Algebra: Changing the Equation
When U.S. Secretary of Education Margaret Spelling announced in March the final report of the National Mathematics Advisory Panel, created by President Bush two years ago to address concerns that many students lack essential skills to become engineers and scientists, she highlighted the importance of algebra. "The panel's research showed that if students do well in algebra, then they are more likely to succeed in college and be ready for better career opportunities in the global economy of the 21st century," Spellings stated. The panel advised that all school districts provide access to algebra for all prepared students-including more as early as eighth grade.
As most administrators know, algebra opens the door to all high school math, says Cathy Seeley, a senior fellow at the University of Texas at Austin's Charles A. Dana Center, which supports K12 education with a focus on mathematics and science. "It's a basic college entrance requirement, so any student who is even possibly going to do postsecondary education needs to pass to keep their options open," she adds. For many students, Algebra 1 is the first math class that requires abstract thinking and problem solving, skills that are invaluable even if a student never uses algebraic standards like the quadratic equation at work.
Unfortunately, algebra is also a key part of the panel's focus and recommendations because it derails many students. "For far too many kids, algebra becomes their first mathematics stumbling block," says Francis "Skip" Fennell, a member of the math panel and outgoing president of the National Council of Teachers of Mathematics. "There's a difference between struggling and frustration. Struggle with a subject and it might take a little time, but there's a level of completion and satisfaction. Frustration is when a student flat out feels like he or she can't do it and walks away and doesn't come back."
Districts around the country are trying a mixture of strategies to help those students who have failed algebra and to better prepare others before they even step into an algebra class. For students who have already failed Algebra 1, there are credit recovery programs that allow them to pass the algebra test without having to retake the class. For students who are behind in math prior to taking algebra, bridge programs help ensure that they have the right concepts in hand before Algebra 1 starts. And better teaching and class structure during Algebra 1 help ensure they can succeed once the course has begun. For the next generation of high school students, exposure to elementary and middle school coursework that introduces abstract concepts means that algebra does not have to be such a stumbling block in years to come.
The Dropout Factor
The consequences of frustration with algebra are clear. The panel's report notes that only 23 percent of grade 12 students are at or above the proficient level in mathematics on the National Assessment of Educational Progress (NEAP) and that there is a growing demand for remedial math education among students entering four-year colleges and community colleges nationwide.
With the concern over algebra success in American schools comes its relationship to high school dropout rates. Los Angeles Unified School District superintendent Roy Romer has stated that algebra is a trigger for more dropouts than any other subject, and a 2006 study at Florida International University found that students who failed Algebra 1 were four times more likely to drop out of high school than those who passed the course.
The trend now is that more states are requiring algebra in high school: More than 20 states require high school algebra for a diploma and/or hold students accountable for algebraic concepts on high school exit exams, according to the Education Commission of the States. Another nine states have policies that will go into effect with future graduating classes. In fact, the latest trend is for states to be adding Algebra II as a requirement for a diploma.
School districts that require all students to pass algebra are faced with a dilemma: how to make sure that their high mathematical standards aren't pushing some students out of school altogether. Asking more of students can actually help decrease dropouts-but it has to be done right with smart programming and student encouragement. (See sidebar.)
Even with a dropout rate at a mere 6 percent, Rockingham County Schools in Greensboro, N.C., takes the issue seriously, according to Terry Worrell, the district's assistant superintendent for curriculum and instruction. For example, dropout counselors give advice to students who are showing signs of leaving school in early grades-such as failing multiple classes-and even find teenagers who have already dropped out, helping them get the credits they need for a diploma.
This school year, the district added an online credit recovery program to help students who have failed algebra and other courses. In Rockingham schools, students typically take Algebra 1 in eighth grade. With the Apex Learning System, a digital curriculum that includes guided instruction and incorporates audio, video and graphics to provide multiple instructional methods for different learning styles, students who haven't been able to pass the course can retake the course in about 80 hours over 80 days on the computer, in a regularly scheduled class with teacher help. If they want, they can move even faster by working after hours as well.
By earning the credit relatively soon after failing the course, students keep from falling far behind their peers. Research from the Consortium on Chicago School Research shows that students who are "on track" at the end of ninth grade are significantly more likely to graduate in four years.
"Algebra 1 is a tough course for some of our students," Worrell says. "Some of it is math anxiety that students develop at a young age, and some is that young adolescents can get discouraged and disengage with school. Our job is to motivate them and help them get through it. We think these programs can do that, and once we get students to believe in their qwn ability, it takes off ."
A similar program gives students at the Aldine Independent School District in Houston a chance to use the PLATO Learning software system to earn algebra credits after failing the course. Like the Apex system, the PLATO credit recovery software is self-paced and offers multiple ways of learning concepts.
