At lunch today, Jonathan told me he wanted a quarter of a grilled cheese sandwich; he then amended that to "half of a quarter."  "So you want an eighth of a sandwich?" I inquired.  "Yes," he replied, and proceeded to ask Heather, as he had several times before, "What's half of an eighth?"  "A sixteenth."  What's half of a sixteenth?'  "A thirty-second."  Then followed a discussion of just what "one thirty-second" means.

After lunch we had some wonderful molasses cookies made by a friend.  There were just enough for each of us to have one, with one cookie left on the plate.  So I asked Jonathan what fraction of a cookie each of us would have if we shared the leftover cookie fairly.  This was confusing for him, so Jon simplified the question and began to lead Jonathan step by step to figuring out the answer.  Jonathan is adept at the concept of one half and one quarter, including the written form that he encounters in recipes.  However, this is a little hard to extend to one fifth, because there's no 2 in "half" and no 4 in "quarter." (More)
Posted by sursumcorda on Tuesday, September 23, 2008 at 2:55 pm | Edit
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Three years ago I read and reviewed Lu Hanessian's Let the Baby Drive, and recently my thoughts have been returning to that insightful book.  Today's Frazz brought it again to mind.

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Posted by sursumcorda on Wednesday, September 10, 2008 at 7:33 am | Edit
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Whatever you think about John Edwards, he isn't stupid, and choosing to admit his adulterous affair while our attention was focused on the Olympic opening ceremonies was probably a smart move.

Russia isn't stupid, either.  They couldn't hope to invade another country without generating some controversy, but doing so while the eyes of much of the world and even more of the news media are on events in Beijing gives them a good chance of being ignored, at least long enough to accomplish their purposes. (More)
Posted by sursumcorda on Tuesday, August 12, 2008 at 8:21 am | Edit
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This is a joke, right?  It doesn't surprise me that some crackpot with "Dr." in front of his name should decide that we could solve the widespread problem of students' appalling inability to spell by merely accepting their mistakes as "spelling variants."  After all, professors of education have promoted weirder ideas, and Ken Smith is only a lecturer in criminology who is fed up with wasting his time trying to correct the failures of his students' spelling teachers.  It's not our children's fault they had the misfortune to be born into an era of standardized spelling.  Dr. Smith's frustration can't be much more than mine as I try to decipher the writings of my intelligent, well-educated, and highly respected colonial American ancestors, who couldn't even spell their own names consistently.

What makes me sure of the intended humor is this passage in the article: Dr. Smith said there was no reason many commonly misspelt words were configured the way they were. The word 'twelfth', for example, would make more sense as 'twelth', he said.  'How on earth did that "f" get in there? You would not dream of spelling the words "stealth" or "wealth" with a[n] "f" (as in 'stealfth' or "wealfth") so why insist on putting the "f" in twelfth?'.  Since a moment's thought about both the origin and the pronunciation of "twelfth" would reveal the answer, Smith must be pulling our legs, perhaps making his point in the spirit of Jonathan Swift's A Modest Proposal.

As the story spreads, however, some folks are finding the idea of this Irish baby fricassee more palatable than not.  All I can say is that my friends who teach college math should have thought of this years ago.  Instead of complaining that your students can't add two and two and get four, much less construct a simple proof, why not simply accept 2+2=5 as a variant sum?  And who are you to decide what's "true" and "proven," anyway?
Posted by sursumcorda on Sunday, August 10, 2008 at 7:02 am | Edit
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I hate to give such horrors any more publicity, so if you already view Planned Parenthood as evil incarnate, don't follow any of the links on John C. Wright's post, Footnote to Modern, Ever-Changing, Ever-Evolving Moral Standards.  If, on the other hand, you still cling to the hope, as I did for a long time, that the omni-present organization might not be utterly irredeemable, you owe it to your children to take a look (with them out of the room, of course—preferably out of the house).  I wish I could cleanse my brain of those cute, Sesame Street-like videos, but sometimes it's useful to know just how bad the situation really is.

I like the idea of socially responsible investing, but this has reminded me that whatever harm might be done by an undesirable gnat stock amongst those in our mutual funds is dwarfed by the camel damage paid for with our tax dollars.

Oh, by the way.  In case you miss it (which I recommend), take my word for it that when the folks at Planned Parenthood use the word "abstinence," they mean something entirely and disturbingly different from what you, I, and the dictionary do. So define your terms carefully (and make them define theirs) before conceding agreement on any point.
Posted by sursumcorda on Tuesday, July 29, 2008 at 6:21 pm | Edit
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My first reaction to the good news that girls are now doing as well as boys in mathematics, at least through high school, was to laugh at the headline, which was "Numbers don't lie: Girls equal to boys in math."  Anyone who knows anything at all about numbers knows that they are frequently used to express untruths.  Nonetheless, it's still good to hear that the distressing gap between male and female performance that once appeared between elementary school and high school has disappeared.

