type = abstract)
Research Questions: One way students may develop conceptual understanding is through working on strands of related mathematical tasks and thus developing and refining their understanding of the underlying mathematical concepts contained in the tasks. The purpose of this study is to illuminate this process by detailing the inherent mathematical structures in such a strand and discuss what aspects of it facilitated student learning. The research questions addressed are: (1) What mathematical structures can be uncovered by exploring/engaging with the combinatorics tasks used in the Rutgers longitudinal study? (2) In what ways are these mathematical structures revealed during students’ problem-solving processes? Methodology: Ten tasks from the combinatorics/counting strand are selected from the Rutgers longitudinal project for this qualitative study. The data available for analysis are in the form of digitized video tapes, verified transcripts, and students’ written work. The analysis focuses on decoding students’ solutions into formal mathematical definitions and theorems. Concept maps are used to illustrate the overall hierarchy of the presented mathematical structures. Findings: There are a total of sixty-three inherent mathematical structures extracted from the formal solutions of ten selected combinatorics tasks. These structures are categorized as definitions, notations, axioms, properties, formulas, and theorems. When classified with respect to the seven relevant sub-domains of mathematics, these structures pertain to: set theory, enumerative combinatorics, graph theory, sequences & sets, general algebraic system, probability theory, and geometry. The analysis suggests that the participating students uncovered many of these mathematical structures primarily in the following ways: (1) Manipulating a concrete model, (2) Listing all possible combinations, (3) Inventing different representations, (4) Seeking patterns, and (5) Making connections. Conclusion and Suggestions: These findings support the following suggestions for practice: (1) Teachers may benefit from studying the underlying structures of a task thoroughly before assigning the task to students, (2) In determining the order of related tasks within a strand, teachers need to consider the sophistication level and the coherence of the underlying structures across tasks, (3) Using concrete models can help students to both develop and verify solutions to complex problems, and (4) Tasks whose inherent structures belong to a variety of mathematical sub-domains can help students build an increasingly interconnected view of mathematics. Significance: This study outlined a method of extracting inherent mathematical structures from mathematical tasks. The results suggest that students have natural abilities to uncover these structures by themselves. It is hoped that this will motivate mathematics teachers to improve the way they think about using problem solving in their teaching.
PhysicalDescription
Form
(authority = gmd)
electronic resource
Extent
195 p. : ill.
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application/pdf
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text/xml
Note
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Ed.D.
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Weiwei Lo
Name
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Lo
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Weiwei
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author
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Weiwei Lo
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Maher
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Carolyn A
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chair
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Advisory Committee
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Carolyn A Maher
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(type = family)
Alston
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(type = given)
Alice S
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internal member
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Advisory Committee
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Alice S Alston
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(ID = NAME-4);
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NamePart
(type = family)
Radu
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Iuliana
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internal member
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Advisory Committee
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Iuliana Radu
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NamePart
(type = family)
Uptegrove
NamePart
(type = given)
Elizabeth B
Role
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(authority = RULIB)
outside member
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Advisory Committee
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Elizabeth B Uptegrove
Name
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NamePart
Rutgers University
Role
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degree grantor
Name
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NamePart
Graduate School of Education
Role
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(authority = RULIB)
school
OriginInfo
DateCreated
(qualifier = exact)
2010
DateOther
(qualifier = exact);
(type = degree)
2011-01
Place
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(type = code)
xx
RelatedItem
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier
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ETD
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(type = host)
TitleInfo
Title
Graduate School of Education Electronic Theses and Dissertations
Identifier
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rucore10001500001
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T3154GK2
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
Lo
GivenName
Weiwei
Role
Copyright Holder
RightsEvent
(ID = RE-1);
(AUTHORITY = rulib)
Type
Permission or license
DateTime
2011-01-08 18:57:54
AssociatedEntity
(ID = AE-1);
(AUTHORITY = rulib)
Role
Copyright holder
Name
Weiwei Lo
Affiliation
Rutgers University. Graduate School of Education
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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
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(TYPE = file)
application/pdf
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application/x-tar
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1392640
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Statistical Profile