Generalization: Developing Mathematical Practices in Elementary School

Persistent Link:
http://hdl.handle.net/10150/556959
Title:
Generalization: Developing Mathematical Practices in Elementary School
Author:
Dumitraşcu, Gabriela Georgeta
Issue Date:
2015
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The process of generalization in mathematics was identified by mathematics education and educational psychology research, out of many mental actions or operations, as a cognitive function fundamentally required in the thinking process. Moreover, the current changes in education in the United States bring forward the dual goal of mathematics teaching and learning: students should have strong and rigorous mathematical content knowledge and students should be involved in practices that define the status of doing mathematical work. This dual role is totally dependent on the process of generalization. This study uses theories and research findings from the field of algebraic thinking, teaching, and learning to understand how the third grade teacher’s edition textbooks of three mathematics curricula portray the process of generalization. I started my study with the development of a theoretical coding system obtained by combining Kaput’s theory about algebra (Kaput, 2008), Krutetskii’s two way of generalization (Krutetskii, 1976), and the five mathematical representations identified by Lesh, Post, and Behr (1987). Then, I used the coding system to identify tasks that have the potential to involve students in the process of generalization. The findings from my study provide evidence that following a well-structured theory, such as Kaput’s theory about algebra, allows us to identify tasks that support algebraic thinking and to create new ones with higher potential to involve children in the process of generalization. Such tasks may support the development of algebraic thinking as a continuous process that should start from early grades of elementary school.
Type:
text; Electronic Dissertation
Keywords:
elementary mathematics; generalization; patterns; properties of operations; textbook analysis; Teaching & Teacher Education; algebraic thinking
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Teaching & Teacher Education
Degree Grantor:
University of Arizona
Advisor:
Civil, Marta; Turner, Erin

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleGeneralization: Developing Mathematical Practices in Elementary Schoolen_US
dc.creatorDumitraşcu, Gabriela Georgetaen
dc.contributor.authorDumitraşcu, Gabriela Georgetaen
dc.date.issued2015en
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.abstractThe process of generalization in mathematics was identified by mathematics education and educational psychology research, out of many mental actions or operations, as a cognitive function fundamentally required in the thinking process. Moreover, the current changes in education in the United States bring forward the dual goal of mathematics teaching and learning: students should have strong and rigorous mathematical content knowledge and students should be involved in practices that define the status of doing mathematical work. This dual role is totally dependent on the process of generalization. This study uses theories and research findings from the field of algebraic thinking, teaching, and learning to understand how the third grade teacher’s edition textbooks of three mathematics curricula portray the process of generalization. I started my study with the development of a theoretical coding system obtained by combining Kaput’s theory about algebra (Kaput, 2008), Krutetskii’s two way of generalization (Krutetskii, 1976), and the five mathematical representations identified by Lesh, Post, and Behr (1987). Then, I used the coding system to identify tasks that have the potential to involve students in the process of generalization. The findings from my study provide evidence that following a well-structured theory, such as Kaput’s theory about algebra, allows us to identify tasks that support algebraic thinking and to create new ones with higher potential to involve children in the process of generalization. Such tasks may support the development of algebraic thinking as a continuous process that should start from early grades of elementary school.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectelementary mathematicsen
dc.subjectgeneralizationen
dc.subjectpatternsen
dc.subjectproperties of operationsen
dc.subjecttextbook analysisen
dc.subjectTeaching & Teacher Educationen
dc.subjectalgebraic thinkingen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineTeaching & Teacher Educationen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorCivil, Martaen
dc.contributor.advisorTurner, Erinen
dc.contributor.committeememberCivil, Martaen
dc.contributor.committeememberTurner, Erinen
dc.contributor.committeememberDougherty, Barbaraen
dc.contributor.committeememberDoyle, Walteren
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