And yet, I wonder.  I don't give any more credence to the idea that boys might be inherently better in math than girls, any more than I do to the idea that girls are naturally superior in reading.  (I do leave room for the idea that certain ways of thinking, some approaches to problems, and even some narrow fields of mathematics, might show sex-specific correlations, because, after all, men and women are inherently, biologically different.  I'm quite certain, however, that differences among individuals are great enough to make sex-related differences of little import.)  What makes me less than elated about this new study is a nagging suspicion of anything that sees parity as the goal.  From the school principal who told me that the ultimate purpose of kindergarten was to get all students on the same level, to the school board members who were much less concerned with student achievement than with making sure no school in the district looked any better or worse than another, I've found that a victory in mere equality often masks a decline in real accomplisment.  Both kindergarten and school district "parity" are often achieved as much by holding some students back as by bringing others forward.  I'm certainly glad girls are doing "as well" as boys in mathematics—but much more interested in how all our students are doing, not only in comparison with each other, with students of the past, and with students of other countries, but most importantly in consideration of actual achievement.  "As good as" is a slippery measurement, and "better than" is little better.  In the company of serial rapists, a "mere" adulterer might feel pretty good about himself.

(It is also worth mentioning that the reason given for poor female performance in the past, that people expected girls to be stupid when it came to math, was certainly not universal, even "50 years ago."  My parents never expected that I would not do as well as my brothers, nor did any of my teachers offer me such a flimsy excuse as gender for poor performance!)
Posted by sursumcorda on Friday, July 25, 2008 at 6:54 am | Edit
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O Divine Master, grant that I may not so much seek...to be understood, as to understand.—St. Francis

I can't resist taking a moment to share another excellent post from Random Observations, which gently reminds me that I need to spend more time trying to understand the point of view of those with whom I disagree, especially if I disagree strongly and emotionally.

If you can't even correctly repeat the arguments of your opponents, how in the world do you imagine you've refuted them?
Posted by sursumcorda on Tuesday, July 22, 2008 at 6:52 am | Edit
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For a monolingual person, I have an inordinate love of languages.  Not only is multi-lingualism increasingly important in today's world, but it does wonderful things for the brain—from increased brain growth in babies to decreased dementia in the elderly.  I wish the great resources available for teaching young children another language had been around when our kids were little, and I wish I had more aggressively pursued what there was.  Be that as it may, I am only a language dilettante, enjoying learning a few phrases of Japanese before our trip there, brushing up on my minimal high school French, and listening to the language CDs from the Hippo Family Clubs.  I wish I were multi-lingual, but face the reality that at my age it just isn't going to happen.

Nonetheless, I should be able to learn, if I put the time and effort into it, enough of a language to get along reasonably well with basic, necessary communication.  Which brings me to the question of why I find myself attracted to almost any language other than the two that would be of the most immediate practical use to learn: Spanish and German. (More)
Posted by sursumcorda on Thursday, July 3, 2008 at 7:01 am | Edit
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I don't recall the era of the 1960s with fondness; it wasn't all bad, but it was a messy, unkind time that accelerated our culture's decline in the areas of civility and decent behavior.  However, there must be more of the 60s in my make-up than I thought:  I'm finding good reasons to distrust The Man.  :)

Just as the National Education Association adamantly opposes home education, the American Medical Association, unnerved, perhaps, by Ricki Lake's popular home birth movie, The Business of Being Born, has taken direct aim at home birth.*  Reaction against yet one more threat to personal freedom has come from across the political spectrum, from the far left to the far right.  Congratulations to the AMA for provoking agreement between pro-choice and pro-life groups.  Wink (More)
Posted by sursumcorda on Saturday, June 28, 2008 at 4:53 pm | Edit
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Equality means everyone gets to run the race. It does not mean everyone comes in first.

John C. Wright and I may not agree on Prince Caspian, but we saw the same message in The Incredibles: the loss of excellence, enthusiasm, and initiative that results when we foolishly favor equality of outcome over equality of opportunity.

The inspiration for Wright's post was a soccer trophy won by his five-year-old son.  Well, "won" is stretching quite a bit, and that's Wright's point.  Everyone on the team received the same trophy, just for showing up.  Or even not showing up; the coach also wanted to give a trophy to Wright's other son, who had quit the team mid-season! (More)
Posted by sursumcorda on Wednesday, June 11, 2008 at 11:12 am | Edit
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So. Studies have shown that length of life can be extended by eating a very low calorie diet, twenty to thirty percent less than a "standard diet." Whatever the standard diet is, you can bet it's significantly less than the average American diet, so we're talking severe calorie reduction here.

Thanks to the University of Wisconsin-Madison (my nephew's current college of choice), the National Institutes of Health, and DSM Nutritional Products of [ahem] Basel, Switzerland, there is a better way. Drinking red wine apparently has similar effects and works by nearly the same mechanism. (If you're ambitious you can read the full report.)

Let's see. To drink, or not to eat...is that a question? I don't care much for wine and even then I prefer whites to reds, but I could manage this.

