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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Okay, so it may not generate any cash income, but my status as a blogger has earned me a free, one-year subscription to the Encyclopedia Britannica online!  Many thanks to Groshlink for the alert.  I'm grateful for the existence of Wikipedia, the hare in the online encyclopedia race, because of its wide-ranging, rapid-response (if not necessarily dependable) fluidity, but the opportunity to be able to access, and link to, a steady, reliable tortoise like the Britannica is not to be missed.

The application site has been swamped, it is claimed, but my blog was approved for the free account in less than 24 hours.  Try it with your blog, before they change their minds!
Posted by sursumcorda on Wednesday, April 23, 2008 at 12:23 pm | Edit
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Sunday's Philadelphia Inquirer story about Diane Goslin is a good summary of, or introduction to, Pennsylavnia's home birth problems. Such struggles are not limited to Pennsylvania, but are a good example, like the recent California homeschooling crisis, of how rights and practices that we have relied on for years—centuries!—in our country can be stripped away in an instant if not specifically written into our laws. I don't blame midwives, like the one who assisted with the deliveries of Noah and Jonathan, for fearing that legislation will bring more restrictions rather than fewer. That's what homeschoolers feared 30 years ago, when the modern home education movement was going through its own birth pangs; in some ways they were right, but when society's attention makes it no longer possible to stay under the radar, the protection of the law becomes necessary.

The concern of the U.S. Supreme Court for the religious freedom of the Amish (Wisconsin v. Yoder) was a significant force in the eventual acknowledgement of the rights and responsibilities of all families in the matter of their children's education, though as California has proved, we must be ever vigilant. The wisdom of the serpent is a complement, not a contradiction, to the harmlessness of the dove.  May the Amish also succeed in establishing recognition of the parents' rights and responsiblities when it comes to the birthing of those children!
Posted by sursumcorda on Tuesday, April 22, 2008 at 5:22 am | Edit
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The Story of an Experiment is another interesting story from Perla (see previous post), which she posted to support her contention that children should not be taught arithmetic, except as connected with real life experiences, until they are at least ten years old.  I write about it here, not because I agree with her, since I most emphatically do not, but because the story nonetheless makes some excellent points.

In the early 1930s the superintendent of schools for Manchester, New Hampshire tried an experiment—several experiments, actually.  Essentially, he abandoned math as it was taught in the elementary schools, and concentrated instead on language and logic:  reading, reasoning, and speaking, with arithmetic introduced only as it came up in the course of the rest of the studies.  The results, as he reports them, were spectacular, with the "new curriculum" students far exceeding the abilities of their traditionally-taught age-mates, even in mathematical reasoning, and where they were behind (in basic arithmetic manipulation) they caught up quickly when formal study was introduced in sixth grade. (More)
Posted by sursumcorda on Thursday, April 17, 2008 at 8:59 pm | Edit
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I can hardly count Perla Adams my friend, since we met online and I only visit her blog occasionally.  It's in my feedreader, but the posts and comments in Spanish get ignored.  I'm not proud of my monolingualism, but must deal with it.  Still, I'm not sure how to speak of her in this introduction.  "Internet acquaintance"?  "Fellow blogger?"  Nothing sounds quite right.  Anyway, this delightful person, of whatever label, recently wrote a post (in English) that provoked me to comment, and when I write that much I usually can’t resist sharing in more than one place, i.e. what I’ve written ends up here.  You can find Perla’s original post on her blog, The Classical Mommy.  (That's actually her main site, with all sorts of interesting things.  The post on math is here.)  My response, with a few modifications, is below. (More)

Posted by sursumcorda on Thursday, April 17, 2008 at 11:05 am | Edit
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Isamu Fukui doesn't make lemonade out of life's lemons, he makes the whole lemonade factory.  As a fifteen year old high school student, he vented his frustrations by secretly writing a novel about a dystopia in which the world is run like a school.  Unbeknownst to him, his father found out, and instead of sending his son to a psychiatrist (I'm extrapolating here), sent the manuscript to a publisher.  Three years later, Fukui is still in high school with a critically acclaimed, published novel and a contract for two more.

