Graduation Year

2010

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Secondary Education

Major Professor

Denisse R. Thompson, Ph.D.

Keywords

Algebra, Cognitive demand, Curriculum, Reasoning, Rational numbers

Abstract

Some scholars have criticized the treatment of proportionality in middle-school textbooks, but these criticisms seem to be based on informal knowledge of the content of textbooks rather than on a detailed curriculum analysis. Thus, a curriculum analysis related to proportionality was needed. To investigate the treatment of proportionality in current middle-school textbooks, nine such books were analyzed. Sixth-, seventh-, and eighth-grade textbooks from three series were used: ConnectedMathematics2 (CMP), Glencoe's Math Connects, and the University of Chicago School Mathematics Project (UCSMP). Lessons with a focus on proportionality were selected from four content areas: algebra, data analysis/probability, geometry/measurement, and rational numbers.

Within each lesson, tasks (activities, examples, and exercises) related to proportionality were coded along five dimensions: content area, problem type, solution strategy, presence or absence of a visual representation, and whether the task contained material regarding the characteristics of proportionality. For activities and exercises, the level of cognitive demand was also noted. Results indicate that proportionality is more of a focus in sixth and seventh-grade textbooks than in eighth-grade textbooks. The CMP and UCSMP series focused on algebra in eighth grade rather than proportionality. In all of the sixth-grade textbooks, and some of the seventh- and eighth-grade books, proportionality was presented primarily through the rational number content area. Two problem types described in the research literature, ratio comparison and missing value, were extensively found. However, qualitative proportional problems were virtually absent from the textbooks in this study.

Other problem types (alternate form and function rule), not described in the literature, were also found. Differences were found between the solution strategies suggested in the three textbook series. Formal proportions are used earlier and more frequently in the Math Connects series than in the other two. In the CMP series, students are more likely to use manipulatives. The Mathematical Task Framework (Stein, Smith, Henningsen, & Silver, 2000) was used to measure the level of cognitive demand. The level of cognitive demand differed among textbook series with the CMP series having the highest level of cognitive demand and the Math Connects series having the lowest.

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