Double-dose algebra helps some students

When Chicago put below-average ninth graders in “double-dose” algebra classes with twice the instructional time, failure rates were high. But double-dose algebra has significant long-term benefits, conclude Kalena Cortes, Joshua Goodman and Takako Nomi in Education Next. Compared to similar students, Chicago’s double-dose algebra students were more likely to graduate from high school and enroll in college (almost always community college). They earned higher ACT scores in math and verbal skills. There’s some evidence they earned higher grades in advanced math and chemistry classes.

Starting with students entering high school in the fall of 1997, CPS eliminated lower-level and remedial courses so that all first-time freshmen would enroll in algebra in 9th grade, geometry in 10th grade, and algebra II or trigonometry in 11th grade. . . .  many students were unable to master the new curriculum, resulting in very low passing rates in 9th-grade algebra.

Instead of bringing back remedial math, CPS assigned below-average students to a regular algebra class and a second  class that included “writing sentences to show how they solved a math problem; explaining how they solved a problem to the class; writing math problems for other students to figure out; discussing possible solutions with other students; and applying math to situations in life outside of school.”

Perhaps because of all the writing, double dosing was especially effective for students with below-average reading skills and “moderately low” math skills.

Double-dosed students scored nearly 0.20 standard deviations higher on the verbal portion of the ACT, were substantially more likely to pass chemistry classes usually taken in 10th or 11th grade, and earned modestly higher GPAs across all of their non-math classes in the years after 9th grade. In other words, the skills gained in double-dose algebra seem to have helped students in other subjects and in subsequent years.

Nearly half of large urban districts use a double dose of algebra for low-skilled students. However, the Chicago study suggests that extra instruction helps students who are not too far behind, but does little for the truly low achievers. Should they get extra math instruction in middle school? Elementary school? Or a path to a high school diploma that doesn’t require algebra?

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Comments

  1. I know I am speaking heresy here, but I believe there should be a way to graduate high school without taking Algebra. I am a fairly well educated teacher, who has worked a pretty wide variety of jobs, and the only time I have ever needed Algebra is in school, either classes I was taking, or classes I was teaching.

    As a profession we need to admit that a large number of our students are not going to college, and don’t want to.

    We need to restore a general education tract designed to create functual citizens rather than try to shove everyone into college prep.

    But it will never happen because of the demographic realities.

    • J. D. Salinger says:

      Why stop at algebra? There are many subject areas that many people don’t ever use in their daily lives.

      • True.

        I would be in favor of a comprehensive reform. I would redesign the system completely. I would set up a vocational track, a general education track and a college bound track.

        • All good, providing that kids would have to qualify for the college prep and voc ed tracks. The latter should have different requirements for different programs, which I would operate as an adjunct to the HS and not part of it; to avoid idiocies like requiring voc ed instructors to have ed-school qualifications. I would also add an accelerated track for schools large enough to have enough qualified students (which are not evenly distributed across schools). I’d model it on MN’s PSEO program, where HS students take college coursework of their choice and the district pays the tuition and aim to get the top students out of HS with two years of college classes. It’s been obvious for decades that the one-size-fits-all approach is not working.

      • Why stop at requiring Algebra for graduation? Why not mandate Trig?

  2. What ever happened to an ounce of prevention?

    Are problems ever seen as systemic ones rather than ones defined by what walks into a particular classroom? Why is there always a knee-jerk reaction to blame IQ (blame the kids) and then rationalize that many adults don’t need algebra? College departments define the math class doors one needs to get through for each career, whether or not you ever need those specific skills. Even vocational schools (many of which give out degrees) require students to take a placement test like the Accuplacer. Many vocational degrees require at least algebra and trig.

    Having taught college math and CS for years, I saw kids change majors because they couldn’t pass college algebra and trig, or couldn’t pass a statistics course. Departments like nursing know very clearly what math requirements can do to one’s career goal. They don’t make those decisions lightly.

    School systems have to try very hard to get all kids through a rigorous algebra course by 8th or 9th grade. While there may be some who really can’t handle the material, it can’t be left to some sort of natural “trust the spiral” process. This guarantees that high schools will have to face a pound of cure.

    My son’s fifth grade teacher had bright kids who didn’t know the times table. What was her solution? She spent a lot of time working on basic skills. Did she complain about the poor job the lower grade teachers were doing? No. I don’t know what teacher/administration issue is going on here, but don’t expect us parents to join one team or another.

