A new report from the American Enterprise Institute (AEI) tackles the U.S. algebra and mathematics dilemma and is the latest to suggest that not all students should be pushed to take algebra in the eighth grade.
“Solving America’s mathematics education problem,” by Duke professor Jacob L. Vigdor, examines cultural shifts that have resulted in new waves of interest in students’ mathematics performance.
Despite a renewed focus on science, technology, engineering, and mathematics (STEM) skills, high school students continue to perform poorly on math tests. That trend continues into college, where many new college students enroll in remedial math courses. The report notes that “the proportion of new college graduates who majored in math-intensive subjects has declined by nearly half over the past 60 years.”
The U.S. is in danger of slowed or lost progress if these trends continue, the report warns.
Moving students through algebra and other higher-level math courses can hurt their knowledge and performance if they enter the classes too soon. For example, in North Carolina’s Charlotte-Mecklenburg Schools, students who took algebra earlier than their peers scored 13 percentile points lower on a standardized test than students who took algebra on a regular schedule.
Some districts have tried to close the math achievement gap by excluding more challenging math topics. But this “dumbing down” hurts students who might want to pursue math majors in college and math-related careers, because they leave high school without skills that other students–their competition in college and the workforce–possess. Over the past 30 years, average SAT math scores have increased 20 points, but there has been a 25 percent drop in the number of college students majoring in math-centered subjects, according to recent research noted in the report.
“The root of America’s math problem is the conflation of two goals: improving the absolute performance of American students and closing gaps between high and low performers,” Vigdor notes. “Following the failure of a significant initiative to accomplish both goals simultaneously—the ‘new math’ movement of the mid-twentieth century—successive reforms have focused attention on bringing lower-performing students up to standards. In the process, the standards have been lowered, and the advancement of higher-performing students has been allowed to languish. Designers of the nation’s mathematics curriculum, in short, have fallen into an ‘achievement-gap trap,’ raising the relative performance of average students in part by permitting the absolute performance of the best students to decline.”
Vigdor writes that many concerns over U.S. math performance surfaced after World War II and the Cold War, when new math concepts became more abstract and students responded by “giving up rather than attempting” to master it. After a short period of renewed interest in math and math-related college majors, interest dropped again.
And with the focus on helping low-performing and average students, top-performing and advanced students have been harmed as math resources are shifted away from them to low-performing students in an effort to boost proficiency scores.
“Studies have verified the predictable consequence: gains to students just below the proficiency level have been offset by losses among more advanced students,” he writes.
He also notes that students who successfully pursue science, engineering, and math majors are those with high math performance on the SAT–“three-quarters of MIT undergraduates have math SAT scores of 750 or better. At a more moderately ranked engineering-focused campus, such as Purdue University, a math SAT score of 530 would place a student at the 25th percentile of the distribution, not the middle.
“The inverse relationship between math-intensive majoring and average math SAT scores suggests that the nation faces a trade-off between offering moderately better math training to the average student and a rigorous training to students with greatest promise.”
This dilemma has carried over into the workforce and U.S. competitiveness.
“The preceding analysis suggests that the United States has made a clear trade over the past few decades. With the twin goals of improving the math performance of the average student and promoting equality, it has made math curriculum more accessible,” Vigdor says. “We can see the drawback to this more accessible curriculum among the nation’s top-performing students, who find themselves either less willing or less able to follow career paths in math, science, and engineering that are the key to innovation and job creation. In the name of preparing more of the workforce to take those jobs, we have harmed the skills of those who might have created them.”
The report contains a handful of solutions that might help struggling students better understand algebra and abstract math concepts, give advanced students a chance to develop even stronger math skills, and retain the nation’s competitive edge:
- Foreign students receive more than half of all doctorate degrees in science and engineering, and two-thirds of those in engineering alone, but many leave the country after they receive their degrees, limiting their potential to contribute to the U.S. economy. But new immigration policy focusing on skills over family reunification criteria could change that pattern.
- Reforming current math curriculum may help, too. The Singapore math model, in which a limited number of topics are covered in a more in-depth way, but this raises questions about U.S. teacher preparedness and the U.S. school structure.
- Tailoring math instruction to a student’s needs, and sorting students by groups according to those needs, may improve math instruction and performance.
“This report makes some good points,” said Linda Gojak, president of the National Council of Teachers of Mathematics, noting that it is important not to oversimplify the problem. “Not every student will go to college and be a math major…but they still need a good foundation in mathematics. I’m not saying we should dumb down the curriculum; what I’m saying is that we should create a curriculum that meets the needs of kids where they are. If a problem were as simple as when should we teach algebra, we could solve it very easily. It’s about teaching math at all levels so kids can make sense of mathematics.”
Added Gojak: “I’m not opposed to kids who are ready for algebra to get it early…[but] I don’t believe that all kids need to take it in the eighth grade.”
She said middle school math curriculum should give students room to explore different math topics that might interest them, and that pushing students into abstract math before they’re truly prepared for it can be detrimental.
Students should all be exposed to some algebra at some point, but equally important, Gojak said, is a solid understanding of how math concepts work, as well as an ability to see and apply math in real-life situations. This, she said, will lead to thought and discussion about what algebra courses should include and what students should take away from the course.