A New Age for Algebra
Solve for x. While many of us first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS mathematics assessment, and American fourth-graders were outperformed by students from eight other countries, including England, Latvia and Kazakhstan. Algebra specifically has a reputation as a gateway to achievement, not only in math, but also in high school, college and work. According to a 2008 report by the California Dropout Research Project, failing algebra I had a "particularly severe impact" on dropout and delayed graduation rates in the Los Angeles Unified School District. Kadhir Raja, a ninth-grade algebra instructor, author and 2011 California Teacher of the Year, has an idea why the course acts as a crucial turning point. By the time high school freshmen reach algebra, some have been struggling with math for a long time. Then comes algebra with its "intimidation factor," he says. Abstract terminology and remoteness from everyday life make it seem difficult and irrelevant, leading to poor performance and disenchantment with math and school. "When students fail over several years, they internalize that they are supposed to fail; success is not meant for them," says Raja.
Algebra = Success?
With mathematical thinking critical for employment in science, technology and engineering, as well as mere survival in the 21st century, educators are renewing their focus on early pathways to math achievement, particularly algebra. "In algebra, you learn so much more than just how to calculate," says Judy Zimny, a former principal in the Dallas Independent School District and chief program development officer at ASCD (formerly the Association for Supervision and Curriculum Development). "Algebra is about how to find the unknowns, how to organize information, how to think critically, how to make decisions and how to see patterns," she says. Such foundational cognitive skills are necessary for success not only in school but also in higher education and the modern job market.
Mike Shaughnessy, president of the National Council of Teachers of Mathematics, says, "It's surprising how many different professions and disciplines require algebra, especially because they end up involving statistics, which are represented using algebraic expressions and equations." Zimny adds, "Algebra also provides a lot of the language that is used at work, especially for people like electricians and engineers."
The rush to cover algebra is not just about keeping up with the Joneses, Singhs or Nakamuras. According to the U.S. Department of Labor, many of the country's fastest-growing occupations, such as network systems analysts and financial examiners, clearly require advanced mathematical skills. In July 2011, the U.S. Department of Commerce reported that people in STEM occupations earn salaries that are, on average, 26 percent higher than those of non-STEM workers, and people with degrees in STEM earn more than others without such degrees, regardless of occupational field.
To successfully enter and complete a STEM program, students need to learn advanced math—typically defined as courses above algebra II—before college. "It's about having more sophisticated and advanced ways to think about things," says Steve Ritter, co-founder and chief scientist at Carnegie Learning, a math textbook and software developer. "Calculus happens to be important in a lot of engineering fields, and statistics is another area that can give you a huge advantage in understanding the world around you."
Curricular policies and enrollment statistics reflect the growing recognition of algebra's importance as a prerequisite for advanced study. The Common Core State Standards for mathematics, which have been adopted by 46 states and U.S. territories, have children solving systems of linear equations in eighth grade. Nationwide, 31 percent of eighth-graders said they were taking algebra in 2007, according to researchers at the Brookings Institution. While the National Center for Education Statistics reports that 35 percent of high school juniors earned credit in algebra II in the 2003–2004 school year, today's eighth graders who take and pass Algebra I will have the option to take Algebra II as high school sophomores, if they take Geometry as freshmen.
Despite these enrollment trends, algebra remains a challenge for many teenagers. In a 2010 survey of 22 postsecondary math instructors, University of Connecticut researchers Jeffrey Corbishley and Mary Truxaw found that nearly all considered algebra a very important prerequisite for college-level math. Unfortunately, the respondents rated incoming undergraduates' knowledge of various algebraic topics as "poor" or "very poor."
Identifying Variables for Success
How is it possible that increasing numbers of middle school pupils are enrolling in algebra, yet college students are matriculating with inadequate skills? One explanation is that pushing children into an algebra course when they are not ready sets them up for failure. Jerry D. Weast, former superintendent of Montgomery County (Md.) Public Schools, says that an analysis of some 34,000 records of college-bound graduates during his 12-year term, which recently ended, revealed that most of them had completed algebra in eighth grade. That does not mean, however, that early algebra is a magic bullet. "If you don't prepare children in early childhood and elementary school, then it's too much of a change to ask them to do algebra in middle school," he says.
Shaughnessy agrees. He advises district administrators, "Look at what kids can do; do a little formative assessment and see how they're doing on ratio, percent and proportion." Only when pupils have mastered these and other basic topics, he continues, is a full-fledged algebra curriculum appropriate. To this end, the NCTM encourages schools to introduce algebraic thinking, concepts and subskills from the earliest elementary grades.
