  The last time I wrote a superhero parody, it was to humiliate someone. I respect you, Ed. So, no blazing power bolts or green force fields.
ET: That's too strongly worded. For instance, conservatives don't deride math, and math is abstract.
Well, yes, they are in favor of memorizing the multiplication table. You are too young to know about the resistance to "New Math" of the late 1950s and early 1960s. In the 7th grade, we learned sets and we did arithmetic in different bases. I enjoyed it. And when we really did need to work in octal and hexadecimal I was grateful.
One of many presentations of Tom Lehrer's "New Math." http://www.youtube.com/watch?v=UIKGV2cTgqA
I am pretty sure that we had that discussion about your neice and her arithmetic a few years ago, and I found for you the very old arithmetic book that taught it. Nothing about arithmetic is natural. Even base10 is a recent invention; and I mean like 1600: http://en.wikipedia.org/wiki/Simon_Stevin. Until the middle 1800s and German Unification, the thaler (dollar) was divided into 12ths, into quarters and thirds  thus despite Hamilton and Jefferson, we have quarter dollars, not 20cent pieces  though many nations did and do have such a truly decimal denomination. My point is that the gridbox for multiplication that your niece learned was one of many such methods taught in years gone by. If you asked Thomas Jefferson to multiply two large numbers, he might have done it the way your niece learned. And she will be taught the way we know. And she will use a calculator.
ET: I also heard that the new, superprogressive, Deweyonsteroids plan: Common Core is not even stressing the students' arrival at correct answers  only the ability to show the work which led to whatever fanciful answer you concocted to otherwisecommon, understandable, and answerable math problems (e.g., 2 + 2 = 5). Not exactly. First of all, you should actually know the Common Core Standards here, not just some secondhand complaint from a conservative blog. I agree that this "Common Core" does show the bankruptcy of public education in that nothing is new or innovative. It is "fall back and regroup."
Your example of 2+2=5 is silly. By what method? Did you put up two fingers on each hand and count them off: 1, 3, 4, 5. You skipped a number. But if the problem is this: Ed can mow the lawn in 45 minutes. Mike can do it in 55. How long will it take them working together? And you have the right method, but make an arithmetic mistake along the way, you still get (some) credit. That's all.
Now, I grant, also, this theory drove Richard Feynman angry. To him, it did not matter what method you used, as long as you got the right answer. Realize that as a genius, Feynman often invented new methods, even as a child. At one point, in junior high or high school, he discovered some cool thing, but when he went to show his buddy, he had another problem because Feynman also invented his own symbols. So, it took his friend a bit of work to convince Feynman that everyone already knew that... Feyman was all about getting the right answer by any method. But to use whatever method or invent a new one, you have to be further down the road than most people in your thinking.
One time, I had a class in civil engineering and one of the girls's father was one of the professors. Someone ribbed her about always being able to get help with her homework. She said she once actually asked for help, and he suggested that this force triange really could be solved more easily by completing the square. She never asked again... See, as the professor, a guy with a Ph.D., and a lifetime of experience in undergraduate bridge truss problems, he knew all the tricks. But you have to get there first. That is why we learn methods. And we do not punish (completely) for an arithmetic error.
As for Dewey and Heraclitus, Ayn Rand's For the New Intellectual kept me from learning anything in humanities classes. I did not have to learn anything. Ayn Rand explained why it was all wrong. I could ignore it. Finally, this last time around 20072010, I actually benefited from my college and university education.
It is not up to me to justify Dewey to you. You can read him for yourself. I understand the errors. I find more value in accepting the gains. To me, Dewey is saying that Berkeley's idealism is wholly unsatisfactory and that theories must be tested against practical programs carried forward. Moreover, if you read Understanding Objectivism by Peikoff and Bernstein, you will see that Peikoff offers his own warning against Monism: attempting to derive all of philosophy from A is A. Dewey wrote:
“If a man cherishes novelty, risk, opportunity and a variegated esthetic reality, he will certainly reject any belief in Monism, when he clearly perceives the import of this system. But, if from the very start, he is attracted to esthetic harmony, classic proportions, fixity even to the extent of absolute security, and logical coherence, it is quite natural that he should put faith in Monism.”  The Development of American Pragmatism. I am pretty sure that Alexander Luria would qualify as a "Hegelian" if you understand that "Marx turned Hegel on his head." Dialectic materialism was derived from Hegel's thought, but is contrary to it. You can reject Luria as a communist and say that no Bolshevik could be right about sociology. But the Bolsheviks wanted to know how to change the environment in order to improve the human condition. Fail as they did in the larger sense, they did make gains at the detail level. This was one of them.
Another was the decipherment of Mayan hieroglyphs. Most scholars accepted the artwok on the pyramids as decorations only. As Marxists, the Russian scholars assumed that any two societies at a given economic level of development, facing similar probllems will develop similar solutions: thus, the pictures were glyphs, like Egyptian writing. As this was the 1950s, in America, the suggestion was condemned as communist. (See Coe, Michael D. (1992). Breaking the Maya Code. London: Thames & Hudson cited in http://en.wikipedia.org/wiki/Maya_script I have the book. It's a good read.)
If you condemn and dismiss eveyrone except Ayn Rand, you are going to be left with a very small box of intellectual tools.
(Edited by Michael E. Marotta on 10/03, 9:04am)

