• Recent Commentaries on Those Recommendations

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    Posted by Satch on March 28, 2012, at 4:56 AM.
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    Whoa, things just got a whole lot esaeir.

    Posted by Maxence on March 5, 2012, at 9:01 PM.
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    I was so confused about what to buy, but this makes it udnrestandbale.

    Posted by Hiroko on March 4, 2012, at 2:10 AM.
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    Many examples of Guess-What-I’m-Thinking and Say-What-I-Want-You-To-Say Questions.

    So far, I’ve only listened to Act One, but it offers a smorgasbord.

    If you play just Act One using their website, the questions start at about 6m 29s.

    Available at: http://www.thisamericanlife.org/radio-archives/episode/424/kid-politics

    Posted by George Hill on January 16, 2012, at 8:42 PM.
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    Practice mental math using playing cards

    multipleswithcards.JPG

    Here’s a game:

    • Take two or three decks of cards.
    • Remove face cards and jokers, then shuffle the remaining cards together and place them face down.
    • Determine which set of multiples each player will try to build (e.g. 0, 6, 12, 18, 24, 30, 36, 42, 48 . . . ); it’s easier if each player has a different set.
    • Going as fast as each player can, players draw a single card at a time. The player can place that card where it would fit in the sequence of multiples; if the player cannot use the card, the player must discard it.
    • Each card represents a single digit; aces represent “1″ and tens represent “0″.
    • When the stack of cards is depleted, the discarded cards may be shuffled and put in its place.
    • When no more cards can be played (e.g. because none of the remaining cards matches a needed digit), the game is over; perfectionists at this point may counterfeit cards with sticky notes.
    • If it is necessary for the game to have a winner, the winner could be the person who is able to find and play the most cards.

    The photo shows one game’s results. The player on the left first built a tower of the multiples of 6 and then a shorter tower with the multiples of 7; the player on the right built a tower with multiples of 9. (Remember: tens represent the digit “0″.) Unplayable cards are laid horizontally in a tower up the middle.

    Posted by George Hill on December 23, 2011, at 7:43 PM.
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    School discipline often parallels adult criminal justice.

    That’s a fact, though an ugly one.

    The important thing, though, is to learn the right lessons from that field.

    Presently, more often than not, it’s the wrong lessons that get applied.

    Listen or read here for some of the right ones . . .

    Story and audio: http://www.npr.org/2011/11/01/141803766/interrupting-violence-with-the-message-dont-shoot

    Transcript: http://www.npr.org/templates/transcript/transcript.php?storyId=141803766

    Posted by George Hill on December 7, 2011, at 5:23 PM.
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    One activity for learning words on a vocabulary list

    Step 1: Start with a word on the list.

    Step 2: Go to a website along the lines of the New York Times.

    Step 3: Search for articles containing that word. (You can use the site’s built-in search box; you could also go back to Google, search for your word, and restrict the results to pages from your site by adding in “site:nytimes.com” with the word you’re searching for.)

    Step 4: Read all of the returned “snippet” results, which show how a bunch of professional writers have used that word in sentences.

    Step 5: Choose two of those articles. Open them in new tabs. Search within the article (usually by pressing Cntr-F or Command-F) for the word. Read at least the paragraph containing the word, and maybe read the whole article.

    Step 6: Tell somebody your own deduced definition for the word.

    Step 7: Compare your definition against a dictionary’s definition.

    Step 8: Give an example of something described by the word. (That is, for the word “magnate,” your example might be Steve Jobs, because he was a rich, influential person who ran a company that made and sold physical objects.)

    Step 9: Give a not-quite example of something described by the word. (That is, for “magnate,” your not-quite exmaple might be Alicia Keys, because she’s rich and influential but does not run a company that makes and sells physical objects.)

    Repeat with each word on your list.

    Posted by George Hill on November 6, 2011, at 2:10 PM.
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    Math Paper

    The problem: the student keeps making minor mistakes within long-division; these mistakes mostly come of messy, crooked, cramped writing; begging and exhortation both fail to lead the student to write differently.

    A solution: math paper.

    Simulated “before” scenario:

    DemoBefore.jpg

    Simulated “after” scenario:

    DemoAfter.jpg

    Files: in Word and as a pdf.

    Disclaimer: Actually, I made this just now. I won’t be able to field-test it for a few days, so I don’t yet know what effect it will have.

    P.S.:

    That little square over the 6 is something that I have already used with success.

    When students do long division that involves dividing something by a two-digit number (like the 2.7 in this problem), they often make the mistake of putting the first digit of their answer in the first available digit position—even though that position (and sometimes the second position) is more properly filled by a zero.

