Algebra, Geometry Classes Vary in Rigor, Says Study
Educators seeking creative solutions
The drive to get every student to take so-called college gateway courses has succeeded, a new federal study finds, but students taking Algebra 1 and Geometry classes are getting considerably less substance than their course titles would suggest.
Nearly all of the class of 2005 graduated having taken Algebra 1, according to the latest iteration of the National Assessment of Educational Progress’s high school transcript study, released this month by the National Center for Education Statistics. Yet if their course materials are any indication, fewer than one in four of those students studied the kind of challenging topics needed to prepare for college-level mathematics.
During the 2005 National Assessment of Educational Progress in mathematics, NCES researchers also collected course transcript data from a representative sample of 17,800 students who graduated with a regular or honors diploma that year. They also analyzed 120 Algebra 1, Geometry, and integrated math textbooks used at the 550 public schools those students attended.
Education watchers hoping to close persistent achievement gaps among students of different racial and ethnic groups long have pushed for all students to take “college-ready” class schedules, including at least four years of high school math, such as Algebra 1 and 2, Geometry, and Calculus. Here, at least, the transcript study shows this push has paid off: Graduates in 2005 earned on average 3.8 credits in math, significantly more than the average of 3.2 credits earned by graduates in 1990. Moreover, from 1990 to 2005, black graduates closed a 6-percentage-point gap with white graduates in the percentages of students earning at least three math credits, including in algebra and geometry.
While nearly all 2005 high school graduates had taken a course called Algebra 1 at some point, the content of those classes varied tremendously, according to a new analysis by the National Center on Education Statistics. The chart breaks down the types of topics actually covered in Algebra 1 courses that researchers classified as beginner-, intermediate-, and rigorous-level classes.
The study found that, on average, two-thirds of topics covered in Algebra 1 and Geometry courses focused on core content topics in each of those subjects, while the other third covered topics in other math areas. Researchers also gauged the rigor of classes based on the topics and questions covered in each book. A course categorized by researchers as beginner-level algebra had more than 60 percent of its material on elementary and middle school math topics such as basic arithmetic and pre-algebra problems such as basic equations. By contrast, a rigorous Algebra 1 courses included more than 60 percent of material on advanced topics such as functions and advanced number theory, as well as other higher-level math subjects such as geometry, trigonometry, and precalculus.
“We found that there is very little truth-in-labeling for high school Algebra 1 and Geometry courses,” said Sean P. “Jack” Buckley, the NCES commissioner, in a statement on the study.
Variations in Rigor
Of graduates who took a course identified by a school as Algebra 1, 32 percent had a rigorous course and 14 percent learned beginner-level material. In classes identified as Geometry, 21 percent of graduates took a class covering rigorous material, while 12 percent covered beginner-level material.
For example, a student taking a rigorous Algebra 1 course covered 11 topics in advanced number theory, compared with only six for students in courses with the same name that researchers classified as beginner- and intermediate-level classes. A student in an Algebra 1 class ranked by the study as beginner-level had no exposure to advanced functions, and more than a quarter of the class was devoted to basic arithmetic and pre-algebra. A student in a rigorous Geometry class likewise covered significantly more topics in coordinate and vector geometry, and significantly fewer topics in basic arithmetic and pre-geometry, than a student in a beginner-level Geometry class.
The proof of the pudding is in the eating: Mr. Buckley said students who took classes that covered more rigorous topics in algebra and geometry scored significantly higher on NAEP than those who studied beginner topics, regardless of the course’s title. In fact, more graduates who took Algebra 1 courses considered “regular” by their schools actually covered rigorous algebra courses than graduates in honors classes, 34 percent versus 18 percent. In geometry, at least, honors classes tended to be more challenging than regular classes: A third of honors geometry classes were rigorous, compared with 19 percent of regular geometry classes. Fewer than one in five students who took an Algebra 1 course considered “honors” by their school actually learned rigorous coursework, including advanced functions and number theory; nearly three out of four students were taught intermediate-level material, with higher proportions of pre-algebra and basic equations.
Racial, Ethnic Disparities
There were no significant differences in the proportion of students of different racial groups who took rigorous Algebra 1 courses—roughly a third of each group—though Hispanic and Asian and Pacific Islander students were more likely than other groups to take beginner-level algebra courses. However, the NCES found that more white students in honors Geometry classes, 37 percent, covered rigorous topics, compared with 21 percent of black and 17 percent of Hispanic students in similarly titled classes.
“It’s not surprising there’s such variation, because there’s not been uniformity among various states with what is meant by rigorous algebra or introductory algebra,’ said J. Michael Shaughnessy, a mathematics professor at Portland State University in Oregon and the immediate past-president of the National Council of Teachers of Mathematics.
“That’s really one of the reasons the [Common Core State Standards] came about. That’s certainly one of the goals put out by the common core, to balance across states the mathematics experience that students will get,” he said, adding that the NAEP transcript study may provide a baseline from which to compare how algebra and geometry classes evolve in response to the common core.
But Mr. Shaughnessy warned that the study’s focus on course materials provides a limited perspective on what students really learn in those classes. “It’s all based on the textbook analysis and the type of questions being asked,” he said. “There’s no question about what the teacher is doing, what supplemental materials are being used, how faithfully it’s being implemented. The study didn’t look at any of that, so we have to be very cautious about it.”
In addition, the transcript study includes only the materials of high school Algebra 1 and Geometry courses, though 20 percent of all 2005 graduates—30 percent of Asian/Pacific Islander students, 23 percent of white students, 10 percent of Hispanic students, and 8 percent of black students—took Algebra 1 in middle school. The transcript study did not evaluate any middle school courses, though some of those may have used the same textbooks as high school courses.
Vol. 32, Issue 26, Pages 6-7