"If they're motivated enough, students can recover the credits quickly by going through the materials and taking the proficiency test sooner," says Carlos Varonne, program director of secondary mathematics at Aldine. "If the students weren't successful the first time, then they won't be just by taking the same course again where the material is presented in the same way. That's why differentiated instruction is so important."
The Aldine district also has programs designed to help ensure that students don't fail Algebra 1 in the first place, a strategy that is popular in many districts. In California, according to the state educational framework, students should be entering ninth grade already having fi nished algebra. For those that haven't, MIND Research Institute has been pilot testing in 11 middle and high schools throughout California a one-year Algebra Readiness program, which uses visual diagrams with accompanying software to present ideas in new, accessible ways. The curriculum walks struggling ninth-graders through the essential math concepts that were covered in grades 2 through 7. The program is designed to ensure that students have a clear grasp on the underlying concepts leading up to algebra that experts say are necessary to be successful once students take the course.
"It's not like pre-algebra, because it literally goes back and rebuilds that foundation," says Andrew Coulson, president of the education division for MIND Institute. "Our approach is to use accessible rigor and visualization to show how the concepts work."
Oxnard (Calif.) Union High School District has one high school class using Algebra Readiness this school year. With a largely immigrant, low-income student population, the district has struggled for several years to ensure that all of its students at six traditional and two alternative high schools succeed in algebra. Jim Short, a district math specialist, says that about a quarter of its students could use help to be ready for Algebra 1. "In our program [with Algebra Readiness], most students are engaged and learning, and their scores on tests so far show that," Short says. "The real proof will be when they move on to algebra, but we're very optimistic."
Seeley says that bridge programs such as Algebra Readiness can help students make the transition from standard arithmetic in traditional elementary and middle-school math to the more abstract ideas that are required for algebra. The Dana Center runs a program, Academic Youth Development, for districts around the country that identifies eighth-graders who are struggling with math and are also social leaders in the school. The summer course includes math content that extends K8 math concepts to prepare students for Algebra 1 alongside youth development coursework on such concepts as being a school leader and how the brain works. The combination is more interesting to students than just a summer math class, Seeley says.
Math in LA
To help struggling students in the Los Angeles Unified School District pass algebra, some LAUSD schools have adopted an optional double-block Algebra 1 course, which means ninth-graders have two periods of algebra a day-the fi rst following a relatively standard curriculum and the second a course specially designed to help students with weakness in the subject, including a more hands-on approach, such as going through a concept in a much more contextual manner. It's a strategy that is catching on around the country and, according to some experts, is a better approach than stretching Algebra 1 into two years.
However, how both double-block and standard Algebra 1 are taught is even more important than the curriculum, say administrators in charge of Los Angeles' secondary education. "We have a particular focus on how to get students into the task, make it relevant and engage them," argues Jeanne Ramos, the director of secondary mathematics for LAUSD. "Too much secondary math is taught in a way that is delivered as 'This is what I will show you, and you memorize it and then regurgitate it.' "
LAUSD administrators are working to develop a mixture of instruction, practice and coaching in its math classrooms. For example, infusing rigorous tasks into all high school math allows the students to explore key foundational ideas for themselves, in some cases over the course of several days. The district has also drawn up dozens of concept lessons for math courses starting in grade 6-where students are given a real-world task and asked to brainstorm about ways to solve it-that give the class an opportunity to explore why math is important in the real world and how to think about its application.
Bridge programs and rethinking how algebra is taught are designed to help students take the step up from the relatively concrete arithmetical concepts they've learned or should have learned in elementary and middle school to the abstract thinking that is required in algebra.
In Los Angeles and many other districts, a parallel approach to these programs is to rethink math in lower grades so that in years to come, students won't find the subject as nearly as big a step. "You can't start the first day of ninth grade with algebra," says Shelley Weston, LAUSD's assistant superintendent of secondary instruction. "The mathematical skills of thinking need to begin at an early age. We need to begin with concepts in third and fourth grade."
The Rockingham County district is launching next year a new math program districtwide with the same goal of starting younger. Math Foundations, which features more manipulatives and problem solving, will be used in elementary school. "We're really rethinking how we've taught mathematics in the past," Worrell says. "We hope that the program will build a generation of students who're ready to take advanced math courses."
With tomorrow's high school students becoming better prepared for algebra, and today's being helped to succeed with strategies as varied as double-block schedules and bridge coursework, districts are already trying to answer the call from the math panel around algebra and schools. The next question will be: What works best and how can it be used to ensure every student succeeds?
Carl Vogel is a freelance writer based in Chicago.