Lift Up Your Hearts!

Someone on one of my Internet forums alerted me to Rush, Little Baby, a Boston Globe article of a few months back.  As articles critical of academically-oriented education for young children, it's a pretty good one, covering many perspectives and giving fair space to the opposing view.

It's still frustrating.

For all that it's a long trek through the article, I finished the trip feeling more as if I had been on an If It's Tuesday, This Must Be Belgium tour of Europe: sound bites rather than substance.  And though I have criticisms myself of some of the ways preschool children are taught, they naysayers in this article are generally setting up straw men to knock down.

The case of William Sidis, for example, is a tired old chestnut, full of half-truths, and in any case there are plenty of reasons to account for his problems without blaming his precocity.

I've written before on the problems with the Baby Einstein study.

Phonics instruction is important, and those who never learn to sound out new words are at a distinct disadvantage as readers.  I've quarreled often enough with schools that teach reading by the infamous look-say method.  But the article's assertion that those who learn to read that way can't really read is ludicrous.  Poor as it may be, that's the way I learned to read, and I'm an excellent reader, having figured out (enough) phonics along the way.  More to the point, I'm sure the author doesn't really mean to imply that Chinese, Japanese, and other speakers of non-phonetic languages aren't really reading....

Studies purporting to show that children who are advanced when they enter school generally lose their advantage in a few years will remain unconvincing as long as most schools offer little or no opportunity for such children to continue to blossom, but instead encourage them to become bored and complacent.  I'm very tired of making that point, but apparently it needs to be made over and over again.  (Martin Luther, on being asked why he preached on justification by faith every week, responded "Because you forget it every week.")  

Most of all, I'm frustrated by the false dichotomy that is always being presented. Of course sitting on the floor with your child and building block structures together is a good thing, as are creating puppet shows, snuggling on the couch reading together, cooking dinner, and a host of other activities.  But why are these things always presented in opposition to showing your child pictures of art works, or butterflies, or words, or mathematical quantities, or introducing them in other ways to the lively world they will later "study" as academic subjects?  The people I know who do the latter also do the former, probably more than most.  I'm sure there are those who plop their kids down in front of "brain-boosting" DVDs or TV shows for hours on end and call it education, but that's no one I know, and even if it were, a few bad apples don't invalidate a practice.  I'll grant this:  IF one only has time to build block castles with a child, OR show the child pictures of art masterpieces, but not both, I'd take the blocks.  But that's a foolish premise, an impossible situation.  Whoever needs to make that choice?

If you have time, check out the Doman Inspired Parenting blog.  I have issues with some of Timothy's parents' choices for his upbringing—not that it's any of my business, but so you know I'm not holding them up as paragon parents.  Nonetheless they've done an absolutely amazing job.  A most intense program of the kind derided in the article, with plenty of activities of the kind promoted (check out their ExploraZone!), the parents also managing a job and a half plus grad school...no, these aren't the Incredibles, but they certainly show the foolishness of the above either/or dichotomy.

Parents should share God's wonderful world with their children in a variety of delightful ways.  All else is commentary.

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. 

The end month of Porter's recent gig was very stressful, with lots of pressure and 80+ hour work weeks.  My father often said that his favorite Bible quotation was "And it came to pass...."  This, too, has passed at last, and we have survived.  Many thanks to those of you who upheld Porter in your prayers.

If anyone wants a measure of how stressful the time was, I need only say that he has spent several days recently working on replacing a neighbor's roof, and some of you remember that two years ago—after replacing ours—he said he'd never, ever do that again. But this is how he chooses to relax these days, finding the physical work a delightful change.

So, onward!  Two days in Roanoke, then who knows?  It's always an adventure. 

Picture this:  During the upcoming Olympics, the second place finisher of a big race suddenly collapses and dies.  Nonetheless, the crowd still celebrates with the winner, and the medal ceremony takes place as if nothing had happened.  It's a tragedy, sure, but that's life, that's sport, and nothing should take away from the winner's glory.

That's not as far-fetched as it might seem.  We don't like to rain on anyone's parade.  No one seems anxious to boycott this year's Olympics, despite China's blatant and unrepentant violation of human rights and international law.  We don't want to hurt our athletes, and that's understandable.  Still, there was a time when celebrations were set aside in the face of tragedy, such as the wedding of my mother's cousin, for which, as the newspaper announcement put it, "nuptials were quiet owing to the late bereavement in the home."

Horses are not people, but the death of Eight Belles, the brave filly who finished second in today's running of the Kentucky Derby, then collapsed with two compound fractures of her front legs and had to be euthanized immediately, will put a damper on the post-race celebrations.  Or at least it should.

When I was in Pittsburgh, we bought some dried pineapple at Trader Joe's, and it was very, very good!  Thus when I saw the same at my local health food store, I snapped it up.  Did I say it was the same?  Not.  Even thought the label did not mention added sugar, this pineapple must have been sweetened, as is the dried pineapple I can buy at the grocery store.  Yuck.  I couldn't eat it, so I cooked it with some dried apricots to make a fruit topping for my breafast muesli.

