Algebra I has long served as a gateway to higherlevel math courses and science courses, such as physics, and has been required for high school graduation as well as admission to most colleges. But taking algebra also can turn into a pathway for failure, from which some students never recover. In 2010, a national U.S. Department of Education study found that 80 percent of high school dropouts cited their inability to pass Algebra I as the primary reason for leaving school.
What’s more, failure to pass state algebra assessments is a more frequent problem for minority students and contributes to a serious achievement gap in math. In the 2012 results of the California Standards Test (CST) in Algebra I, for instance, just 39 percent of Hispanic eighth graders scored proficient or advanced, as did 20 percent of Hispanic ninth graders. The results for African American students in the two grades were 32 percent and 16 percent, respectively. In contrast, white students tested at 60 and 34 percent proficiency or better.
Members at a recent District Administration Leadership Institute speak about algebra programs in their districts. Click video to view.
It should come as no surprise that algebra poses a formidable challenge for all students, who must get used to a brave new world of variables, coeffcients, and quadratic equations. The problems posed by algebra are numerous, though, say experts in mathematics education, math teachers, and administrators. So are the solutions that a number of school districts have implemented.
And while those district leaders are looking toward the Common Core State Standards in Algebra I to uniformly improve the quality of algebra teaching and learning, they also have resorted in the meantime to their own innovative approaches. They include screening for students equipped to take the course as early as eighth grade, more effectively engaging all algebra students in the classroom, creating real-life, concrete examples of algebra in everyday life, and better managing individual student progress.
The Problem with Algebra
“Algebra I is an entire math course that focuses for the first time on students’ abstract thinking in math classes and on the symbols which represent that thinking. It’s more conceptual,” points out Nigel Nisbet, the director of content creation at the California-based MIND Research Institute, which develops interactive K12 math programs. Many students have considerable diffculty making the transition to that kind of thinking, Nisbet adds.
Coleman Kells, principal of the Earhardt Middle School in the Riverside (Calif.) Unified School District, says that while algebra is considered a critical course in a high school career, too many algebra courses have fallen short and left students confused and unsuccessful. “Algebra classes can be either doorways (to success in school and afterward) or barriers,” Kells observes, adding that, too often, students have not understood the concepts and operations in that subject.
Daniel Chasen, a professor of education at the University of Maryland, insists that there are larger educational issues at stake in taking algebra, mostly for struggling students. “It’s going to be a place where student disengagement from school is going to show up, especially for kids skeptical of schooling,” he says.
A big part of the problem, adds Evie Eddins, a math program specialist for grades 6 through 12 at the Sarasota (Fla.) County Schools, is getting teachers to focus on real-world uses of the formulas and operations posed in algebraic problems, which would make the subject more understandable—and interesting—to students. “What’s been lacking is the teachers’ understanding of how the math is used— how the curved surface of a car headlight determines how that light shines on the road or how to determine the amount of paint required to cover the curved surface of a thermos,” Eddins explains.
The Promise of the Common Core
As far as solutions go, math teachers and math curriculum specialists are anticipating, with some trepidation, the implementation of the Common Core State Standards. In most states, those standards will go into effect in the 2013-2014 academic year or in 2014-2015.
For starters, the Algebra I standards will follow the Common Core model of increasing rigor, resulting in more pressure on students and teachers. In Georgia in the 2011-2012 year, almost 59 percent of students failed to achieve proficiencyon a brand new, end-of-course statewide exam in Algebra I tied to the Common Core standards in that subject. That percentage exceeded the 53 percent of students who had failed the test a year earlier, before more demanding Common Core elements were incorporated.
Educators like Riverside’s Coleman Kells and Sarasota’s Evie Eddins look forward to the Common Core’s small number of standards—barely a dozen—which will ensure in-depth coverage for each standard compared to the relatively thin coverage resulting from several dozen standards previously in place.
Another attraction of the Common Core is a marked emphasis on real-life uses of otherwise abstract algebraic thinking. Although district administrators are free to devise with their own examples, the Common Core website for Algebra I offers suggestions.
Two examples might be estimating how much water and food is needed for emergency relief in a devastated city of 3 million people and how those supplies might be distributed; or designing the layout of the stalls in a school fair so as to raise as much money as possible. “Instead of memorizing formulas,” says Kells, “students will study (algebra’s) applications.“
And even though Sarasota County students placed second in Algebra I proficiency among all the districts in Florida in 2011-2012, Eddins says the uniformity of the Common Core standards will provide a valuable way of measuring how the results of her district’s students compare to those in other states.
Success So Far in Sarasota
The Sarasota County Schools, and other districts around the country, have not been waiting for the launch of Common Core standards in Algebra I, Eddins reports. The algebra teachers are teaching differently from what they have in the past, and their approaches are paying off, with 71 percent of all Algebra I students achieving proficient or advanced status on the very first Florida Comprehensive Test in Algebra I last spring.
Eddins explains that now, the district’s math teachers more carefully identify eighth graders deemed capable of taking the course and who fulfill at least four of five criteria, including high math grades and scores, to qualify for Algebra I. That approach has paid off and last year, nearly 100 percent of the eighth graders who took the course proved proficient or better.