    Writing in a regular zero would muddy up the algorithm (because we don’t ask the student to write out the results of multiplying, in this case, 2.7 by 0), but a little square-box pseudo-zero seems to do the trick of forcing the first non-zero digit into the right spot.

    Posted by George Hill on October 27, 2011, at 2:01 PM.
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    Roadmap Through Mental Math Facts

    The problem: the student does not yet know, but needs to know, basic math facts from memory—and has muddled on for years using fingers or calculators—and sees going back and learning all those facts as an impossibly large task.

    A solution: show (a) that all those facts fit on a single piece of paper, (b) that they can be learned a few at a time, (c) that the student already knows quite a few, and (d) that the student will be able to see progress immediately.

    Here’s a demo:

    Roadmap-MMF-demo.jpg

    Checkmarks indicate facts that the teacher has seen the student already pull from memory in the course of doing other math; the squares indicate facts that the teacher has seen the student not know.

    The “Goal” column is for setting target dates by which to master certain chunks of facts.

    The “T” column should be filled in when the student thinks she knows the fact; the “K” column is for when the student knows she knows the fact.

    Here are PDFs:

    Roadmap-MMF-Student.pdf

    Roadmap-MMF-Teacher.pdf

    The first is for the student to keep; the second is for the teacher to keep (so as to track progress for multiple students).

    Posted by George Hill on October 10, 2011, at 11:27 AM.
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    “We don’t do stuff like that here.”

    Learning from primatology about some reasons for misbehavior and about the possibility of improving it:

    http://www.radiolab.org/2009/oct/19/new-baboon/

    Posted by George Hill on October 7, 2011, at 5:44 PM.
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    Required listening . . .

    . . . optimized for even the most jaded student or teacher.

    To avoid a spoiler, I’m embedding the audio (a segment from Radiolab) here:

    Only after listening to the whole thing should a person go to the source (here).

    Posted by George Hill on September 18, 2011, at 2:04 PM.
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    Design

    Regarding hardware and software:

    The logic of Apple software icons and button placement alone is a science that is still not understood by the bulk of product designers. I have a microwave oven made by Sharp that has a giant icon button for popping popcorn, but the start and stop buttons are unremarkable and buried in a number of text only buttons making it hard to find the most used buttons in poor light or without reading glasses.

    A lot of dumb mistakes made in product development cost nothing to do right, if anyone with the power to force a correction even notices the flaw. At one point I stuck a green dot over the start button and a red spot over the stop button and the microwave seemed a lot more compliant with the standards of icon use I expect from my Apple computer products. That microwave design would never have gotten by a Steve Jobs final inspection without that obvious defect in user interface being fixed.

    The colored stickers eventually wore off, and we are back to the Microsoft sort of learning curve due to stupidity in design. We have owned that microwave for several years now, and it still ticks me off when I can’t find the right button quickly.

    From: http://www.mactech.com/2011/08/25/gregs-bite-steve-jobs-creativity

    I’m no Steve Jobs, but here’s a thumbnail of a handout that (I hope) helped me get a certain point across regarding thesis, claim, evidence, and retelling:

    TCEversusRETELLING.jpg

    It’s fun to have the Apple/Microsoft difference as something to contemplate when preparing a lesson.

    Posted by George Hill on September 11, 2011, at 7:13 PM.
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    “You are wonderful!”

    “Thank you! I’ve worked hard to become so.”

    From: http://www.youtube.com/watch?v=lC6dgtBU6Gs

    Posted by George Hill on August 28, 2011, at 2:45 PM.
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    Regarding: “Ours is not to reason why; just invert and multiply.”

    See Hung-Si Wu’s “What’s Sophisticated about Elementary Mathematics?” in the Fall 2009 edition of American Educator. Full text (pdf) here.

    Posted by George Hill on August 7, 2011, at 5:33 PM.
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    $24,000,000,000 Bonus Lesson

    Via (some time ago) the great Dan Meyer’s http://delicious.com/ddmeyer/showandtell/ feed.

    Posted by George Hill on August 7, 2011, at 5:05 PM.
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    Being able to do far more than this would be good . . .

    Thanks, xkcd, for promoting embedding!

    . . . but you gotta admit that for all Americans to be able to do at least this would be very, very nice.

    (I’ve lost count of the number of fairly old students who weren’t able to find China or Africa when I handed them a globe.)

