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Prospective teachers’ developing fraction ideas

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TitleInfo
Title
Prospective teachers’ developing fraction ideas
SubTitle
a case study of instructor’s moves
Name (type = personal)
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Richardson
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Deidre C.
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1970-
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Deidre C. Richardson
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author
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Maher
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Carolyn A
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Carolyn A Maher
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Advisory Committee
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chair
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Uptegrove
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Elizabeth B
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Elizabeth B Uptegrove
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Advisory Committee
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internal member
Name (type = personal)
NamePart (type = family)
Powell
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Arthur B
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Arthur B Powell
Affiliation
Advisory Committee
Role
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internal member
Name (type = corporate)
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Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School of Education
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school
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2019
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2019-01
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2019
Place
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xx
Language
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eng
Abstract (type = abstract)
Recent data from a cross-national assessment, the Programme for International Student Assessment (PISA), place the United States performance in mathematics at 38 out of 71 countries (OECD, 2016) – one clear indication of the ongoing need for the improvement of mathematics education. This improvement relies, in part, on improving undergraduate mathematics education for prospective teachers of mathematics who should learn mathematics in a manner that encourages active engagement with mathematical ideas (National Research Council, 1989).  

Despite the importance of teacher rational number knowledge, the ways in which they successfully acquire that complex body of knowledge are not well understood (e.g. Depaepe et al., 2015; Krauss, Baumert, & Blum, 2008; Newton, 2008; Senk, 2012; Son & Crespo, 2009; Tirosh, 2000). Teachers’ capability of building and using different representations of math ideas, including rational number concepts, are considered important areas of mathematical knowledge that must be developed in order to provide meaningful learning experiences for students (National Governors Association for Best Practices & Council of Chief State School Officers, 2010; National Research Council, 2003). Studies on preservice teachers’ thinking about fractions have shown that while they bring some knowledge of fractions to their undergraduate mathematics classes (Mack 1990; Tirosh, 2000; Park, Güçler & McCrory, 2012), their misunderstandings are still similar to those reflected in children’s fractions learning (e.g. Ball, 1988; Osana & Royea, 2011; Zhou et al., 2006) . Studies have also reported that prospective teachers often enter teacher preparation programs with beliefs inconsistent with the conceptual teaching of mathematics (Ball, Lubienski & Mewborn, 2001; Strohlmann et al., 2015). If improvement in the teaching and learning of mathematics is to be realized, understanding how prospective teachers build and justify their solutions to rational numbers problems will be of importance.

This research, a component of a design study grant funded by the National Science Foundation, investigates how prospective teachers extend knowledge of rational number ideas, how they justify solutions and how their beliefs about teaching and learning mathematics evolve. The study also explores the instructor’s role and interventions employed within the classroom environment. The students worked on mathematically rich fractions tasks using Cuisenaire rods as they developed representations to understand the concept of unit fraction, to compare fractions, and to build ideas of fraction equivalence. The study is guided by the following research questions:
1.What role does the instructor play in the prospective teachers’ building and justification of ideas?
2.What types of interventions does she employ?
3.What changes, if any, in prospective teachers’ beliefs about doing, teaching and learning mathematics can be identified over the course of the intervention?

The videotaped data of six female subjects in a mathematics class at a liberal arts college were captured with two cameras for two 60-minute class sessions. During the sessions, students explored fractions ideas while working with partners in small groups, discussed solutions, and built models to justify solutions. Two sessions of videotaped data, transcripts, student work, beliefs assessments and observation notes were analyzed using the analytical model described by Powell, Francisco, and Maher (2003).

This study contributes to an under-researched body of literature by examining instructor’s pedagogical and question moves as prospective teachers build representations of rational number concepts and justifications for solutions to problems within an undergraduate mathematics course. Its findings may be of value to colleges of education as they redesign curricula intended to improve prospective teachers’ understanding of and capability for representing rational number ideas.
Subject (authority = RUETD)
Topic
Mathematics Education
Subject (authority = ETD-LCSH)
Topic
Mathematics teachers -- Training of
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_9381
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (290 pages : illustrations)
Note (type = degree)
Ed.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Deidre C. Richardson
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Title
Graduate School of Education Electronic Theses and Dissertations
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rucore10001500001
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NjNbRU
Identifier (type = doi)
doi:10.7282/t3-c7qy-7m59
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
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Richardson
GivenName
Deidre
MiddleName
C.
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RightsEvent
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Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2018-12-02 14:36:30
AssociatedEntity
Name
Deidre Richardson
Role
Copyright holder
Affiliation
Rutgers University. Graduate School of Education
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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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2018-12-17T23:40:54
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2018-12-17T23:40:54
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