Addressing the Algebra Crisis
In recent years, many jurisdictions throughout our country have experienced their share of educational crises – such as “whole language“ and “fuzzy math“ in general – and “TERC” in particular. Even now, the state is still in the grips of an “algebra crisis.”
The problem became apparent 20 years ago when the report A Nation at Risk warned of a "rising tide of mediocrity" in the public schools. The report claimed that too few students were taking the more rigorous courses in high school. Twenty years later, enrollment in college-prep courses is way up; unfortunately however, evidence indicates that student learning is about the same as it was back then.
In this decade, some reports have stressed the importance of algebra in middle school; students who succeed in algebra usually do better in the rest of school and in their careers than those who do not. Well-intentioned school boards and administrators often hope that early enrollment in algebra will reduce the achievement gap attributed to race or family income, as enrollment in middle-school courses called "Algebra" have increased. Judging from results on objective statewide tests, however, many middle-school students are not learning the subject, even those with passing grades.
The strongest predictor of failure to learn algebra is not race or income; it is a lack of adequate academic preparation. The problem begins before students get to their first algebra class. Many school districts have watered down the content of pre-algebra courses, removing important but difficult and essential material. The districts want more students to pass math classes, and they want to guarantee high pass rates by making the classes easy. Unfortunately, classes without content set students up for later failure in algebra.
The depth of the problem varies. In some schools, the percentage of eighth-grade algebra students is moderately correlated to scores on typical standardized tests. In those schools, algebra readiness is still being used as part of the placement decision.
In other schools, placement decisions appear unrelated to academic preparation. In the worst cases, most, or at least a significant number, of students are placed in algebra by eighth grade, regardless of readiness.
Some school districts seem to be guiltier of misguided placement strategies than others. The results are often disastrous. Failing to learn algebra in eighth grade results in large numbers of students repeating algebra in ninth grade, even though success is not ensured the second time around.
If repeating algebra in ninth grade is out of the questions in a number of households, then the rush toward “tutoring” comes in. Teachers and/or schools, and/or textbooks, and/or school climate, and/or large classes, and/or student apathy, and/or other “bad” students become ready targets of blame for the failure of students to master algebra by eighth grade. Readiness, or lack thereof, seldom enters the equation as a possible reason for such failure.
Admirably, many states now embrace the learning of algebra by the end of eighth grade as a long-term goal; however, the strengthening of academics from kindergarten on is necessary before this goal can be fully met. Algebra placement rates ought to depend on student readiness. Seventh-grade student scores on standardized tests should at least be important factors in student placement in eighth-grade courses.
At times, individual state policy adds to the problem. For instance, middle schools receive more credit on California's accountability index for eighth graders who take the algebra test than for those who take the general math test. This encourages school districts to place too many students in eighth-grade algebra. The state should discourage algebra over-placement by taking away some credit on the accountability index for algebra exam failures.
To make things worse, in recent years the push in many school system has been to start as many super-advanced seventh graders as possible into Algebra I. Back in the 1980s, it was considered a privilege for an eighth grader to be placed in Algebra I. These days many seventh graders, as a result of parental and peer pressure and ill-advised administrators, are taking Algebra I, even though most are not developmentally ready to do so. These students end up in a formal Geometry class as eighth graders, when most are even less ready to tackle conjectures, theorems, and proofs.
It is, however, a reality – a political reality – that schools must deal with. Algebra I by the end of eighth grade is concept that is here to stay.
At the independent school where I work, The Barnesville School, a good number of students take essentially two years to study algebra. As seventh graders, these folks are given a hard-nose, very traditional Algebra I course, (none of that “Analysis” stuff), with lots of problem-solving opportunities thrown in as warm-up and class activities.
As eighth graders, these same students are not accelerated upward into a Geometry or Algebra II class. Vertical acceleration is not the answer at this stage in the development of many middle schoolers. Instead, I expose them to a course designed for them to apply the algebra they know. In the process, they’re also exposed to informal geometry (no proofs, but lots of content such as the Pythagorean relationship, similarity, and trigonometric functions).
Part of this eighth grade course, entitled “Applications of Algebra and Geometry,” also includes the study of combinations and permutations, probability. These are topics that are only superficially dealt with in middle and high school math courses. These students go into considerable depth into mathematical subjects that challenge conventional wisdom and help them understand numbers and how humans use them to make sense of the world around them.
So, if Algebra I is to be mastered by the conclusion of eighth grade, then let us think about having students exposed to two years of algebra – one generally to learn the basics, the discipline, the problem-solving methodology and structure; then a follow-up where these basics are applied consistently, every day. Time for study and reflection is what middle and high school students need, yet schools seldom provide it due in part to curricular, physical, and time constraints.
This “algebra crisis” is serious, yet not terminal. Algebra for all is good; without conceptual changes, however, we could end up with algebra for none.
Any comments? E-mail me at firstname.lastname@example.org