Not to be defeated, however, I set about making my own dried pineapple out of canned pieces (rings work best) heated in a low-temperature oven.  Voila!  Wonderful!  Delicious!  The only trouble is that a can of pineapple shrinks to something so small—and so tasty—one could easily devour an entire batch in one sitting.  (One didn't, but it was a close thing.)

The acoustics in our house are such that the sound from the television is loudest in every room except the one in which the TV resides.  Perhaps that is not literally true, but to those trying to work or sleep while someone else watches television, it certainly seems that way.  Hence our joy when Porter's "thank you award" came from IBM:  a set of wireless headphones.

Fortunately, there was no need to understand in detail the instructions, which contained several gems.

This wireless headphone is worked based on optical-electricity transition.

Well, of course.  What else would it be worked based on?

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.

On rare occasions I have the opportunity to hear National Public Radio's Car Talk program, which I find amusing as well as informative, which is saying something since I have little interest in cars beyond their usefulnes in getting me from Point A to Point B.  (Okay, so I make an exception for a certain Ford GT, but that has more to do with the people involved than the car itself.)  The shows usually feature a "Puzzler," which since it involves cars often leaves me clueless.  But every once in a while (well, twice) there has been one that I have solved almost instantly, which of course makes me feel great.  Thus the inspiration to share them with you all.  The first was many years ago, and the second I heard today, so you can gather from that how good a Puzzler puzzler I am, or perhaps how often I hear the show.  For a hint, I can say that my ability to solve them both so quickly was due to personal experience with the situations involved.

Puzzler #1

Puzzler #2

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.I quarrel with the application of this research to any conclusion other than "We need to study this further."  For one thing, The laboratory rats in question were college students, whose brains might reasonably be expected to have already become capable of abstract thought.  It would be risky to apply anything learned from them directly to six-year-olds.  For another, the "concrete" examples appear—thought it's hard to tell for sure from the article—to be abstractions themselves.  Thinking about a measuring cup filled 1/3 full of liquid is more similar to thinking about a circle than it is to pouring liquid from an actual, physical cup.

Believing my own brain to be reasonably competent at both mathematics and abstract reasoning, I was shocked at how difficult I found the problem.  I couldn't get my mind around what they were trying to show.  What finally gave me the necessary clue was actually the measuring cup example, but thought about abstractly, as numbers.  Thinking about its physical properties was, indeed, distracting from the underlying mathematical concept, but the abstract symbols were no more helpful.  When I finally thought about the problem in terms of numbers alone, then answer was obvious, and to my mind much more easily explained abstractly—though I do still have a problem with the third example in the measuring cup system, so I may be missing something even though I got the correct answers.  I'll be very interested to hear what other people think.  Especially my reader from Oswego.  :)

I wouldn't change the way I taught anyone mathematics based on this study alone, but I would be very interested in hearing the results of a similar study done with other demographics: not only children of different ages, but also adults of various occupations and levels of education.

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!

With polygamy in the news these days, it seems a good time to report on my discovery of one of our stranger cousins. Fourth cousin five times removed to both Porter and me (through different lines), Aaron Johnson, born in 1806, the tenth of the thirteen children of Didymus and Rahuna (Stephens) Johnson, was just another name in my genealogical database, discovered during a convoluted search for the ancestors of Stephen Johnson, husband of Lucina Burr (sister of Porter's great-great-great grandmother) whose grave we found last summer in a small cemetery in Haddam, Connecticut.

Just another name, that is, until I found Aaron's entry in Paul Franklin Johnson's invaluable Genealogy of Captain John Johnson of Roxbury, Massachusetts. It's not unusual to find ancestors with more than one spouse, thanks to disease, war, and complications of childbirth. Large families were also not uncommon. But Aaron's entry stands out for covering two pages with his eleven wives and forty-three children! A perusal of the data makes all clear: although born in Haddam, Aaron died in Utah. Although the book presents only bare-bones genealogical data, Aaron's pages read like a history of the Mormon Church; in fact, he was apparently one of the church pioneers and was even a bishop.

That's a long way from Haddam.

It's easy to dismiss the Yearning for Zion Ranch as a collection of kooks, but even kooks have rights in this country, or should. Innocent chidlren, especially, should have their rights firmly protected, including the right not to be torn from their homes without clear and compelling evidence of immediate danger.  Yet the State of Texas has abused the children of the Yearning for Zion families in just that way, on the strength of one anonymous phone call accusing one man of abusing his 16-year-old wife.  Over 400 children were turned over to strangers, subjected to medical examinations, and even though there was no evidence of abuse have still not been allowed to return home.

The Fundamentalist Church of Jesus Christ of Latter Day Saints (not to be confused with the "mainline" Church of Jesus Christ of Latter Day Saints, commonly called Mormons) certainly is bizarre, and if they are forcing people to marry against their wills (underage or not), if they are breaking the laws of Texas, they are in the wrong.  But living in an isolated community, wearing old-fashioned clothing, and teaching one's children that obedience is a godly virtue are not crimes, no matter how odd they might seem to mainstream America.  If the laws against underage marriage have been broken, let them be investigated and prosecuted with due process, not with hysteria and actions that will forever scar young lives.

