The Nation's Report Card: Algebra I and Geometry Curricula--Results from the 2005 High School Transcript Mathematics Curriculum Study. NCES 2013-451

The 2005 National Assessment of Educational Progress (NAEP) High School Transcript Study (HSTS) found that high school graduates in 2005 earned more mathematics credits, took higher level mathematics courses, and obtained higher grades in mathematics courses than in 1990. The report also noted that these improvements in students' academic records were not reflected in twelfth-grade NAEP mathematics and science scores. Why are improvements in student coursetaking not reflected in academic performance, such as higher NAEP scores? The Mathematics Curriculum Study (MCS) explored the relationship between coursetaking and achievement by examining the content and challenge of two mathematics courses taught in the nation's public high schools--algebra I and geometry. Conducted in conjunction with the 2005 NAEP HSTS, the study used textbooks as an indirect measure of what was taught in classrooms, but not how it was taught. In other words, the textbook information is not used to measure classroom instruction. Textbooks served as an indicator of the intended course curriculum (Schmidt, McKnight, and Raizen 1997). The chapter review questions in each textbook were used to identify the mathematics topics covered (or subject matter content) and the complexity of the exercises (or degree of cognitive challenge). Chapter review questions, and not the entire textbook, were coded because the questions have been found to be representative of the chapter content and complexity level in previous studies (Schmidt 2012). The study uses curriculum topics to describe the content of the mathematics courses and course levels to denote the content and complexity of the courses. The results are based on analyses of the curriculum topics and course levels developed from the textbook information, coursetaking data from the 2005 NAEP HSTS, and performance data from the twelfth-grade 2005 NAEP mathematics assessment. The study addresses three broad research questions: (1) What differences exist within the curricula of algebra I and geometry courses?; (2) How accurately do school course titles and descriptions reflect the rigor of what is taught in algebra I and geometry courses compared to textbook content?; and (3) How do the curricula of algebra I and geometry courses relate to subsequent mathematics coursetaking patterns and NAEP performance? In this report, curriculum topics, course levels, and grade 12 NAEP mathematics scale scores are used to describe the findings of the study. Curriculum topics are based on summaries of the textbook content that a school reported covering in an algebra I or geometry course. The six broad categories of curriculum topics used to describe the mathematics content found in both algebra I and geometry textbooks are: elementary and middle school mathematics, introductory algebra, advanced algebra, two-dimensional geometry, advanced geometry, and other high school mathematics. A glossary is included. (Contains 3 charts, 15 figures and 10 tables.)