    Also available here:

    http://xkcd.com/850/

    Posted by George Hill on August 4, 2011, at 10:50 PM.
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    Facebook Version of American History

    Full version at:

    http://www.nytimes.com/interactive/2011/07/04/opinion/20110704_OPART.html

    Snippet:

    facebook-american-history.jpg

    Posted by George Hill on July 29, 2011, at 11:17 AM.
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    Real-life Math Conundrum

    Cheerios from Wikipedia

    If you have to buy Cheerios from an overpriced store, is it better to buy a very-overpriced small package or a less-overpriced large package?

    Details:

    Last Tuesday evening I absolutely had to buy enough Cheerios to make trail mix for the next few days.

    But the discount store that I have recently discovered was closed.

    My only option was a well-known pharmacy chain.

    I would be able to hit the discount store two days later to get more Cheerios, but I had to buy enough to get me through till then.

    The pharmacy offered Cheerios in an 8.9 once box for $3.39—which is 38.1 cents/ounce.

    It also had a 14 ounce box for $4.99 (as I recall)—which is 35.6 cents/ounce.

    I didn’t know the exact price at the discount store, but I was sure it would be cheaper there.

    If I bought the small box, I’d be way overpaying per unit, and I’d only have a little bit of cereal.

    If I bought the small box, I’d be spending an extra $1.60 on overpriced cereal, but it would be less overpriced than the small box and I’d have more cereal.

    Possibly complicating things, of course, was that I didn’t know the exact price at the cheaper place.

    I stood there for about five minutes trying to think it through (which further complicates things if you factor in the value of my time) and then went with a decision based mainly on intuition.

    But this drove me nuts for the rest of evening.

    Finally, as I was brushing my teeth, I came up with a way to think about this that makes it much easier to see the right thing to do.

    So, the question is: what’s the right thing to do?

    Posted by George Hill on July 26, 2011, at 2:43 PM.
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    I’d heard the rumors . . .

    . . . but I just now decided to go looking.

    http://threesixty360.wordpress.com/2009/06/10/the-first-bunch-of-ways-to-multiply/

    See also:

    http://threesixty360.wordpress.com/25-ways-to-multiply/

    Posted by George Hill on July 26, 2011, at 2:01 PM.
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    I wasn’t sure if these three items, together, would quite rise to the level of a bonus lesson . . .

    . . . but the scales were tipped by the fact that I later heard a student humming the tune.

    Posted by George Hill on July 20, 2011, at 4:51 PM.
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    Where will the continents be 250 million years from now?

    I was thrilled to find

    http://www.science.org.au/nova/newscientist/ns_diagrams/104ns_011image2.jpg

    (which is amazing)

    via

    http://www.science.org.au/nova/newscientist/104ns_011.htm

    via

    http://en.wikipedia.org/wiki/Pangaea_Ultima

    via

    http://en.wikipedia.org/wiki/List_of_supercontinents

    via

    http://en.wikipedia.org/wiki/Pangaea

    (which is pretty cool itself)

    (since it has . . .

    Pangea_animation_03.gif

    . . . on it).

    Posted by George Hill on July 16, 2011, at 6:13 PM.
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    Those cumulative effects can be either good or bad.

    SATadvice.JPG

    I’d rather teach kids to keep their eyes open for 3-4-5 right triangles than teach them to make rulers out of SAT answer sheets.

    The cumulative effect of learning to rely on making a ruler in those circumstances—is that the student comes to see math as something they will never really understand.

    The cumulative effect of learning to notice 3-4-5 right triangles—is that the student sees that complicated problems often have very simple solutions.

    (Oh, and the student ultimately finds nothing mysterious or frightening about the SAT; rather, the test becomes just a game, sort of like Sudoku.)

    Posted by George Hill on July 16, 2011, at 3:54 PM.
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    Lead classroom discussions the way Neal Conan leads talk-show discussions.

    First, here’s what not to do: don’t lead discussions the way that Tom Ashbrook does.

    For example, an On Point show chosen more or less at random:

    http://onpoint.wbur.org/2010/07/21/killer-whales-tanks-and-tensions

    You can start listening at 33:30; the show’s scheduled guest is talking.

    • At 33:35, Ashbrook introduces a caller, talking until 33:45 (totaling 10 seconds).
    • At 33:45, the caller asks a question, talking until 34:15 (totaling 30 seconds).
    • At 34:15, Ashbrook restates the question, talking until 34:30 (totaling 15 seconds).
    • At 34:30, the guest starts to answer the question.

    Compare with Neal Conan in a Talk of the Nation show taken completely at random:

    http://www.npr.org/2011/07/07/137676981/reassessing-anonymity-in-12-step-programs

    You can start listening at 6:48; the show’s scheduled guest is talking.