Write a book for yourself alone, so you can say just what you want, let someone else promote it, and have the publishers come begging you for more.  Works for me!  And a far better use of teen ambition than working for gender-blind college dorm rooms.

Thanks to Jon who directed me to the GeeK Dad article on Fukui's book, Truancy
Posted by sursumcorda on Friday, April 4, 2008 at 12:16 pm | Edit
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My morning routine often includes the SAT Question of the Day; the mental exercise is not only fun (at least when your future doesn't ride on it), but also, I'm assuming, good for my brain.  But I've begun to worry about the system, because it's too easy.

Mind you, I didn't find the Scholastic Aptitude Test easy when I took it in high school; I did quite well but not close to a perfect score (which was 1600 back then).  What's more, I would expect to do better now, since I've had some 40 more years of experience since then.  So I'm not really complaining that the questions are rarely challenging for me; what I find concerning is that they don't seem to be much of a challenge, period.  The number of respondents who get the question right is almost always more than half, and often quite a bit more for the Verbal questions.  People don't do as well on the Math questions, but still far better than I would expect for an exam that's supposed to be challenging our brightest high school students.  I realize those who undertake the daily question are a self-selected population, which may explain their success.

Nonetheless, the level of difficulty still surprises me.  I recall the SAT being interesting and even somewhat fun, but not a cakewalk by any means.  It's true that I studied quite a bit more math after taking the test in 10th grade, but so far I've not seen a question requiring higher math—often they can be done with common sense and/or grinding through the multiple-choice responses

So, my questions:  Has the SAT really become that much easier over the years?  Is the Question of the Day deliberately taken from the easier parts of the test?  Is the idea that our faculties decrease once we get out of school just a myth?  Contrary to popular belief, is motherhood actually a challenging and stimulating profession that keeps the mind agile?  I rather like those last two ideas.
Posted by sursumcorda on Friday, April 4, 2008 at 5:40 am | Edit
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Not a proper post today, but I must keep my readers checking in.  :)  A post on Random Observations led me to this Boston Herald essay by Michael Graham: Campus "Activism" Redefined.  As one commenter remarked, it's too late to be an April Fool joke.  Not content with co-ed dorms on college campuses, the latest push is for gender-blind dorm rooms. Whoopee!

To be fair, I think they're actually talking about letting you choose your own roommate regardless of sex, rather than yet another big shock when a freshman meets his or her roommate for the first time.  Still, it remains a stupid idea. (More)
Posted by sursumcorda on Thursday, April 3, 2008 at 4:38 pm | Edit
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My teacher readers have permission to roll their eyes now, but I've finally figured out the reason for those stupid vocabulary exercises we did in school—look up the word, define the word (don't just copy the dictionary), use the word in a sentence ("XXX is a vocabulary word" doesn't count), test on Friday.  I dutifully complied, but don't believe I learned any new word that way.  I'm very good at remembering something long enough to pass a test, but what increases my vocabulary is reading, hearing, and using new words in context.

Having subscribed (thanks to my father) for many years to A.Word.A.Day, and recently extended my random vocabulary fun to Free Rice (thanks to my brother), I realized that the point of vocabulary work is not to learn new words!  The purpose is to increase one's awareness of new words.  Perhaps slower, more careful readers do not have this problem, but I devour books, and any word I don't know is glossed over, its general meaning derived from context and the word itself forgotten.  However, if my awareness of the word has been raised through seeing or hearing it before, even if I don't know the meaning it will begin to pop out of the page at me, and gradually become incorporated into my working vocabulary.

