America’s math problem

In America’s search for education equality, we’ve watered down math instruction, argues Jacob Vigdor in Education Next. That’s hurt high achievers without helping low achievers.

In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the “new math” movement sought, unsuccessfully, to bring rigor to the masses, and subsequent egalitarian impulses led to new reforms that promised to improve the skills of lower-performing students. While reformers assumed that higher-performing students would not be harmed in the process, evidence suggests that the dramatic watering down of curricular standards since that time has made our top performers worse-off.

. . . America’s lagging mathematics performance reflects a basic failure to understand the benefits of adapting the curriculum to meet the varying instructional needs of students.

When Charlotte-Mecklenberg schools placed below-average-performing eighth graders into algebra, they proved more likely to pass algebra by 10th grade, but less likely to pass geometry or advanced algebra ever, Vigdor notes. By contrast, Chicago improved success rates for below-average students by giving them a “double dose” of  algebra tailored to their needs.

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  1. Math wars have been around forever it would seem, but IMO, there is no reason why students should not be able to master basic algebra by high school (students in other countries get far earlier exposure than US students do, as a general rule).

    The issue of hurting high achievers at the expense of low achievers is a sore point with me, since we generally spend far more on the bottom end of the bell curve than the opposite end of it.

    Students who aren’t challenged in school (which includes high and middle achievers) will lose interest in learning, and by definition school.

  2. Since when do we care about high achievers? “They can take care of themselves”, right?

    • The “they’ll do fine, anyway” mindset has been around since my FIL started teaching in the 30s, but I do think it has worsened as a result of the focus on the achievement gap and the insistence on heterogeneous classrooms. Let no child get ahead.

  3. We need to realize that comparing our HS students with those in many/most other countries is not an equal comparison, as those countries have already removed many students from their college-prep track, often by exam, and I’m betting that their equivalent of our lowest spec ed kids never enters a regular school. Most countries also do not have our insistence on one-size-fits-all curriculum and our insistence that students with vastly different abilities and motivation can have (meaningful) identical outcomes. I am not convinced that all/most of our students can master basic algebra by HS – although more would do so if our k-8 math curriculum and teacher math knowledge were better.

    As I posted on the homeschooling post, failure to challenge smart kids is one of a number of ways schools push families to the homeschooling decision. I get the impression that a significant number are also special needs kids who aren’t making progress and/or aren’t suitably placed (as in inappropriate mainstreaming).

  4. ….. sought, unsuccessfully, to bring rigor to the masses, and subsequent egalitarian impulses led to new reforms that promised to improve the skills of lower-performing students.

    This pretty much describes American education since the 1960s.

  5. Florida resident says:

    On the topic of old post.
    Here is Steve Sailer’s review of the book
    “How Children Succeed” by Paul Tough :

    I especially like this from the review:
    “Lately, Tough has followed the lead of his social-science mentor James Heckman, the great University of Chicago statistician who won the quasi-Nobel in Economics in 2000 by more or less giving up trying to disprove The Bell Curve ”
    “It’s not as if much has emerged over the last 18 years to prove him wrong. Heckman’s seminal 2008 paper “The Economics and Psychology of Personality Traits” deals with IQ’s intractable economic importance:
    …IQ surpasses any single Big Five personality factor in the prediction of the two academic outcomes, college grades (r = .45) and years of education (r = .55). Big Five conscientiousness is by far the best personality predictor of grades (r = .22).…Conscientiousness predicts job performance (r = .13; corrected r = .22) better than does any other Big Five factor, but not as well as IQ does (r = .21; corrected r = .55). The importance of IQ increases with job complexity, defined as the information processing requirements of the job: cognitive skills are more important for professors, scientists, and senior managers than for semiskilled or unskilled laborers.…In contrast, the importance of conscientiousness does not vary much with job compllexity … ”
    “Tough has one child, so he’s still in the self-assured phase. It’s not until the second child comes along with all his own individuality that you realize you weren’t really raising your first child; he was raising you to his own specifications.”

  6. Momof4,

    IMO, the only reason why many students (and by that comparisons, adults as well) struggle with math (including higher math concepts) is a direct result of poor math preparation in elementary school.

