Graduation Year

2010

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Secondary Education

Major Professor

Gladis Kersaint, Ph.D.

Committee Member

Robert Dedrick, Ph.D.

Committee Member

John Ferron, Ph.D

Committee Member

Denisse Thompson, Ph.D.

Keywords

content analysis, curriculum, placeholders, labels, generalized numbers, literal symbols

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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