The article doesn't say what happens when you combine the starvation diet with drinking red wine, though the picture it evokes in my mind is not exactly one of robust health....
Posted by sursumcorda on Tuesday, June 10, 2008 at 8:33 am | Edit
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With all due respect for everyone's personal choices, and with free acknowledgement that in our diversity of educational options lies our strength, here's an excerpt from today's Frazz for a moment of homeschooling joy:

Posted by sursumcorda on Saturday, June 7, 2008 at 6:44 am | Edit
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While chatting with the dental hygienist yesterday, I learned about a science project that had been assigned to her fifth-grade son: Each student was assigned a "body system"—perhaps circulatory, digestive, respiratory, etc.; I didn't get the details—and told to make up a game using questions about that system.  At first glance that seems reasonable, perhaps even interesting. Games are not a particularly efficient way to learn facts, but they can be an enjoyable way of masking the repetition that is required to commit them to memory.  Certainly making up the questions is a good exercise.

However, the amount of time and effort required for this project was 'way out of proportion to the science knowledge gained, most being devoted to extraneous matters:  the game must have a well-made game board, with a detailed, typed instruction sheet, and a sturdy, well-decorated box.  Such a project might be a joy for some students but torture for their less-crafty classmates—and to what purpose?  Whatever one might think of the merits of training fifth graders in manual dexterity and design, it seems unfair to base a science grade on such work, and in any case one ought not to pretend that it is science that is being taught.

This assignment is yet one more example of how those who claim they don't have enough time to teach properly waste the students' time with busywork.  Craft projects instead of science, PowerPoint presentations instead of written reports, browsing the Internet for images instead of writing paragraphs, and tweaking fonts and backgrounds instead of improving sentence structure!  It's bad enough when a teacher allows a student to get away with such nonsense; to require it is ludicrous.

My theory is that the teacher in question is using her students as slave labor to create classroom materials for future years, so I encouraged the hygienist to make sure the project comes home after it has been graded. 
Posted by sursumcorda on Tuesday, May 6, 2008 at 8:28 am | Edit
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Thanks to Tim at Random Observations for alerting me to this interesting commentary on John Steinbeck's The Grapes of Wrath.  The book and the movie derived from it have formed our national image of the Depression and the Dust Bowl.  The trouble is, that's a false impression.  Like Amadeus and Braveheart, The Grapes of Wrath tells a good story based on historical events, but without letting the truth get in the way of the narrative.

Someone with a solid knowledge of the historical situation might be able to imbibe the story without harm, but the rest of us, unfortunately the majority, are learning history through these media, and learning it wrong.  We're left with a mish-mash of fact and fiction we may never sort out, and upon which we will unconsiously base our philosophical, political, social, and moral decisions.

Whoever said (I've seen various attributions), "Let me write the songs of a nation, and I care not who makes its laws," might just as well have been speaking about its popular books, television shows, and movies.  The only antidote besides a healthy (uncynical) skepticism is a solid grounding in history, preferably from several viewpoints.  Mea culpa; my own knowledge of history is abysmal, and I did not do much to help our children achieve more.  But if I were designing a home eduation program now, the tripod on which I would rest the entire academic program, beginning from the earliest stages, would be: language, mathematics/logic, and history.  Those who are strong in these three areas will not easily be duped.
Posted by sursumcorda on Monday, April 28, 2008 at 11:00 am | Edit
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Study Suggests Math Teachers Scrap Balls and Slices is a New York Times article about research at Ohio State University that may have profound implications for the teaching of mathematics to young children.  Unfortunately, just what those implications may be is completely obscure to me, as it is, I daresay, to the researchers.

I've written before (here, and here) about my belief that many children can learn abstract math concepts much earlier than is commonly supposed, and do not need to be limited to practical, real-world mathematics until they reach Piaget's magical age of abstract thinking.  So I suppose I should have been pleased to read about a study that purports to show that children actually learn mathematical concepts better through abstract symbols than they do through practical examples.  Not so; I'm also a fan of practical math, and believe both to be important.  In any case, it's hard to draw any conclusions one way or the other from this research—or at least from the Times report.

In the experiment, students were taught a mathematical concept either through abstract symbols or through concrete examples such as combining liquids in measuring cups.  They were then asked to apply that knowledge to figure out the rules of a game.  Those who had learned the concept abstractly did better at that application than those who had learned through the concrete examples, and also better than those who had been taught first the concrete examples and then the abstract ones.  Supposedly the real-world examples actually obscured the underlying math.

I'm going to break the post here, because some of you will want to look at the puzzle yourselves before reading about my experiences.  I strongly encourage you to read the article, but if you don't do that, at least follow the link and click on the link in the upper left under "Multimedia" that will show you the problems.  (It's a javascript pop-up, and I can't figure out how to insert it here without offending someone's copyright.)  Then click the "more" link after this paragraph to continue reading this post. (More)

Posted by sursumcorda on Friday, April 25, 2008 at 11:27 am | Edit
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