Graduation Year

2018

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Curriculum and Instruction

Major Professor

Eugenia Vomvoridi-Ivanovic, Ph.D.

Committee Member

Jennifer Wolgemuth, Ph.D.

Committee Member

Sarah VanIngen, Ph.D.

Committee Member

Mile Krajcevski, Ph.D.

Keywords

Content Analysis, Geometry, Mathematics Textbooks, Opportunity to Learn

Abstract

I conducted a content analysis to examine the treatment of the surface area and volume concepts within four published middle-grades mathematics textbook series. In particular, I examined the treatment of the surface area and volume concepts in terms of the location of surface area and volume lessons in the textbook and the number of pages and lessons devoted to these concepts. I also investigated the sequence of the instructional blocks of surface area and volume lessons. In addition, I evaluated the tasks included in these lessons in regards to the performance expectations of students, the types of visual representations of 3D objects, and the level of mathematical complexity. At last, I examined the extent to which the content of surface area and volume lessons address the Common Core Content Standards (CCCS) for 6-8 geometry that are aligned with these topics.

I used content analysis to analyze relevant content in a total of twelve middle-grades student edition mathematics textbooks from two popular textbook series, Go Math!(GM) and Glencoe Math (GMC); and two alternative textbook series, Connected Mathematics 3 (CM) and University of Chicago School Project (UCSMP). First, I used Flanders’ (1994) counting method to examine the physical characteristics of textbooks, such as the location of the surface area and volume lessons in the textbook, the number of pages and lessons devoted to these concepts. Second, I analyzed the sequence of the instructional blocks of surface area and volume lessons by using content analysis. Third, I adapted the Trends in International Mathematics and Science Study [TIMSS] (2002) Performance Expectations for Mathematics Framework to examine the performance expectations of students within tasks. Fourth, I developed and used the Visual Representations of 3D Objects Framework to examine the types of visual representations of 3D objects included in the tasks. Fifth, I employed the Mathematics Framework for the 2007 National Assessment of Educational Progress (NAEP) to examine the level of mathematical complexity of tasks. Finally, I created the CCCS for 6-8 Geometry Components guideline to examine to what extend the surface area and volume lessons address the geometry content standards.

Results indicated that the majority of textbooks place the concepts of surface area and volume towards the end of the textbook. Small percentages of instructional pages and lessons are devoted to these concepts in all textbooks. Findings also revealed great similarities among the instructional blocks of lessons within three textbook series (GM, GMC, and UCSMP). The majority of tasks within all textbook series contain miniscule amounts of important performance expectations such as justifying and proving and visual representations of 3D objects such as nets and pictures. A significant amount of tasks are of moderate complexity across all textbook series. Analysis also showed that the CM textbook series offers the greatest opportunity for students to generate visual representations of 3D objects and contains the largest amount of high complexity tasks. At last, nearly all lessons address the appropriate geometry content standard among all textbook series. Limitations of the study, implications for mathematics education, as well as recommendations for future research are also presented.

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