So for me, and I suspect many others, vocabulary lessons are useless outside of the context of an environment rich in words, but given that context they are a useful tool after all.  I wonder, however, if they are of any use at all to children who will not go on to encounter the words in real life.  Another example of the rich getting richer and the poor poorer, I suppose.
Posted by sursumcorda on Monday, March 31, 2008 at 6:20 pm | Edit
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Thanks to the Prodical Kiwi(s) Blog for alerting me to this video of a talk by Sir Ken Robinson on nurturing (or not nurturing) creativity.  It wasn't as informative as I had hoped, but it hits some high points and is at least amusing.  Not everyone can take the time to read John Taylor Gatto's phone book sized The Underground History of American Education.  My apologies to all my teacher readers (who no doubt wish they had more freedom to nurture creativity) and epecially the university professors.  :)  I really like the story of dancer and choreographer Gillian Lynne.

Posted by sursumcorda on Saturday, March 29, 2008 at 6:05 pm | Edit
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I’ve been a fan of the Mars Hill Audio Journal since the early 90s, though only an intermittent subscriber.  I enjoy and appreciate its insight into life and culture, but generally prefer to receive information in printed, rather than spoken, form.  Plus I was tired of finding places to store the cassettes.

Recently I re-subscribed, because they now offer an mp3 version.  This I can take with me on my walks, and it takes up no physical space in the house.  Works for me. (More)

Posted by sursumcorda on Thursday, March 20, 2008 at 10:23 am | Edit
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Eternal Vigilance Is the Price of Liberty

Whether you attribute that quotation to Wendell Phillips, Thomas Jefferson, or Patrick Henry, it's the truth, and no less true when it comes to the rights of parents to educate their own children. (More)

Posted by sursumcorda on Tuesday, March 18, 2008 at 9:02 am | Edit
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I am on an Andrew Pudewa kick.  I first discovered his Institute for Excellence in Writing through an online forum for early childhood education, and—as usual—once I'd heard of him, his name started coming to my attention in other ways.  A friend of ours is the principal of a private Christian school which emphasizes academic excellence as well as a solid Christian worldview, and she and her teachers waxed so enthusiastic about his program for teaching writing that she even sent me a sample videotape of one of his lectures.  It didn't take me long to get hooked.  For the first three minutes, I found Pudewa's voice to be annoying; after that I was so intrigued by what he was saying and how he was presenting it that it didn't matter.

Now I'm not averse to spending money on educational materials for our grandkids, but they're not yet old enough for the writing materials, which are a bit pricey to buy on speculation, especially since there might well be a subsequent edition or two by the time they would be used.  Fortunately for my curiosity, one of our favorite homeschooling families was impressed enough to try it out, and I'm looking forward to hearing about their experiences. (More)

Posted by sursumcorda on Wednesday, February 27, 2008 at 3:05 pm | Edit
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Those of you who begin each day with my Morning Coffee page are already familiar with the Geography Zone challenge.  Thanks to DSTB you will now see a new geography quiz in the list, National Geographic's GeoBee.  This is a tough one, not only because it covers more than locations (natural resources, culture, and religion for example), but because the questions are not always multiple choice.  Not only is it necessary to come up with the answer on one's own, which is much more difficult than merely choosing, but spelling counts.  I mis-spelled "Montpelier."  :(

Posted by sursumcorda on Friday, February 22, 2008 at 9:37 am | Edit
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It's been a while since we paid college tuition (though the loans linger on), and even longer since we paid for private schooling pre-college (Heather's kindergarten and first grade years), but the desire to compare the cost of a trip to Antarctica to other forms of education led me to some shocking discoveries.

The educational system in America, like the health care system, is in terrible shape.  Don't get me wrong.  I have yet to be convinced that the situation is better in any other country, and the number of people who flock here from overseas, both to our doctors and to our schools, is ample evidence that I'm not the only one.

What's more, anyone who knows me knows my strong belief that the solution to neither problem lies in more governmental funding and/or control (it's always "and," anyway), but rather in more freedom of choice.  Despite my passionate thoughts on the value of home education, the three-fold cord of public, private, and home education is much stronger than any one of them separately.  Equally important is always to be thinking outside the box, and that (at long last) brings me to the heart of this post:  the cost of education. (More)
Posted by sursumcorda on Friday, February 22, 2008 at 8:08 am | Edit
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