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The spring issue of Education Next has a forum on whether changes are needed in No Child Left Behind. Check out the graph on the variation in reading and math standards among the states: It’s a lot easier to reach proficiency in some states than others.

Christine Rossell writes about magnet schools, which remain popular. The first magnet opened in Tacoma in 1968 as a desegregation tool.

Barry Garelick writes about what he learned about math education as a tutor of proof-less geometry students, the father of a second grader who wasn’t being taught addition and a government analyst temporarily assigned to a senator’s staff.

The National Council of Teachers of Mathematics “recommended that students learn ‘strategies’ for learning number facts rather than memorize those facts.” Calculators were emphasized; teachers were urged to decrease time on paper-and-pencil computations, including long division and fractions, the use of rounding to estimate, rote memorization and practice and direct instruction by the teacher. Instead, students were supposed to discover math concepts for themselves.

Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students’ not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering and taking ownership of the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride.

Texts that are based on NCTM’s standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches “mathematical thinking” rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without teaching him to swim.

Garelick wanted the senator he was advising to question the National Science Foundation’s funding of “fuzzy” math curricula. But Lynne Cheney, then a fellow at the American Enterprise Institute, was campaigning against fuzzy math, and he was working for a Democrat.

I told (Democratic staffers) about the open letter from the two hundred mathematicians and urged them not to confuse the message with the messenger. “This is a real issue,” I said. “Kids aren’t learning the math they need to learn.”

Garelick wanted to brief the senator on the issue. The staffers said it was impossible: The Democratic senator couldn’t be on the same side of the math debate as the Republican vice president’s wife.

Update: Thanks to Steve in Comments for mentioning the American Institute for Research report which compares math curricula in the U.S. with high-scoring Singapore. AIR praises the U.S. “emphasis on 21st century thinking skills, such as reasoning and communications, and a focus on applied mathematics,” but notes the U.S. students “must begin with a strong foundation in core mathematics concepts and skills, which, by international standards, they presently lack.”

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Comments

  1. Terrific post!

    I can’t wait to read the entire Garelick article.

    “Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned.”

    This has always been the problem with progressive/constructivist education. Something that could make sense is pushed into the realm of absurdity when it is treated as religion devoid of empirical verification.

  2. It’s also a thumbnail sketch on why the Dems are losing election after election. Idiots. I’m really tired of the same old same old GOP, but given the quality of the opostition.

  3. Team politics works both ways. More people should be willing to get off the team bus and think for themselves. It really is OK to be issue oriented, rather than team oriented. Unfortunately, too many people have fun being part of the team, and the team that has the majority gets the power. As for the politics of education, this article is just another reason for putting the power and choice (and the onus) into the hands of the parents.

    For another nail in the coffin of discovery/reform math:

    New AIR Study Compares the Quality of U.S. Math Instruction with Singapore, a Recognized World Leader

    at http://www.air.org

    At the end of the Executive Summary of the AIR report, there is this:

    “The U.S. mathematics system has some features that are an improvement on Singapore’s system, notably an emphasis on 21st century thinking skills, such as reasoning and communications, and a focus on applied mathematics. However, if U.S. students are to become successful in these six areas, they must begin with a strong foundation in core mathematics concepts and skills, which, by international standards, they presently lack.”

    I went to school in the 20th century, back when reasoning and communication skills apparently weren’t important. Toss NCTM a tidbit, but that is a big “however”. In other words, none of it will work unless you “… begin with a strong foundation in core mathematics concepts and skills, which, by international standards, they presently lack.” The report seems to advocate a national standard for a curriculum. Apparently, it’s not just a matter of tweaking the NCTM standards.

    In an on-air interview (NPR’s Talk of the Nation), Steven Leinwand, one of the authors of this report, cites “coherence” as the number one factor in the superiority of Singapore’s math curriculum. And, by the way, there is also a “quality differential” for all of the components of the system. He seemed quite pleased (?) with the idea that it is good to study the educational techniques of countries that do well on international tests, as if this is some sort of profound concept.

    Yes, this is the same Steven Leinwand who said a few years back:

    “It’s time to recognize,” wrote Steven Leinwand, math adviser for Connecticut’s Department of Education, “that, for many students, real mathematical power, on the one hand, and facility with multidigit, pencil-and-paper computational algorithms, on the other, are mutually exclusive. In fact, it’s time to acknowledge that continuing to teach these skills to our students is not only unnecessary, but counterproductive and downright dangerous.”

    What is one of the math curricula that Singapore Math is compared to? Everyday Math. Take a look. It’s a big report.

  4. Regarding the AIR study, it’s actually pretty good despite the fact that Leinwand is involved. He seems to be in the process of changing his stripes. Maybe the money is better on the other side of the argument, who knows. In any event, the report, from what I’ve heard from mathematicians reviewing it, is balanced. It does contain some stupid statements, like Singapore’s weaknesses compared to the US, is that the US programs have more reasoning involved etc etc. But in the end, it always comes down to the same conclusion. US math programs just don’t stack up. THe comparison with EM is not as bad as you might think. EM doesn’t come out looking good, let’s put it that way.

    BG