Advanced or intermediate algebra? Honors or basic geometry?
When it comes to high school math, the labels may not really matter — or necessarily predict what's in the textbook.
Those revelations are part of the Education Department's new study of high school math courses, released Tuesday. During their review of almost 18,000 high school students' records and textbooks, the investigators found as many as a third of the textbooks weren't about the subject printed on the cover. And within the subjects, the course titles were subjective and didn't really reflect the courses' difficulty.
"We have heard about grade inflation. Now we have course title inflation," said Linda Rosen, chief executive officer of Change the Equation, a coalition of business leaders pushing higher math and science standards. "Learning the course titles don't have much meaning in terms of high expectations and rigor is quite problematic. It's counterproductive if we provide impressive names but rather meaningless transcripts."
The findings have consequences for college-bound students. Admissions counselors look not just at grades but also at coursework on students' transcripts.
The findings also suggest that many elementary teachers are not preparing students for high school-level math and that many students who complete Algebra I and Geometry courses are not prepared for future classes, either during later high school years or in college. Educators at all levels are being forced to leave students behind or spend time on remedial material.
Parents and school administrators alike also should read the findings carefully. Simply enrolling students in the most difficult-sounding course is no guarantee they are receiving the most rigorous instruction or even using a textbook appropriate for their level. And schools, which spend millions on textbooks each year, might not be making the best investments during a time of limited resources.
The report graded textbooks on three different levels: beginner, intermediate and rigorous. But those labels didn't always match up with how schools labeled their classes.
The study found that 73 percent of students who took an Algebra I course labeled "honors" were actually using a curriculum that would be appropriate for one called "intermediate" course. And students who signed up for a "regular" course were more likely to receive a rigorous curriculum than those who enrolled in one called "honors" by an almost 2-to-1 margin.
In geometry, students who took "honors" courses were about twice as likely to receive intermediate textbooks than rigorous.
"You want the course title to reflect reality," said Freeman Hrabowski, president of the University of Maryland-Baltimore County and chairman of the President's Advisory Commission on Educational Excellence for African Americans. "If it's going to be honors, it should have some special meaning."
The researchers found that 65 percent of algebra courses focused on that subject while about 35 percent focused on elementary- and middle-school math skills or other topics that would typically be taught in other high school courses.
Similarly, about 66 percent of geometry courses covered that subject while 34 percent focused on other math topics, such as elementary- or middle-school math skills or algebra.
Part of it is because students are arriving in classrooms unprepared.
"The reality is: not all kids we get in high school are ready for algebra," said Dale Nowlin, a math teacher from Columbus North High School in Columbus, Ind. "You fill the gaps as you can."
The National Center for Education Statistics, the Education Department's data arm, based their results on looking at 17,800 students at 550 public schools in 2005 and then their 12th grade math assessment years later. The researchers also examined about 120 different textbooks and curriculum during that period.
"We had a very detailed picture of what the students had to do to pass those courses," Jack Buckley, National Center for Education Statistics chairman.
But the picture, he acknowledged, was incomplete.
The results were only representative for students who earned diplomas. Those who did not complete a traditional high school program in four years were not included in this study, nor were students who took Algebra I or Geometry courses while in the eighth grade.
In 2005, 78 percent of all high school graduates took an Algebra I class in high school and 20 percent took it before entering high school. In that same year, 83 percent of students took geometry courses in high school but just 1.5 percent took the class before high school.
The analysis also did not look at teachers' tests, but merely questions included in the end-of-chapter review questions. There is no way of telling if teachers used those textbooks as a roadmap or how their lessons mirrored their texts.
The researchers, none the less, used their analysis of course materials to check student performance on standardized tests during students' senior years.
There was no significant difference in test results between those students who took intermediate and rigorous Algebra I sections. But students who had rigorous instruction in Algebra I were likely to perform better on their exams than those in beginner courses.
Students who received a truly rigorous curriculum scored statistically significantly better than their peers in geometry on achievement tests, as well.
"As students take more rigorous material, they score higher," said Buckley, the Education Department's statistics chief.
He noted, however, it was difficult to determine the level of instructions based solely on the course's title.
"One of the issues going on in our high school is course mislabeling," he said.