Commissioner, National Center for Education Statistics
National Assessment of Educational Progress
Algebra I and Geometry Curricula: Results from the 2005 High School Transcript Mathematics Curriculum Study
March 12, 2013
Today, I am here to share with you results from our new report, Algebra I and Geometry
Curricula: Results from the 2005 High School Transcript Mathematics Curriculum Study.
This is the first study from the National Center for Education Statistics (NCES)
to explore the content and level of challenge of high school algebra I and geometry
courses in public schools across the Nation. The study uses data from the National
Assessment of Educational Progress (NAEP) High School Transcript Study and the NAEP
There are several reasons why we undertook this study. The data we have collected in the High School Transcript Study over the years have shown a steady increase in numbers of mathematics courses that high school graduates have completed. Not only are graduates taking more courses, but they are also taking more high-level courses. This is true for White, Black, and Hispanic graduates. However, there has not been a comparable increase in the NAEP twelfth-grade mathematics scores over the same period, and the achievement gaps separating Black and Hispanic graduates from White graduates have not changed much. Therefore, we wanted to know the actual content of the courses graduates were taking, and if there might be a disparity in course content observable for White versus Black or Hispanic graduates.
The Mathematics Curriculum Study explores the content and challenge of algebra I and geometry courses taught in high school. The study was conducted as part of the 2005 NAEP High School Transcript Study. It was based on a nationally representative sample of 17,800 public high school graduates, representing a population of about 2 million graduates. The graduates in the sample were in 550 high schools around the country. The study incorporated the transcripts and NAEP mathematics scores of these graduates, along with over 120 algebra I, geometry, and integrated mathematics textbooks used by their schools. While these textbooks were being used in 2005, the data we obtained from them is still relevant. In 2009, the most recent High School Transcript Study, we examined lists of the textbooks schools were using in that year and found very few differences, compared to the books in use in 2005.
The participating schools provided titles of the textbooks they used in their mathematics
courses, and the teachers indicated what chapters they intended to cover in their
courses. The review questions at the end of each chapter in the textbooks collected
were coded for content and challenge, using a coding system first developed for
the Trends in International Mathematics and Science Study. The textbook data was
summarized at the student level to provide the results for the study.
Six broad curriculum topics for the materials covered in algebra I and geometry courses were identified in the study. These broad topics refer to the mathematics content areas that graduates covered in their courses, including elementary and middle school mathematics, introductory and advanced algebra, two-dimensional and advanced geometry, and other high school mathematics, which refers to topics traditionally taught after algebra II, such as trigonometry and pre-calculus. The algebra I and geometry courses taken by the graduates were also grouped in three course levels—Beginner, Intermediate, and Rigorous—according to the topics and the degree of challenge of the textbooks used in the courses.
The study has some limitations. First, its coverage is restricted to public high school graduates who obtained a regular or honors diploma and who completed either algebra I or a geometry course in high school. Graduates who took algebra I before high school were not included in the algebra I results, while graduates who took geometry before high school were not included in the geometry results. Second, because the population of focus is graduates, dropouts are not included in the results. Third, the textbooks served as a measure of the intended curriculum for algebra I and geometry courses. The study could not measure how well the course curriculum was implemented in the classroom. Fourth, the study cannot identify cause and effect relationships between courses and student performance.
All of the study results reported today are based on samples, which means that there is a margin of error associated with each score or percentage. Therefore, in the report we only identify those differences in scores or percentages that meet our standard for statistical significance.
Algebra I Results
On average, the nation’s algebra I courses devoted about two-thirds of their content to algebra, with about 37 percent to introductory algebra and 28 percent to advanced algebra. About 13 percent of the content of the average algebra I course was elementary and middle school mathematics, while nearly a quarter was devoted to geometry or other high school mathematics.
Rigorous courses devoted about 10 percent of their content to elementary and middle school mathematics. Both the beginner and intermediate courses devoted more of their content to this topic. Conversely, rigorous algebra I courses devoted 16 percent of their content to other high school mathematics, more than either beginner or intermediate courses. Regardless of course level, algebra I courses devoted between 62 and 67 percent of their content to introductory and advanced algebra topics, with rigorous courses putting more emphasis on advanced algebra topics than either beginner or intermediate courses.
Few racial/ethnic differences were found among graduates by the algebra I course level. About 24 percent of Asian/Pacific Islander graduates and 19 percent of Hispanic graduates took beginner algebra I courses, which were higher than the 12 percent of White graduates taking such courses. Two factors should be kept in mind when considering these higher percentages. First, the study looked at high school graduates, not all twelfth-grade students. In 2005, the high school drop-out rate for Hispanics was 22 percent, compared to 10 percent for Blacks, 6 percent for Whites, and 3 percent for Asian/Pacific Islanders. Second, there were differences in the percentages of graduates who took algebra I before entering high school across race/ethnicity. In 2005, 30 percent of Asian/Pacific Islander graduates took algebra I before entering high school, compared to 23 percent of Whites, 8 percent of Blacks and 10 percent of Hispanics. These students were not part of the algebra I results in the study.
High schools typically designated the algebra I classes they offer as two-year, regular, and honors classes. In the study, we compared the course levels we developed to the school course descriptions. Regardless of the school designation, most graduates in algebra I courses had an intermediate level course. The study found that graduates in regular algebra I classes were more likely to receive a course ranked as a rigorous level course than graduates in honors algebra I classes. Only 18 percent of the graduates in honors algebra I classes had a rigorous level course, compared to 34 percent of graduates in regular algebra I classes.
When looking at the nation’s geometry courses, about two-thirds of the coverage was devoted to two-dimensional and advanced geometry. Around 42 percent of the content focused on two-dimensional geometry, while 24 percent focused on advanced geometry. About 13 percent was devoted to elementary and middle school mathematics, while 21 percent covered algebra and other high school mathematics.
Beginner geometry courses devoted 14 percent of their content to elementary and middle school mathematics, which was more than either intermediate or rigorous geometry courses. Rigorous geometry courses devoted more coverage to both two-dimensional and advanced geometry than either beginner or intermediate courses.
About 67 percent of graduates had a geometry course ranked as intermediate. Around 21 percent of the graduates had a rigorous level geometry course, while 12 percent had a beginner level course. When the data are broken down by race/ethnicity, the distributions for Black, Hispanic, and Asian/Pacific Islander graduates showed similar proportions to White graduates.
Geometry classes offered by high schools were typically titled as informal, regular, and honors classes. Regardless of the school course title, most high school graduates received a course ranked as an intermediate level geometry course. About 54 percent of graduates in informal geometry classes, 68 percent of graduates in regular geometry classes, and 62 percent of graduates in honors geometry classes were in courses ranked as intermediate level. Graduates in honors geometry classes were less likely to receive a beginner level course and more likely to receive a rigorous level course than graduates in either informal or regular geometry classes.
When looking at the performance of graduates on the NAEP twelfth-grade mathematics assessment, graduates in rigorous algebra I and geometry courses scored higher on NAEP. Graduates in rigorous algebra I courses had a mean NAEP algebra score of 146, compared to 137 for graduates in beginner courses. Graduates in rigorous geometry courses had a mean NAEP geometry score of 159, which was higher than the scores for graduates in beginner or intermediate geometry courses. White graduates had higher NAEP algebra and geometry scores than either Black or Hispanic graduates, regardless of the level of the algebra I or geometry course.
There is much more information available, both in the full report and on the NAEP High School Transcript Study web site (http://nces.ed.gov/nationsreportcard/hsts/math_curriculum/).In conclusion, we would like to offer our sincere thanks to all the school administrators, teachers, and students whose participation made this report possible.