Math Education: An Inconvenient Truth

Watch an excellent explanation of current math instruction and alternatives to it. I’ve never before seen such clear demonstrations of current math education. It really helps make the current math controversies much more concrete. Go to You Tube.

2 thoughts on “Math Education: An Inconvenient Truth”

  1. Well, if the “back to basics” movement are consistent with the video’s commentator, please count me out. I would highly suggest this video be watched to understand how this described “back-to-basics” movement (in Washington State) would be a triumph of ignorance over knowledge.
    The commentator, MJ McDermott, (an educated meterologist, self-described) praises rote long-hand multiplication, and argues forcefully that other approaches are subject to making errors, and therefore not be taught. That is, only the basic algorithms should be used, and that books which push alternative methods must not be used in the schools.
    In addition, a basic criteria for judging whether some approach should be taught is whether you (the parent) can understand it. Since most adults can’t handle simple arithmetic facilely, this criteria would be a complete disaster for education.
    She demonstrates long multiplication and long division. These are the algorithms of which she approves — and only approves. That is she only approves of techniques that require memorizing an automatic way to come up with the answer, and long multiplication and division are it. (Let’s ignore for now the fact that the “basic” algorithms used in Europe, and South America are different).
    Her beginning comment is that if you want your child to know how to multiply and divide by the 5th grade, you should not use the following books….
    A technique she particularly dislikes (it is error prone, she says) is the use of the basic arithmetic law of that multiplication distributes over addition. That is, a*(b+c) = ab+ac, and that our number representations (place value) is a sum (612 = 600 + 10 + 2).
    The example she uses and disapproves of (from the teacher’s manual) is
    26*31 = 26*(30+1) = 26*(3*10 + 1) = 78*10 + 26 = 780 + 26 = 806.
    Now, the teacher’s manual makes this whole process much more complicated than necessary (perhaps a reflection of the lack of math skills of elementary and middle school teachers, and the people who write the books), but it took me less than 5 seconds to do it in my head. Practice is necessary to do this well, but no pencil and paper is necessary.
    No one can be considered “numerate” (to use John Paulos’ term) if they can’t do this problem in their head — it’s too simple. And mastery of such techniques are required for estimation, and interpolation skills.
    Yet, she argues that the only way to do this, and should be taught is the long multiplication way.
    Yes, the long method should be taught to mastery, but so must these other methods. Students must become facile with numbers, not just blindly memorize.
    “Tricks” are fun to learn also: multiplying by 5 is the same as multiplying by 10 and dividing by 2; don’t we all use this to calc sales tax? See
    As important, get rid of the damn calculators. There is no single factor contributing to keeping people from handling basic math than the laziness caused by use of calculators. From my perspective, the only math course which should allow calculators is a course where one needs the answers to logs or trignometric functions such as sin, cosine, etc. And, no graphing calculators either — one cannot possibly understand an equation by having the calculator do it.

  2. Larry, I could only just-barely disagree more. The first thing I found amusing about your post was your reference to the Law of Distribution a law which (according to Doctor Bill Quirk, formerly professor of mathematics at Penn State) is not mentioned explicitly ONCE through TERC. Makes it kind of an ironic argument, doesn’t it?
    You’re right, that sort of multiplication should easily be done in your head… when you’re our age. At age ten, I don’t expect that much. Further, as McDermott points out, what happens when you stray into larger numbers? I defy you to calculate 238762*145435 in your head and… they get much bigger, you may have heard. The Standard Algorithm is the easiest, most straightforward way to calculate that, aside from the lattice (which is the same method carried out with a different aesthetic), but even that requires the time to draw the lattice so I don’t see the advantage.
    Now, your refutations of McDermott. I don’t think she said only algorithms should be used, I don’t think even said anything shouldn’t be taught. I think the general thrust was, algorithms are standard, easy, as flawless as it gets, and that the other methods were less so. Cluster solving is great for doing things in your head, teach it if you like- did she ever forbid it? But making it central… tsk tsk, that’s a disservice.
    I wasn’t aware that Europe and South America performed multiplication differently. I’ll look into that, I’m curious if it’s really different or if, as most people fail to recognize (I think you did) the same method done a little differently. I have my suspicions.
    Finally, parents: since parents, ideally, help their kids with their homework, it’s best if they are at least remotely familiar with the method.
    It’s interesting to me that you can deny a method which has been used for centuries- a method used and taught by Leonard Euler, analysis incarnate, by Riemann and Poincare… all these great minds who at one point or another (even late in their careers) surely must have used long division a few times- then turn around and trumpet the new ways while quoting Paulos, a man who spends chapter upon chapter discussing how easily people are duped, and come off feeling snug as bug in your progressive conviction.

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