Sarasota County students take Algebra I in ninth grade, and almost 70 percent of them achieved proficiency or advanced standing last year.
Second, Algebra I teachers undergo professional development during the school day to better help them use connections between algebra and real-world applications, whether to graph the acceleration or deceleration of a racing car or analyze the arc of a basketball during a jump shot.
When Florida districts only had to meet 20 state standards in Algebra I, from almost 40 over the past decade, it helped proficiency rates, Eddins says. “We’re looking at teaching for depth and understanding,” she adds.
Fewer standards means teachers can spend more time and go into depth in Algebra I standards such as “Linear, Quadratic, and Exponential Models” and “Solving Systems of Equations.” And Florida’s adoption of the Common Core standards in Algebra I will help all students, Eddins says, because the standards place a premium on the more concrete ays that formulas and operations relate to everyday life.
The district has also created more frequent assessments to better track students’ progress and work with those falling behind. Three years ago, Eddins worked with the district’s math teachers to create district mathematics benchmark assessments. administered three times per year to Algebra I students. (Separate benchmark assessments covered K8 math as well as geometry.) The computer-based assessments take place three times: in early fall, the end of the first semester, and in early spring.
Most Sarasota County students take Algebra I in the ninth grade. Those who do not pass the Florida Comprehensive Test in Algebra I in ninth grade can take a two-week summer program offered by the district preparing them for a retest. For those who do not pass the retest, or who do not take the summer program, the district’shigh schools also offer a semester-long remedial algebra course, which failing students can take in the fall or spring prior to testing again.
“None of us are satisfied,” Eddins says of last year’s 71 percent proficiency rate. “But considering the newness of the test, it’s a good starting point.
A High-Tech Solution
Earhardt Middle School in California, meanwhile, piloted a program in two Algebra I classrooms during the 2010- 2011 year using the HMH Fuse program, which included using iPads and specialized apps, developed by Houghton Mifflin Harcourt and which included an online version of the publisher’s Algebra I textbook. The results were impressive: 78 percent of those students using the Fuse curriculum attained proficient or advanced scores on the 2011 California Standards Test for Algebra I, 19 points higher than two Earhardt classes which had simply learned from the paper version of the HMH textbook.
The Fuse students had ready access online to their textbook, as well as to formative assessment, that showed where they were wrong in solving a problem. With every right answer, they could bring up several more problems at the touch of a finger on the screen.
And the e-textbook’s author, Edward Burger, a mathematics professor at Williams College and a former comedy writer for Jay Leno, draws in students with 400 video segments on the iPad that give entertaining lessons on algebraic equations, most of which they watch at home or outside of class. “You wouldn’t think an algebra video would be entertaining. This guy was exciting to listen to,” says Jay McPhail, Riverside USD’s technology coordinator. “I wanted to go back and take algebra again.”
During class time, teachers focus on individual student progress. “We think it’s the game changer,” McPhail says of the Fuse program.
After the pilot year ended, the school continue the FUSE program in two Algebra I classes. “We’re not where we want to be,” Kells says. “But our results are much higher than they were and are showing us a pathway.”
What also changed the game, Kells adds, was allowing students to keep the iPads 24/7, which encouraged them to work on algebra games or read during after-school events, and which encouraged parents to watch the videos with their children.
It proved a successful journey. “The goal is to have everyone pass algebra by the time they leave here,” Kells says. “Our struggle is to get them from ‘okay’ to ‘good.’”
Progress on Main Street
For three years, the Main Street Middle School in the Soledad (Calif.) Unified School District has taken professional development seriously. And since 2005, when only 4 percent of the eighth graders in Algebra I were proficient and none were considered advanced according to the state test, the school’s algebra program has improved. Last year, 46 percent of students taking algebra were proficientand 24 percent were advanced, says Principal Amelia Jimenez.
More than half of the school’s eighth graders, 90 percent of whom are Hispanic and more than half eligible for the free and reduced-price lunch program, take Algebra I. The remaining eighth graders take Algebra Readiness.
Three years ago, the school implemented the “Explicit Direct Instruction” program (EDI) from DataWORKS Educational Research for all subjects. Teachers are trained for three days before the school year starts with two more professional days during the school year. The training introduces the practices of EDI.
Once in class, teachers carefully follow those practices. They begin each class by reviewing what students have learned in previous classes as it relates to the day’s lesson. Another EDI requirement is that every daily lesson has a specific objective, such as “compute the x- and y-intercept and graph a linear equation.”
“Teachers are constantly checking answers and stopping to re-teach” students who give wrong answers, Jimenez says, another feature of EDI training.
The students have their own whiteboards, consisting of a plastic sheet over a piece of paper and an erasable marking pen, on which they try to solve problems. The teacher asks students how they came to the answer, and if 80 percent or more have the correct answer, she moves on. Students also get a one- or two-question “exit quiz” near the end of class.
Students who answer correctly receive a more challenging question for homework, while those who do not rework the problems at home.
As to the question of whether algebra is necessary, Jimenez offers an unwavering answer. “It’s the gateway to higher math courses. If we took algebra away from some of our students, we’d be closing doors and taking away opportunities from them.”