A truce in the math wars

Mathematicians and math educators attended a “peace summit” to settle the math wars, reports the Washington Post. Participants were surprised to discover a wide area of agreement:

¥ Heavy reliance on calculators in the early elementary grades is a bad idea.

¥ Elementary school children must have automatic recall of number facts, meaning that, yes, they have to memorize multiplication tables.

¥ Children must master basic algorithms. The meeting participants spent time defining the word “algorithm,” which means a set of rules for solving a problem in a finite number of steps.

Math makes you smarter, according to an article linked by Chris Correa.

In next month’s issue of Intelligence, an interdisciplinary group of researchers propose a new hypothesis to explain the Flynn effect. The Flynn effect refers to the puzzling rise of IQ scores all over the world during the twentieth century.

Popular explanations of the Flynn effect often note improvements in nutrition and increased access to formal schooling, but these authors emphasize the changing nature of mathematics education and the possible effects on the prefrontal cortex. This is because fluid intelligence (the ability to reason and deal with unfamiliar problems) has rapidly improved in recent history. They suggest contemporary education requires kids to get a lot of practice with prefrontally-based fluid cognitive skills.

Via Eduwonk.

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  1. Interesting discussion. How is it that children are expected at once to be familiar with mathematical algorithms and not use calculators? I blog more about this here.

  2. Andy Freeman says:

    > How is it that children are expected at once to be familiar with mathematical algorithms and not use calculators?

    Huh? Algorithms, including mathematical ones, predate calculators by a couple of thousand years.

    There is no Royal Road. If you don’t know the fundamentals, you’re going to lose to folks who do.

  3. dfriedman,

    In this case, they’re talking about standard algorithms like the ones for mutli-digit arithmetic. New math replaces these with calculator use, which makes life difficult for students in algebra when variables come into place.

  4. “Advanced students in high school used to be the only ones to study geometry, but now most third-graders solve problems involving 3-dimensional representations on a regular basis”…is this really true? My perception is that formal (Euclidean) geometry used to be part of the high school curriculum for nearly everyone, but has now become less common.

  5. Who says IQs have been rising all over the world? Isn’t that begging the question? Anyway, it ain’t happening in my school district.

  6. Definitely agree with the whole calculator bit. I was quite shocked in middle school when my friend asked me what 9 * 8 was. Granted, she was in a rush to complete a math assignment, but still. Multiplication tables (up through twelve times twelve) should be so basic and ingrained that the answers should jump into your head instantly, imo. My friend had become so dependent on calculators that she had trouble thinking of the answer to a very simple problem.

  7. In my view the value of Euclid goes beyond conceptualizing shapes. Yes, there are graphing programs that do some marvelous manipulations of objects in three dimensions.

    But as to the value of Euclid: Euclid presents a logical framework that has stood over 2300 years and pre-dates the Bible. If memory serves me, the 13 Books of Euclid contain 456 proofs, each building on prior proofs that grow out of Euclid’s “common notions.” Working through the drawings and doing the proofs facilitates logical thinking.

    The logic is independent of the drawings as Einstein and Hilbert observed. To understand non-Euclidean geometry, we must understand Euclidean geometry. Non-Euclidean geometry, as we all know, is used in understanding Einstein’s Theory of Relativity. The graphing systems are pretty much Euclidean that we encounter and there is a significant discussion as to whether the universe is open or closed – that is do parallel lines really meet? Messing with Euclid’s Fifth Postulate leads to a new realm that, at least for me, I could not really understand without first having done Euclid. The proofs require a leap in logic that comes from getting into the machinery of Euclid and then tinkering with it. Without that understanding, it is difficult to move into the mathematics that cannot be shown on a two-dimensional screen – such as when we contemplate super string theory with far more than four dimensions. That’s when our fundamentals come in mighty handy.

    Fascinating stuff.


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