March 2013

**Authors:** Janis Brown, Kathryn Schiller, Stephen Roey, Robert Perkins, William Schmidt, Richard Houang

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:

- What differences exist within the curricula of algebra I and geometry courses?
- 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?
- 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. Table A lists the content found within these curriculum topics.

Elementary and middle school mathematics |
Basic arithmetic and pre-geometry |
---|---|

Introductory algebra |
Pre-algebra, basic algebraic equations, and basic number theory |

Advanced algebra |
Advanced equations, basic functions, advanced functions, and advanced number theory |

Two-dimensional geometry |
Basic geometric concepts and properties of shapes |

Advanced geometry |
Three-dimensional geometry, coordinate geometry, and vector geometry |

Other high school mathematics topics |
Trigonometry, pre-calculus, statistics, validation and structuring, discrete mathematics, finite mathematics, and calculus |

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, High School Transcript Study (HSTS), Mathematics Curriculum Study, 2005.

Course levels are rankings of courses that high school graduates took based on the combination of content and challenge of each course, as determined by the textbooks used. Courses were assigned only one course level. These rankings were developed separately for algebra I and geometry courses. For both courses, the three levels are beginner, intermediate, and rigorous (table B).

Beginner |
Covers more introductory material and less advanced material than an intermediate course |
---|---|

Intermediate |
Contains a balanced mix of both introductory and advanced material. |

Rigorous |
Covers more advanced material and less introductory material than an intermediate course. |

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, High School Transcript Study (HSTS), Mathematics Curriculum Study, 2005.

Results presented in this report are based on the 550 public schools and around 17,800 high school graduates selected for this study. This sample represents approximately two million public high school graduates from across the nation in 2005. Only high school graduates earning a regular or honors diploma are included in the analysis of this report, as is consistent with the reporting of the 2005 NAEP HSTS results. In addition, only graduates who took algebra I or geometry as high school courses were included in the study results. In 2005, 78 percent of all graduates took algebra I during high school and 20 percent of graduates took algebra I before entering high school. About 83 percent of all graduates took geometry during high school and 1.5 percent of graduates took geometry before entering high school.

The NAEP twelfth-grade mathematics results are reported as average scores on a scale of 0 to 300. The algebra and geometry scores are presented in the report to reflect performance on algebra I and geometry content, as opposed to overall mathematics performance. The MCS reports results using National Center for Education Statistics (NCES) statistical standards; findings from t-tests are reported based on a statistical significance level set at .05 without adjustments for multiple comparisons.

The NAEP twelfth-grade mathematics results are reported as average scores on a scale of 0 to 300. The algebra and geometry scores are presented in the report to reflect performance on algebra I and geometry content, as opposed to overall mathematics performance. The MCS reports results using National Center for Education Statistics (NCES) statistical standards; findings from t-tests are reported based on a statistical significance level set at .05 without adjustments for multiple comparisons.

A few studies have analyzed textbook information and usage as a means to explain the apparent disconnect between coursetaking and achievement (Cogan, Schmidt, and Wiley 2001; Schiller et al. 2010; Tornroos 2005). The MCS adapted and built upon the methodology of these prior studies. See the Technical Notes of this report for a detailed description of the study methodology. While this study examined curriculum topics and course level of an algebra I or geometry course, it did not measure how well the curriculum was implemented in the classroom. In addition, only those graduates who took algebra I and geometry while in high school were included in the analyses. Therefore, students who took algebra I or geometry before entering high school were not included in the respective analyses because the textbook information was not collected. This limitation may be evident in the algebra I results, as those graduates who took the course in middle school were not included in the study results. Results from this study cannot be used to establish cause-and-effect relationships between mathematics textbooks and student mathematics coursetaking and performance.

**Download sections of the report (or the complete report) in a PDF file for viewing and printing:**

**PDF 1 of 2**(8.5 MB)

Report Cover

Table of Contents

Executive Summary

Introduction and Overview

Mathematics Course Profiles

**PDF 2 of 2**(7.4 MB)

Comparison of School Courses

Coursework and Performance

Technical Notes

Glossary

References

**The complete report: NAEP Algebra I and Geometry Curricula PDF**(14.4. MB)

**NCES 2013-451** See the **entry in the NCES products and publications database for contact and ordering information**, and for links to similar topics.

**Suggested Citation:**

Brown, J., Schiller, K., Roey, S., Perkins, R., Schmidt, W., and Houang, R. (2013). *Algebra and Geometry Curricula* (NCES 2013-451). National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education. Washington, DC.

For more information about this topic, visit the Math Curricula section of the NAEP website.

Last updated 11 March 2013 (MS)

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