    Our middle school used CMP in math for years. The high school math teachers used to trash the math skills of the kids coming in from our middle school. The high school created new algebra classes that had “labs” for improving basic skills. Did the high school ever tell our lower schools that they had to focus more on mastery of skills? No. I had the head of the math department tell me that our middle school had to make sure our kids worked harder. Nope. It couldn’t be the school’s fault. The only way we got rid of CMP was because some parents demanded that the school offer the same algebra course as the high school so that some kids could be prepared for geometry in 9th grade.

    What I see is a curriculum/philosophy wall between K-8 and high school. Schools and teachers dare not criticize their own. They don’t want to address basic issues of curriculum and competence and how they can really screw things up. Thank goodness for the parents of the good students who teach their kids at home. Then, all you have to do is to raise some doubt with IQ, peers, bad parents, and poverty to make it seem impossible to separate the variables, especially by the time kids get to high school.

    • “School systems have to try very hard to get all kids through a rigorous algebra course by 8th or 9th grade.”

      Sadly, true, even though we know the task is impossible. That is the problem. Instead, we should concentrate on getting all kids through basic numeracy (say Pre-Algebra) and getting those who will need Algebra and higher math classes what they need. (Which will be easier for all involved if we give up the pretense of forcing all to take Algebra)

  3. Your entire premise is flawed. There’s no evidence that kids are doing poorly in elementary school math, and thus doing poorly in algebra.

    Quite the contrary. State tests and the NAEP all show exactly the opposite. Kids are doing well and improving constantly in elementary school math, then flatlining in middle school and getting worse–on average–in high school.

    This is not evidence for “kids weren’t taught’. This is evidence for “math gets harder and not everyone has the ability for advanced math”.

    • It could also be proof that what is tested at the elementary levels lack the proper rigor or pacing to prepare someone for higher levels of math. You can’t just pick one possible reason for the observed results and say that it is the definite cause. We see correlation, but don’t have the cause identified yet.

  4. Roger Sweeny says:

    Yes, vocational schools give placement tests, and have various courses that require math beyond the basics. And, yes, nursing schools do, too.

    However, the jobs that the schools are supposed to be preparing their students for rarely involve actually using those mathematical skills. It is in that sense that “many adults don’t need algebra.”

    Now, it is certainly true as a purely pragmatic thing that they have to know enough algebra to pass those courses. But that’s a very different kind of “need.”

  5. Roger,

    While the statement ‘many adults don’t need algebra’ might ring true, it’s a given fact that without a solid working knowledge of algebra, many STEM careers will be unreachable by high school students, graduates, or adults.

    There’s a reason why you have to know algebra in order to be admitted to nursing school, electricians school, and many other programs which are STEM oriented. A lack of knowledge about algebra will usually wind up getting you (or someone else) seriously injured or killed (and look out for the lawsuit afterwards).

    It’s not that our students do poorly in math after leaving elementary school, rather it’s the issue that by definition, US students hold their own against their peers worldwide through elementary school, start to slip a bit in middle school, and have fallen completely behind by high school.

    I’d LOVE to know why this is happening, and what can be done to stop it. As another article states at the site, the U.S. is the biggest spending on education, but as studies have shown, spending more doesn’t always produce better results.

    Look at the 2 BILLION that Kansas City, Missouri was ordered to spend on it’s schools by a federal judge, and how achievement plummeted despite outspending every other school district in the state for a decade.

    Hmmmm

  6. Also,

    Higher math teaches problem solving, critical thinking, and analysis skills, which if you ask most employers, are skills that many workers lack these days.

  7. twitter_danlemayPI says:

    We have been having this discussion at my school. Ninth/Tenth grade is too early to be making decisions that will limit choice post high school. Let’s get as many through algebra and geometry as possible.

    • “Let’s get as many through algebra and geometry as possible.”

      I think we all could agree with this. The question is should the cost of doing so be putting graduation out of reach for those who will never need or use Algebra?

