Where Are You Going, Where Have You Been? Quotes …

(7) In second semester calculus, there were three chapters full of formulasthat could all be derived from the first formula in the chapter, but neitherthe book nor any of the teachers pointed out that all but the first formulawas derivative. There appeared to be much memorization needed to learneach of these individual formulas. I happened to notice the relationshipthe night before the midterm exam, purely by luck and some coincidentalreasoning about something else. I figured I was the last to see it of the1500 students in the course and that, as usual, I had been very naive aboutthe material. It turned out I was the only one to see it. I did extremelywell but everyone else did miserably on the test because memory under examconditions was no match for reasoning. Had the teachers or the book simplyspecifically said the first formula was a general principle from whichyou could derive all the others, most of the other students would havedone well on the test also.

Where Are You Going, Where Have You Been

SparkNotes: Where Are You Going, Where Have You Been?
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What is necessary to help a student learn variousconceptual aspects of algebra is to find out exactly what he does not understandconceptually or logically about what he has been presented. There are anynumber of reasons a student may not be able to work a problem, and repeatingto him things he does understand, or merely repeatingthings he heard the first time but does not understand, is generally notgoing to help him. Until you find out the specific stumbling block, youare not likely to tailor an answer that addresses his needs, particularlyif your general explanation did not work with him the first time or twoor three anyway and nothing has occurred to make that explanation any moreintelligible or meaningful to him in the meantime.

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I like to use a soft cotton-lycra blend knit (it won’t pill like rayon or bamboo knit), 1 inch wide elastic, and sew-in bra cups. Make sure the bra cups are your appropriate cup size and that you like the shape they give you. Slightly padded cups will keep your girls from “tuning in Tokyo.” I buy cups in the garment district, where there are lots of different shapes to choose from. If your resources are more limited, Dritz makes cups .

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Where Are You Going, Where Have You Been ..

I am not saying that all the things children learn mechanically in elementarymath are necessary to learn or are best learned mechanically. But someare. And I would consider learning to recite number names in order andnumber names by groups ("counting" and "counting by groups") and learningto do what I have referred to as simple addition and subtraction as examplesof crucially important mechanical skills. Some mechanically learned skillssimply allow you to make intellectual leaps you might not have been ableto make at all if you were not able to quickly and somewhat automaticallyperceive relationships you had not become extremely familiar with or "primedfor" previously by memorization, repetition, drill, and practice. ()

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I think the only trick will be making sure where you sew the quilting fabric to the jersey bra fabric doesn’t pucker. If the top of the bra and dress aren’t exactly the same size (and the bra is smaller) the bra edge will cause the dress to pucker. Does that make sense?

“4 things you should know if you want to be a Buddhist monk”

There are many subject areas where simple insights are elusive untilone is told them, and given a little practice to "bind" the idea into memoryor reflex. Sometimes one only needs to be told once, sees it immediately,and feels foolish for not having realized it oneself. Many people who takepictures with a rectangular format camera never think on their own to turnthe camera vertically in order to better frame and be able to get muchcloser to a vertical subject. Most children try to balance a bicycle byshifting their shoulders though most of their weight (and balance then)is in their hips, and the hips tend to go the opposite direction of theshoulders; so that correcting a lean by a shoulder lean in the oppositedirection usually actually hastens the fall. The idea of contour plowingin order to prevent erosion, once it is pointed out, seems obvious, yetit was never obvious to people who did not do it. Counting back "change"by "counting forward" from the amount charged to the amount given, is asimple, effective way to figure change, but it is a way most students arenot taught to "subtract", so store managers need to teach it to studentemployees. It is not because students do not know how to subtract or cannotunderstand subtraction, but because they may have not been shown this simpledevice or thought of it themselves. I believe that counting or calculatingby groups, rather than by one's or units, is one of these simple kindsof things one generally needs to be told about when one is young (and givenpractice in, to make it automatic) or one will not think about it.