    • At 6:52, Conan introduces a caller, talking until 7:05 (totaling 12 seconds).
    • At 7:05, the caller asks a question, talking until 7:52 (totaling 47 seconds).
    • At 7:52—Conan doesn’t do or say anything! Instead . . .
    • At 7:52, the guest starts to answer the question.

    If you listening to both programs frequently, as I do, you’ll notice that Ashbrook and Conan follow their respective patterns consistently.

    Ashbrook’s pattern gets more and more annoying; Conan’s gets more and more admirable.

    Note that Ashbrook takes a total of 25 seconds to introduce a caller and restate the caller’s question—which is almost as much time as the 30 seconds that the caller gets on air.

    Note that Conan takes a total of 12 seconds to introduce a caller, period. He doesn’t waste time or steal the scene or disrupt the conversation’s flow by restating the question.

    Note also that Ashbrook’s caller gets only 30 seconds on air, compared to Conan’s caller’s 47 seconds.

    (Also, let it be noted that Ashbrook consistently cuts his callers off, not giving them a chance to say good-bye, much less ask the guest a follow-up question. Conan usually thanks them after the guest answers the question; he thanks the callers before they ring off; and he gives them a chance to say good-bye.)

    One obvious effect of Ashbrook’s method is—he either doesn’t get many people to call in, or if they are calling in, very few of them actually make it onto the program.

    Conan’s method, on the other hand, results in many more callers per show.

    (This, by the way, is why the Ashbrook example was only “more or less” at random. It took me about three tries before I could find a show in which I could even find a caller asking a question just by clicking at random spots on the player. Most of my random clicks kept hitting spots where Ashbrook or his guests were talking; I didn’t feel like sitting through an entire program to find the rare spot where a guest made it on.)

    Posted by George Hill on July 9, 2011, at 6:57 PM.
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    “Says who?”

    Students will often state sweeping, negative, fatalistic opinions as if obvious fact:

    • I’m never going to learn this.
    • All men are jerks.
    • School is a waste of time.

    Teachers usually know intellectually—and from experience—that directly contradicting such an assertion tends to lead the student to dig in deeper.

    But a teacher’s typical instinctive reaction is nonetheless to directly contradict the assertion.

    I’ve recently stumbled across a phrase that has been working wonders and that I’m now using as my default response to such assertions:

    • Says who?

    Faced with that question, a student will then likely go down one of two paths.

    The student might reflexively assert something like “everyone knows that”—in which case it’s reasonably easy for subsequent Socratic inquiry to create some doubt in both premises.

    Or the student might go straight to realizing (though not saying) that the honest answer is “I say that”—in which case the student takes ownership over an opinion instead of hiding behind it as if fact. Once the student realizes that it’s an opinion, the student becomes more open to evaluating its accuracy and usefulness; sometimes the student is immediately horrified into backing away from the earlier blanket assertion even without any further prompting.

    Posted by George Hill on July 8, 2011, at 8:41 PM.
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    View. Discuss.

    For bonus points: compare, contrast, evaluate, apply.

    Posted by George Hill on July 6, 2011, at 12:10 PM.
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    The Virtues of a Second Screen – New York Times

    I’ve only skimmed it—but I skimmed it on my second screen.

    From: http://www.nytimes.com/2006/04/20/technology/20basics.html

    Posted by George Hill on July 5, 2011, at 9:43 PM.
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    Build relationships right—and succeed brilliantly.

    Moth Radio Hour # 201, Segment 1, is pretty darn close to required listening.

    The link leads to a page that will let you play the “Moth Hour 201 Broadcast” in its entirety.

    You need a (free) account to listen to it. It took me about a minute to set myself up with an account.

    Segment 1 runs from 2m 25s to 14m 28s.

    It’s so worth listening to in its entirety.

    Posted by George Hill on June 27, 2011, at 6:21 PM.
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    Jaw-Dropper

    Moth Radio Hour #402, Segment 1, is entertaining, if bizarre.

    (It’s for adults, not kids. I’d consider it R-rated, though the Motion Picture Association of America would probably call it only PG-13.)

    But that’s not the point.

    The point is that, at about the 16-minute mark, it spins off on a tangent that offers an astonishing insight into a scene that very few people see first-hand, although many people see the scene’s less-extreme analogue every day.

    If you aren’t going to listen from the start, what you need to know is that the speaker is Steven Burns, who played Steve on Blue’s Clues, and at the 16-minute mark he segues into a one-minute anecdote about his work for the Make-a-Wish Foundation.

    Posted by George Hill on June 19, 2011, at 5:54 PM.
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