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Concepts of variable in middle-grades mathematics textbooks during four eras of mathematics education in the united states

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Material Information

Title:
Concepts of variable in middle-grades mathematics textbooks during four eras of mathematics education in the united states
Physical Description:
Book
Language:
English
Creator:
Dogbey, James
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Analysis
Curriculum
Placeholders
Labels
Generalized numbers
Literal symbols
Dissertations, Academic -- Secondary Education -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: This study used content analysis to investigate the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States (New Math, Back to Basics, Problem Solving, and the NCTM Standards era: 1957 - 2009). It also examined the nature of support that the curricula provide for teachers to enact variables ideas in the classroom. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. Formal definitions for variables were found in 11 of the 12 students' editions examined. The characteristics of the definitions for variables found in the different curricula were, however, different from one another. The uses of variables as placeholders and as labels dominated the uses of variables in the mathematics curricula. The least used category of variables was as an abstract symbol. When examined in terms of the content areas, the use of variables as placeholders dominated Number and Operations, and Algebra contents. In Geometry, Measurement, and Data Analysis and Probability content areas, the use of variables as labels was predominant. Overall, the data did not reveal any systematic or drastic change in the treatment of variable ideas during the 50 year period within which this study is situated. There was however, a steady increase in the use of variables as varying quantities across grade levels, and the four eras of mathematics education in the United States. There were also some noticeable changes in the treatment of variable ideas found in Math Connects curriculum when compared to the treatment in the other three curricula. The data collected also supported the evidence of guidance provided to teachers in the respective curricula to enact variable ideas in the classroom. However, the amount of guidance identified was limited in the majority of the curricula. Limitations of the study, implications for curriculum and teacher development, as well as recommendations for future research are also presented.
Thesis:
Dissertation (PHD)--University of South Florida, 2010.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by James Dogbey.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains X pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
usfldc doi - E14-SFE0004600
usfldc handle - e14.4600
System ID:
SFS0027915:00001


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Full Text
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ABSTRACT: This study used content analysis to investigate the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States (New Math, Back to Basics, Problem Solving, and the NCTM Standards era: 1957 2009). It also examined the nature of support that the curricula provide for teachers to enact variables ideas in the classroom. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. Formal definitions for variables were found in 11 of the 12 students' editions examined. The characteristics of the definitions for variables found in the different curricula were, however, different from one another. The uses of variables as placeholders and as labels dominated the uses of variables in the mathematics curricula. The least used category of variables was as an abstract symbol. When examined in terms of the content areas, the use of variables as placeholders dominated Number and Operations, and Algebra contents. In Geometry, Measurement, and Data Analysis and Probability content areas, the use of variables as labels was predominant. Overall, the data did not reveal any systematic or drastic change in the treatment of variable ideas during the 50 year period within which this study is situated. There was however, a steady increase in the use of variables as varying quantities across grade levels, and the four eras of mathematics education in the United States. There were also some noticeable changes in the treatment of variable ideas found in Math Connects curriculum when compared to the treatment in the other three curricula. The data collected also supported the evidence of guidance provided to teachers in the respective curricula to enact variable ideas in the classroom. However, the amount of guidance identified was limited in the majority of the curricula. Limitations of the study, implications for curriculum and teacher development, as well as recommendations for future research are also presented.
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