    Students who fall behind in elementary school often spend years trying to catch up in middle and high school, and for most of them, they’ll struggle and get frustrated. I agree that the one size fits all concept isn’t workable, but a lot of math in grades 1 through 5 is done with a working knowledge of basic math facts in addition, subtraction, multiplication, and division…throw in fractions and decimals…home run

    • GoogleMaster says:

      The lag starts before kindergarten. Some children enter K having been taught their numbers, some simple arithmetic, telling time, and distinguishing coins by their parents. Some other children do not have this advantage and will start out their school careers a year or more behind already.

  7. Vigdor comes to the unsurprising conclusion that just requiring algebra in 8th grade does not guarantee improved results.

    “we’ve watered down math instruction, argues Jacob Vigdor in Education Next. That’s hurt high achievers without helping low achievers.”

    Unfortunately, he doesn’t realize that it has been watered down so low that it’s the cause of a lot of low achievement. Under the guise of problem solving and understanding, K-6 math has reduced mastery of the basics and put the onus on the student (parents). Schools trust the spiral and hope that engagement and motivation will get the job done. It doesn’t work. Schools can’t just lead the student to water and then blame IQ when it doesn’t work. They have to look at the details, separate the variables, and define an absolute scale, not just look for relative improvements on fundamental flaws in the system. Go ahead and separate students by ability and willingness to work hard, but that’s just the start.

    • Go ahead and separate students by ability and willingness to work hard, but that’s just the start.

      The problem is, you aren’t allowed to separate students that way because of the unpleasant demographical realities that result.

      • Too true, and I think that is part of the issue driving the choice of weak and/or flawed curricula. If mastery of specific material (as in Singapore Math, CK etc) is required for decent grades and advancement, the lower-ability and less-motivated fall to the bottom; thereby running into unacceptable demographic realities. Of course, the other factors are ideology and teacher content knowledge, particularly at the ES-MS levels. If they’ve been indoctrinated into the progressive mindset, Readers’/Writers’ Workshop, spiral math and other content-lite/free approaches, they don’t believe in teaching content and, ir they don’t know enough math, grammar, composition and content acrosss the disciplines, they can’t teach it. It’s a perfect recipe for educational mediocrity.

        • “I think that is part of the issue driving the choice of weak and/or flawed curricula.”

          That’s why schools pick Everyday Math with it’s “trust the spiral” philosophy. Schools know that full inclusion is a problem, but here is a curriculum that tells them what they want to hear; that it’s OK; that the curriculum works by definition. Kids will learn when they are ready. If it doesn’t work, then it must be because of IQ or that schools just need to try harder with engagement and motivation. The onus for learning is on the student, not the schools. Enough parents fix the problems at home that they don’t see the fundamental flaw, especially when it conflicts with their assumptions. Schools don’t ensure mastery of basic skills in spite of what they say about balance. CCSS won’t fix this; it won’t change what’s in their hearts and minds. They will continue to talk about the glories of conceptual understanding and engagement while kids still get to fifth grade not knowing the times table. I call it brain research misdirection. They talk about research and overlook fundamental issues of whether even the minimally agreed upon basics of mastery ever get done. By unlinking understanding from mastery of basics, they try to take the high ground of learning while lowering expectations at the same time. At the very least, those expectations are transferred to the student. They ask parents to turn off the TV, check homework, and model an interest in education (along with notes telling parents to practice math facts even though they know which parents won’t do it), but overlook the fact that many parents are doing so much more. And they wonder why there is an academic gap. They helped create it. While there will always be differences in scores between students, the average on an absolute scale should be much higher. Research, however, is done trying to find even the tiniest bit of relative improvement given that you don’t touch their beloved assumptions.

          Then magically, this lack of separation disappears in high school. Apparently, they can’t deny the issue any longer. However, most middle schools start this process with math and languages. Pressure comes down from high school. This is how our middle school was forced to get rid of CMP and replace it with proper pre-algebra and algebra textbooks. They had to offer the same algebra class as the high school. Parents demanded it. They had to provide a proper path to a second year language course. However, nothing seems to drive higher and more rigorous expectations into the lower grades. CCSS won’t do it. Middle school has become an intense area where kids have to make the nonlinear transition from the “kids will learn when they are ready” ideas of elementary school to the take responsibility for your own learning, give zeros as wake-up calls learning of high school. Time and again, the onus is placed on the student. They point to students who are successful without asking what went on at home. It’s a lot more than turning off the TV and going to museums. It seems that the roles are reversed. Schools want to do just the enrichment and engagement, but they want parents to work on math facts. They want to do just the enrichment and engagement, but have students watch lecture videos at home. It appears that they don’t mind lecturing as long as someone else is doing it.