On Algebra, High Expectations, and the Common Core

I'm currently working on a long article about the Common Core, which focuses mostly on the new standards' implications for the humanities. But while I was reporting the piece, one thing I heard from critics of the Core was that is might be dangerous to connect high school graduation requirements with the Core's expectation that all students conquer algebra. Why? Because, in the words of Anthony Carnevale of the Georgetown Center for Education and the Workforce, "Education reform has stalled on Algebra 2. The more you demand it, the more drop-outs you have."

In today's New York Times, Andrew Hacker agrees that algebra is unnecessary for most students, though he doesn't mention that because 48 states and territories are planning to adopt the Common Core, the energy in school reform is tilting very much in favor of algebra. Here's the crux of Hacker's argument:

To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.

California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.

“There are students taking these courses three, four, five times,” says Barbara Bonham of Appalachian State University. While some ultimately pass, she adds, “many drop out.”

Hacker suggests that instead of algebra, students should be required to take statistics, a type of math that he sees as more influential in the political and business worlds. He'd like students to spend less time on polynomials and more time learning how the Consumer Price Index is calculated.

There's a strong argument to be made that math is taught poorly in many schools, with little attention paid to how most people are likely to use numbers in the real world, or how math is applicable to economics, the sciences, and government. But this argument also has a disturbing slippery slope quality; if teenagers find any somewhat obscure task difficult (like reading Shakespeare or doing library research), should they be allowed, or even be encouraged, to avoid learning it? A great teacher can often spark interest in a subject a student thought she would never enjoy. One reason to have more rigorous academic standards is to leave open the possibility of that magic happening more often for more young people, and to make sure unfair streotypes about who is "academic" don't prevent kids from discovering unexpected passions. 

These debates are ultimately about tracking: whether it's fair or desirable to expect all K-12 students to work through the same academic standards, or whether it makes sense, especially in the high school years, to do some sorting according to students' interests, strengths, and weaknesses. Many high schools, of course, already sort students through honors, Advanced Placement, and International Baccalaureate tracks; the goal of the Common Core is to get all students performing at those levels.

In other Western nations, such as Germany and Switzerland, it would be considered absurd to say that all 16-year olds should be spending their days learning the same stuff. Nevertheless, that is the tenor of current mainstream education reform thinking in the United States, and I expect we'll be arguing loudly in the coming years over whether that ideology is admirably idealistic or willfully naive. 

7 thoughts on “On Algebra, High Expectations, and the Common Core

  1. EngineersKnowBest

    No student should be granted a degree without passing basic math and by any measure, algebra is extremely basic math.

    Reply
  2. Megan Pledger

    In NZ, in the last three years of High School we have a qualifications course – NCEA Level 1, 2 and 3 respectively. So everyone starts off doing NCEA level 1 in the third to last year of school and keeps going as far as they can/want. So when they leave school they could have a qualification at level 1, level 2 or level 3 (or none). About 80% of kids who attempt level 2 get the qualification. And vocational training after school builds on the same system so it can start at Level 1/2/3/4 and go to Level 7 IIRC.

    This three level High School qualification system means that High School isn’t an all or nothing situation.

    But it’s pretty tough on the kids because it means national exams 3 years in a row.

    Reply
  3. Bruce William Smith

    The north central Europeans have the better approach. Looked at from the perspective of a dual education system, the issue is no longer one of passing algebra in order to earn a relatively worthless high school diploma; preferred is a system wherein every young person can earn a qualification (a sneaky word, with a particular meaning in labor economics not commonly understood by Americans) of more worth than a high school diploma, and one in which one does or does not study intermediate algebra depending upon its relevance to the educational career one has chosen. This means general education for everyone for nine years, not twelve; and in those first nine years intermediate algebra is only attempted in high achieving systems, which ours won’t be even after the introduction of the Common Core.

    Reply
  4. becca

    Aren’t you making an assumption here? That “rigorous standards” (which are usually enforced via standardized testing) can help a “great teacher” to “spark interest” for students?
    I see no data to suggest this is the case, an many anecdotes suggest the default result is actually the opposite.

    More formal instruction can be counter-productive. When it comes to remedial instruction in community college settings (and this means algebra for mathematics), shorter course sequences produce better student outcomes. Part of that may be an artifact of the fact financial aid can’t always cover courses that don’t bear proper college-credit, or that these are typically busy adult students, a chunk of whom will drop out in any given semester (thus, the more semesters you ask them to sit through, the worse your outcomes, period). But it’s imaginable that there’s more too it than that- that the way we teach math is counterproductive.
    Personally, I suspect there are few “great teachers” when it comes to math- only teachers who gel with certain students. Math is not verbal, and it is tricky to communicate and teach. And in all subjects, different students respond differently to different instruction styles.

    There is a huge amount of racism/classism/ugliness with tracking as it is implemented in many US schools. There is a huge amount of ugliness in what are seen as less-than rigorous standards. Those are real problems, but requiring every individual pass to pass algebra to get a diploma will not help address them.

    Reply
  5. EB

    I don’t understand why it would be called “tracking” if students had to demonstrate proficiency in K-8 math before being scheduled for Algebra 1, and had to pass Algebra 1 with a C or better before being scheduled for Algebra 2. It’s not as if you can do well in those subjects, no matter how good the teacher, if you haven’t mastered what goes before. To me, it should instead be called “readiness.” And if it took a student longer to reach readiness, that should be OK.

    Reply
  6. michael mcknight

    hi.. hope this finds everyone well.

    Wondering why … in 2012 we are interested in Standardizing Public Education and moving toward a national curriculum??

    This standardization… with assoicated tests have a very predictable out come of winners and losers!!

    Funny to me… people argue over the content of this stuff … algebra …latin… does not matter…

    who benefits?

    hmmmm… interesting times…

    be well and i enjoy your writing…michael

    Reply

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