The firestorm over California's decision to require all eighth-grade students to take Algebra 1 provides a remarkably good overview of much of what is wrong with the state of math education in the country today: The focus is in the wrong place, and the real problems remain unaddressed.

California's decision to require all eighth-grade students to take Algebra 1 was driven by federal requirements of standardized testing, when someone in Washington noticed that some eighth-graders were being tested on sixth- and seventh-grade standards.

In truth, California doesn't have any eighth-grade standards in mathematics. From kindergarten through seventh grade, students are taught and tested on a variety of math topics, including arithmetic, measurement, statistics and probability. Algebraic reasoning is also taught in elementary school, beginning very early and growing into a fairly substantial part of the sixth- and seventh-grade curricula.

Algebra 1 is, incrementally, the next step in the process after seventh grade, not a quantum leap to a whole new realm of mathematics. Students who have successfully completed seventh-grade math are supposed to be ready to take Algebra 1 in eighth grade, in the same way that students who complete sixth-grade math are supposed to be ready for seventh grade.

Whether we teach Algebra 1 in eighth grade or ninth grade, it won't do much good if the students don't remember (or never learned) what they were taught before. My work has led me to believe the skills learned in fifth grade are indispensable for success in Algebra 1, and too many students are progressing through the system without having mastered those. We should be asking why students are arriving in Algebra 1 unprepared, whenever they get there.

Algebra as a 'gateway'

Algebra is frequently referred to as a "gateway" because the class is a requirement for a high school diploma. That imagery is all too apt: The system is designed to make sure students pass through Algebra 1, without regard to whether they understand or remember anything being taught.

Those who are successful in high school algebra frequently pass it by memorizing rules and formulas and using them to get the "right answers" most of the time. Instead of being an introductory course to rigorous abstract thinking, Algebra 1 becomes more like one of the Stupid Pet Tricks we see on late-night TV.

By performing on command — jumping through a series of flaming hoops — students earn the reward of their realm: good grades. By training students to jump through those hoops on the standardized tests, school districts protect their funding. Everyone feels good, but it isn't clear how much is really being learned.

A quick look at California's high school exit exam reveals that the state doesn't consider remembering algebra to be essential: Of the 80 multiple-choice questions on math, 68 are based on sixth- and seventh-grade standards. Only the remaining 12 are from Algebra 1, and there are no questions beyond that level. Students get seven chances to pass, and many still do not.

Arithmetic in college

The prevalence of remedial-level algebra classes in four-year and community colleges is an indication of how big the problem is. This fall, there will be three basic algebra classes taught at California Lutheran University, with subject matter not substantially different from high school's Algebra 1. It is a remedial course we require of students who scored poorly on the Scholastic Aptitude Test (SAT) they took as part of their college applications.

On the first day of that class, I will administer a basic number-sense test. The arithmetic it contains is geared for fifth-graders, but my college students usually struggle mightily with it. Some score as low as 15 out of 40; no student has yet to do better than 85 percent.

Faced with the gaps in their knowledge of basic arithmetic, my students usually resort to blaming their failings on a lack of innate math skills. They explain, in one-on-one meetings, that math just doesn't come easily to them, as if they suffer some disability that must be accommodated rather than overcome with hard work.

During the semester, the students become impatient with any lesson on theory, preferring only to hear how to get "the right answer." They have come to accept the notion that math is about doing, without understanding. One student put it bluntly: "I really don't like all this discussion of why we do things. I much prefer simply to be told what to do so I can do it."

Her admission was all the more striking because she is one of the students studying to become an elementary school teacher. Those students are required to take a class about the concepts behind the algorithms they will someday be expected to teach. The goal in that teacher-training class is to provide students with a deep enough understanding of math to be able to explain why we "carry the one" or what it means when we divide fractions. Before they can ponder these deeper meanings, however, students must already know how to do the arithmetic. They often do not, so we spend much of the time going over material they were supposed to have learned in elementary school, but didn't.

Breaking the cycle of failure

Here is the weak link in the chain of math education, and here is where the attention should be focused — on a commitment to require that elementary school teachers have a strong mathematics background, and that they understand how the basic math they teach provides their students with the building blocks to better comprehension at the next level, not just the skills they need to pass the next test.

The current focus on students in middle school and beyond is too little, too late. While it may sound good to promise "more highly qualified math teachers," most students don't usually meet a "math teacher" until after most of the damage has been done.

Politicians should be talking about providing resources to train elementary school teachers — present and future. Universities should commit to eliminating the need for remedial college algebra classes by focusing on how math is taught in teacher-training programs and how it will be taught in elementary schools. Local school boards should be insisting that current elementary school teachers not only can do the math they are expected to teach, but also understand what they are teaching and why it is important. That's what is needed to make sure students are ready for Algebra 1, whether it is in eighth grade or ninth.

— Victor Dorff of Agoura Hills is a math educator who teaches at California Lutheran University. He has written math exercise books for seventh and eighth grade, pre-algebra and algebra.