Preparation for algebra also includes getting everyone excited about math. Instead of what he calls "naked algebra," in which the material is taught abstractly in isolation from its applications, Shaughnessy advocates making algebra more interesting by integrating it with other subjects, such as science and history, and other foundational mathematical topics, such as geometry and statistics. Corporations hungry for talent in STEM disciplines share this goal. The large government and defense contractor Raytheon, for example, sponsors several math competitions, scholarships and activities.
Best methods for teaching algebra is also an area of significant research and debate. In September 2010, the American Educational Research Association published a review of instructional methods in algebra that examined 82 studies involving more than 22,000 participants. The greatest gains came from programs that prioritized conceptual over procedural understanding. Multiple Solutions When searching for new ways to improve algebra education, district administrators have a plethora of choices, many of which have solid evidence of effectiveness. For example, Carnegie Learning, which was recently acquired by the Apollo Group, offers widely used mathematics curricula that blend computer-based learning with textbooks. In their algebra courses, Ritter says, "the Cognitive Tutor software works continuously to evaluate student knowledge and individualize instruction using adaptive learning technology, while the classroom activities emphasize collaboration, problem solving and communicating about mathematics, which is not done as well on software." (Read about the innovative algebra programs in related stories, "Innovative Products and Programs for Teaching Algebra".)
The teacher plays a crucial role on both sides of the equation. For example, instructors provide just-in-time assistance when students are using the software to review math lessons and do problem sets. In a recent experiment at the Moore (Okla.) Independent School District, students who were randomly assigned to classes using Cognitive Tutor outperformed others taught by the same teacher with a traditional textbook on the Educational Testing Service's algebra I exam. Another well-established company, Texas Instruments, offers a technology-based solution that can be used in any math class. The TI-Navigator system wirelessly connects individual Texas Instruments calculators to a central device, allowing teachers to monitor what students are doing on their calculators in real time. "What you need to see is how they are thinking," Zimny says. "That's where the math concepts come in and misunderstandings come in, and that's where you want to be able to redirect and guide them." Instead of exhorting pupils to show their work, Zimny says, teachers can use the TI-Navigator system to assess understanding and tailor lessons at any time.
A relative newcomer to the educational technology scene, the nonprofit MIND Research Institute offers a blended approach particularly suited to schools with high ethnic and linguistic diversity. Working in a computer-based, gamelike environment, students guide an animated penguin named Jiji past obstacles by using math. For example, a simple algebra problem shows Jiji standing in front of a gap in her path. Above this obstacle are two sets of blocks, which are stacked on top of each other to illustrate the expression "2x." Repairing Jiji's path requires selecting the correct number of blocks to fill the gap. "The unique feature of our program is that we introduce math concepts without the use of language, numbers or symbols," says co-founder Matthew Peterson in a demo video on the organization's Web site. "Students can be problem solvers right away."
District administrators can implement innovative algebra curricula even without investing in new computers, software or handheld devices. A mathematics curriculum for middle school, Big Ideas Math, combines collaborative discovery learning with direct instruction to instill a set of fundamental concepts. Created by Ron Larson, a professor at Penn State and renowned author of mathematics textbooks, and Laurie Boswell, an experienced math teacher, Big Ideas Math grew out of the NCTM's Focal Points for K8 and the Common Core State Standards. "Each year, textbooks became thicker and thicker because of different state standards. Textbooks were sometimes 1,000 pages long, and Ron really wanted to fight that," says Denise McDowell, vice president of sales and marketing at Big Ideas Learning, which created Big Ideas Math. "Every student can be successful in algebra I if they have the foundations that lead up to it. And that is precisely what a narrower and deeper curriculum will help you do," she says. Though it has only been out for a year, Big Ideas Math has been implemented in 30 school districts in Florida, and in 2010, it won a Textbook Excellence Award from the Text and Academic Authors Association.
Making it Work
Regardless of the program or product you use, professional development cannot be ignored. "Even if you've got a good algebra curriculum, that alone won't save you. You have to have people able to execute it with quality and skill," says Weast. Montgomery County's schools have tried many strategies for teaching algebra, but Weast's advice is simple. "Invest in your workforce," he says. One lesson he has learned is that enhancing teachers' skills takes time and requires them to develop both content and pedagogical knowledge. Once that is achieved, however, a district will have the capacity to implement many different curricula or programs, rather than having to take a one-size-fits-all approach.
Just as no educator would argue that a child should be placed into algebra without proper preparation, none of the programs and products can be effective without their being supporting resources for instructors and administrators. Workshops, online training, site visits by external program staff, and ongoing evaluation are all potential components of a successful change in curriculum or pedagogy. In the end, though, algebra alone does not guarantee success in school or a STEM career. "For every student to be able to survive any math class," Raja says, "you've got to have consistent teaching, every year, every class."
Lindsay Oishi is a freelance writer and doctoral candidate in educational psychology at Stanford University in Palo Alto, Calif.