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It is easy to see children do not understand place-value when they cannotcorrectly add or subtract written numbers using increasingly more difficultproblems than they have been shown and drilled or substantially rehearsed"how" to do (by specific steps; i.e., by algorithm). By increasingly difficult,I mean, for example, going from subtracting or summing relatively smallerquantities to relatively larger ones (with more and more digits), goingto problems that require (call it what you like) regrouping, carrying,borrowing, or trading; going to subtraction problems with zeroes in thenumber from which you are subtracting; to consecutive zeroes in the numberfrom which you are subtracting; and subtracting such problems that areparticularly psychologically difficult in written form, such as "10,101- 9,999". Asking students to (demonstrate how they) solve (the kinds of)problems they have been "taught" and rehearsed on merely tests their attentionand memory, but asking students to (demonstrate how they) solve kinds of problems (that use the concepts and methods you have been demonstrating,but "go just a bit further" from them) helps to show whether they havedeveloped understanding. However, the kinds of problems at the beginningof this endnote do not do that because they have been contrived specificallyto psychologically mislead, or they are constructed accidentally in sucha way as to actually mislead. They go beyond what the students have beenspecifically taught, but do it in a tricky way rather than a merely "logicallynatural" way. I cannot categorize in what ways "going beyond in a trickyway" differs from "going beyond in a 'naturally logical' way" in orderto test for understanding, but the examples should make clear what it isI mean.
and some authors may well not have written any word in the paper.
The lost world, found
Everybody loves dinosaurs – as long as they’re just bones in a museum. Steven Spielberg’s rollercoaster thriller, adapted from Michael Crichton’s bestselling novel, brings these prehistoric beasts back to life with a clever conceit: scientists have discovered how to harness dino DNA from fossilised amber and billionaire John Hammond (Richard Attenborough) has created an island zoo where spectators pay top dollar to view the cretaceous giants. All well and good until the security system fails and T-Rex and friends go on a chomping rampage.
For many people, this may be the only bit of her writing that they've ever read. And it’s worth hunting down. When somebody is damaged and lost in the world, we always wonder how that came to be. Was there something in their past that made them steal, made them vulnerable; was there an incident, some family member, an ongoing abuse? In this case, yes, there was. A college aged girl tells of her problems, these issues she has, but we have no idea how deep it goes, how messed up she really is. But what keeps this story from being merely a dark tale of power gone awry is the way the protagonist handles her future, the way she forgives and moves on. She is unique, and yet, she is all of us.
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Computers and calculators have lots of circuits through essentiallyon/off switches, where one way represents 0 and the other way, 1. Electricitycan go through these switches really fast and flip them on or off, dependingon the calculation you are doing. Then, at the end, it translates the stringsof zeroes and ones back into numbers or letters, so we humans, who can'tread long strings of zeroes and ones very well can know what the answersare.
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How dare I make a list of the top ten short stories ever, right? Who the hell do I think I am? Well, obviously I’m a fan of fiction, of the short story form. I’m also an author. And I now have my MFA in Creative Writing as well. Does that make me an authority? Yes, on stories that I love—that’s it, nothing more. These may work for you or they may not. You’ve probably heard of many of them, but I hope you’ll track down the ones that are not familiar and give them a read. I tried to pick a few stories from each of the main genres I love, but overall, I wanted stories that I have a fond memory of reading. Can I remember parts of it, lines, or scenes? Does the weight of what I read still rest in my heart? I can honestly say yes, that all of these stories have had a profound impact on my writing career, as they are, in my opinion, as flawless as stories can get.
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Reading "The Lottery" in high school had a profound impact on me and is one of the reasons I write. It also made me fall in love with the short story format.
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I took a shortcutin question 15 although I did not have to; but I did it because I thoughttheir answers to questions 13 and 14 showed an understanding that "0" wasa numeral, and I didn't want to spend time in this particular lesson tryingto get them to see where "0" best fit with regard to order. If they hadsaid there were only nine numerals and said they were 1-9, then you couldask how they could write ten numerically using only those nine, and theywould quickly come to see they needed to add "0" to their list of numerals.