Ten years ago, the highly respected mathematician Lynn Arthur Steen wrote an article entitled, “Algebra for All in Eighth Grade: What’s the Rush?” Well, now we know what the rush is…or do we? Steen sets up the issue with a couple of rhetorical questions:
How can a subject that for many adults serves as a metaphor for frustration suddenly be the top priority for soccer moms and internet dads? And why do so many parents suddenly demand of their schools and their children something they themselves neither mastered nor loved?
He then proceeds to give several arguments in favor of algebra: it provides access to higher education and jobs, it is the language of the information age, it is the mark of a rigorous education… in short, it is “the key to access in our technological society.”
But then come the counterarguments:
- Relatively few students finish seventh grade prepared to study algebra. At this age students’ readiness for algebra — their maturity, motivation, and preparation — is as varied as their height, weight, and sexual maturity. Premature immersion in the abstraction of algebra is a leading source of math anxiety among adults.
- Even fewer eighth grade teachers are prepared to teach algebra. Most eighth grade teachers, having migrated upwards from an elementary license, are barely qualified to teach the mix of advanced arithmetic and pre-algebra topics found in traditional eighth grade mathematics. Practically nothing is worse for students’ mathematical growth than instruction by a teacher who is uncomfortable with algebra and insecure about mathematics.
- Few algebra courses or textbooks offer sufficient immersion in the kind of concrete, authentic problems that many students require as a bridge from numbers to variables and from arithmetic to algebra. Indeed, despite revolutionary changes in technology and in the practice of mathematics, most algebra courses are still filled with mindless exercises in symbol manipulation that require extraordinary motivation to master.
- Most teachers don’t believe that all students can learn algebra in eighth grade. Many studies show that teachers’ beliefs about children and about mathematics significantly influence student learning. Algebra in eighth grade cannot succeed unless teachers believe that all their students can learn it.
So, where does this leave us? Steen’s conclusion is a sensible one: everyone should take algebra, but not necessarily in eighth grade. As the title of his article asks, What’s the rush?
The rush is that many states, including California and Massachusetts, are now mandating algebra in eighth grade, which moves the argument from whether we should implement this to how we should implement it; Steen’s four bullet points are real, and passing laws won’t wash them away. This is not to say that all eighth-graders really do study algebra, but Weston is surely not the only system in which Algebra I is simply not even offered at the high school: we expect all incoming ninth-graders to enter with an Algebra I background. I don’t know about other school systems, but Weston has attempted to address all four of Steen’s points, though the frst three are of course easier to remedy than the fourth. Nationwide about one third of eighth-graders study algebra, for better or for worse. Weston, of course, is Lake Wobegon, so all of our students are capable of learning algebra in eighth grade.
For much more depth of this question, read Tom Loveless’s article, “The Misplaced Math Student: Lost in Eighth-Grade Algebra,” or his full report from the Brown Center of the Brookings Institution. Here are a few interesting excerpts from this 16-page document:
At first glance, this appears to be good news… Research also suggests that students who take algebra earlier rather than later subsequently have higher math skills. These findings, however, are clouded by selection effects — by the presence of unmeasured factors influencing who takes algebra early and who takes it late…
The push for universal eighth-grade algebra is based on an argument for equity, not on empirical evidence. By completing algebra in eighth grade… students are able to take calculus in the senior year of high school… From this point of view, expanding eighth-grade algebra to include all students opens up opportunities for advancement to students who previously had not been afforded them, in particular students of color and from poor families. Democratizing eighth-grade algebra promotes social justice.
One catch. Course-taking is a means to an end, not an end in itself. Students take math courses to learn mathematics. Will policies mandating algebra for all eighth graders mean that the nation’s students learn more math? Not necessarily…
Loveless then goes on to cite statistics that show that “the typical eighth grader in an advanced math course knows less today than in 2000.” Hmmm…
…Any teacher who stops to teach misplaced students fractions shortchanges the well-prepared students who sit in that algebra class… There will be advocates, despite the data presented here, who will continue to argue for placing low-performing eighth graders in algebra classes. They believe that a more rigorous course is always preferable to a less rigorous one. Many do not believe that students must learn basic mathematics in order to successfully tackle higher-level mathematics… Algebra teachers already feel the strain of such unrealistic expectations.
Anyway, do read the entire article.
Here are some excerpts from Loveless’s conclusion:
One hundred twenty thousand students are misplaced in their eighth-grade math classes. They have not been prepared to learn the mathematics that they are expected to learn… Two groups of students pay a price. The misplaced eighth-graders waste a year of mathematics, lost in a curriculum of advanced math when they have not yet learned elementary arithmetic… Their clasmates also lose — students who are good at math and ready for algebra. These well-prepared but ill-served students also tend to be black and Hispanic and to come from low socioeconomic backgrounds. Teachers report that classes of students with widely diverse mathematics preparation impede effective teaching, that too many students arrive in algebra classes unmotivated to learn… Universal eighth-grade algebra is creating more problems than it solves, with 120,000 students not learning the mathematics that they need to know and hundreds of thousands of their classmates paying an educational price along with them.
Fortunately Weston is different. But read the whole article, as I said above.
On a slightly different but closely related matter, I need to mention a comment I overheard at the next table at Tavolo: “I don’t understand why kids have so much trouble with algebra. It’s nothing but finding the value of x.” No, that’s not what algebra is about. Sigh.