  8. “Your entire premise is flawed. There’s no evidence that kids are doing poorly in elementary school math, and thus doing poorly in algebra. Quite the contrary. State tests and the NAEP all show exactly the opposite. …”

    The NAEP is extraordinarily easy. Parents should go to their web site, look at sample 4th grade test questions and the horrible percent correct scores. Look at the questions and ask yourself if kids are really that stupid. Ask yourself what schools do in their one hour plus of math a day. Examine curricula like Everyday Math. Look at their simple and very small homework requirement. There is a reason why places like Kumon are so popular. There is plenty of evidence that affluent families help their kids at home with the basics. Schools tell parents to do that.

    “This is evidence for “math gets harder and not everyone has the ability for advanced math”.”

    You still can’t or won’t separate the variables and calibrate the level. With that attitude, I recommend that parents have their kids’ IQs tested. But what will happen when they do poorly in school? Will you point to some other variable?

    • “. Look at the questions and ask yourself if kids are really that stupid. ”

      That’s a pretty obnoxious word to describe the lower half of the ability spectrum. But yes, as someone who teaches kids in the lower half, they do find that math to be a significant challenge, even several years later.

      It’s not the curriculum. It is, in fact, IQ, or cognitive ability, or whatever you want to call it. It’s still the best proxy there is.

      There will be high IQ kids that don’t achieve to their ability, and there will be low IQ kids who outperform their IQ. Not everything must be explained. But anyone who think that the math performance falloff is caused by weak or unchallenging curriculum in the earlier years is simply desperately searching for someone to blame, rather than recognizing the obvious answer.

      • “That’s a pretty obnoxious word to describe the lower half of the ability spectrum. ”

        Reread my post and look in the mirror. You’re the one who claims that NAEP gives you the answers. I’m the one telling parents to judge for themselves. You’re the one who can’t or won’t separate the curriculum and IQ variables. That’s why I tell parents that they should have their kids’ IQs tested – to protect them from low expectations from people like you.

        “Not everything must be explained.”

        There you have it. It doesn’t have to be explained but it’s “obvious”.

  9. “Now, it is certainly true as a purely pragmatic thing that they have to know enough algebra to pass those courses. But that’s a very different kind of “need.””

    It’s the important one. It’s the kind that opens and closes doors. What’s the point of talking about anything else?

  10. “Let’s get as many through algebra and geometry as possible.” … “I think we all could agree with this. The question is should the cost of doing so be putting graduation out of reach for those who will never need or use Algebra?”

    There are two separate issues here, and CCSS fails to address them. Actually, it makes the problems worse. On one hand, it allows K-6 to continue their full inclusion, “they will learn when the are ready”, spiraling curricula, and on the other hand, it forces kids to get through a one-size-fits-all pseudo algebra II level of math in high school. Low expectations in the lower grades create problems that won’t be solved by double doses of algebra in high school. Apparently, learning is “natural” in the lower grades, but when people are paying attention in high school, schools have to cram it down their throats. Kids are required to take responsibility for their own learning and become life-long learners. What happened to natural?

    It’s one thing to be pragmatic about education in high school, but quite another to let that philosophy drift into the lower grades as a reason to ignore systemic problems. Many adults may not need algebra, but are you picking them or creating them? There is clear evidence that many of these people are created.

    • Barry Garelick says:

      Good points, Steve. For more info on this issue, Laurie Rogers has pretty much nailed the destructive effect of constructivist teaching in math, which passes for math education in many of the lower grades. See http://betrayed-whyeducationisfailing.blogspot.com/2012/11/in-defense-of-direct-instruction.html

    • The same problems exist in ELA; balanced literacy and Readers’/Writers’ Workshop. Get back to direct instruction in real phonics, spelling, grammar and composition. Forget journaling and personal anecdotes and teach the kids how to do ordinary writing clearly and correctly. Construct/rebut an argument and support it. For college-prep kids, add academic writing.

  11. stickypixel says:

    I like it because students got higher scores on the ACT with double-dose. I enjoy Algebra and I think its good to know. It may not be needed, but it is helpful.

  12. I found it really interesting that double-dosing algrbra classes not only helped to raise math scores, but raised ACT verbal scores as well. Yes, some students might not use algebra after high school, but given that this program yields other benefits as well, it might be worth keeping it around.

  13. Roger Sweeny says:

    Educationrealist has a “from experience” perspective on double dose algebra and this piece of “educational research.” It isn’t pretty.

    http://educationrealist.wordpress.com/2012/11/10/algebra-terrors/