"Laws against underage marriage."  Hmmm, I wonder where the activists are?  The ones who think it's so natural for children to have sex that they're pushing for condom distribution in middle schools?  The ones who insist 13-year-olds need access to abortions—without parental consent or even notification?  It's okay for young teens to be sexually active and have abortions, but not okay for them to marry and have children?  Now that's what I call a bizarre belief system!

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!

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.

I don't believe for a minute that the secret of their success was in what the students didn't learn, but what they did.  Reasoning is a skill, and those who have been taught to think logically can be expected to out-perform those who have not.  Before considering that the early teaching of mathematics will "dull and almost chloroform the child's reasoning faculties," one would have to see the accomplishments of those who learned both reasoning and the multiplication tables.

What I suspect is going on here, besides the laudable emphasis on logic and language, and the deliberate connections made between learning and real life, is that the old curriculum was teaching math as if mathematics comprised rote arithmetic skills alone, and these were taught—most likely by teachers with no understanding of the math themselves—with no context, no grounding in real life.  Thus the children learned nothing about math, but only how to plug numbers into formulas, and that poorly.

Real learning does not paralyze the brain, but fear does.  The errors described in this article are of the same kind and degree as those made by the bright fifth graders John Holt describes in How Children Fail, which he attributes primarily to the fear that comes of seeing math as irrational and incomprehensible—just a collection of magic formulas into which one casts numbers and hopes for the best.  In my own experience, I remember being taught what seemed to be a dizzying array of disconnected formulas for finding surface areas and volumes of various solids, none of which would stick in my mind even long enough to make it through a test.  Only later, when I made the monumental discovery that math actually could be expected to make sense, did I discover that one could derive most of the formulas with a little thought; then the fear went away and I could even remember most of them.  :)  Similar fears assailed me in the conversion of temperatures between Fahrenheit and Celsius; I could never keep the formulas straight.  Again, a little logic (and the knowledge of a few data points, such as 32°F = 0°C) fixed that problem—but I had been taught not to think, but to apply formulas blindly.

So I'm sure the superintendent's experiment helped the children's mathematical reasoning, not by keeping them away from harmful knowledge, but giving them reasoning skills and by taking away the fear engendered by long hours spent in rote learning.  That doesn't mean rote learning is bad, especially at an age when children memorize things as a matter of course.  Can it possibly be more harmful to memorize subtraction facts or historical dates than Star Wars characters and commercial jingles?  It does mean that memorization should be done in short, frequent doses—that's more effective, as well as more enjoyable—perhaps a few minutes every day, and should be only one small part of the total mathematical experience.

Jonathan is memorizing Scripture; not just short verses, but entire psalms, and when his mother gets around to posting his recitation of Psalm 1 I'll include a link.  :)  What's more, he's learning the King James Version, full of words and verb forms no longer in his everyday language experience.  Not that I have any complaint, because whatever one might say about the KJV's comprehensibility and the accuracy of some of the translation, it's still the most poetic version we have.  If he were merely memorizing words it would be of limited value, though even "just words" would establish a foundation he could build on as he matured.  But he's not merely memorizing words; he's learning what they mean, and of course it's all in the context of a family life in which the truths are worked out in practical, daily living.  In this situation, I find it hard to imagine the learning is harming his developing brain.  :)

Frequency, consistency, and context are powerful keys to learning, whatever the subject.  So are delight and the absence of fear.  If I could teach elementary-age students only arithmetic or logic, I would choose logic, but that's a false dichotomy.

Take time to read the article, it really is enlightening.  Note also the shadier side of the superintendent's experiment.  Not wanting to deal with complaints from his more articulate, educated parents, he chose for most of his experimental classrooms those "located in districts where not one parent in ten spoke English as his mother tongue. I sent home a notice to the parents and told them about the experiment that we were going to try, and asked any of them who objected to it to speak to me about it. I had no protests."

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.

Research on the Teaching of Math (one of the links Perla included in her post) is interesting; it is also disturbing, because some of the researchers seem to be amongst those who are afraid of mathematics themselves.

As you may or may not know from things I have posted, if I must give myself a label (which I usually don't), I'm closer to the "unschooler" side of the continuum, though I do believe in organization and discipline.  I also greatly respect Raymond and Dorothy Moore and agree wholeheartedly that children under the age of 10 should not be in school.  (Personally, I would extend that to at least 14.)  However, that doesn't mean I would withhold "formal" instruction from them, even workbooks.  There is a world of difference, which the researchers seem to have missed, between academics in a school setting and one-on-one, relaxed instruction at home that is sensitive to the child's needs, desires, and capacities.  In that context, a workbook is just a tool like any other, to be used or misused.

I am glad to see that some of the writers realize the importance of much immersion in mathematical language, even while recommending delay of mathematical study.  Because mathematics is a language, and as such much better grasped at an early age.  You certainly know much more about multi-lingualism than I do, but wouldn't you agree that those who learn second or third languages at a very early age learn them much, much better than those who wait till 10 or 12 to begin?  I've read studies (sorry I can't give a link) that show that language learning is physically different in the brain for early and late learners.  I strongly suspect that's also true for mathematics.

The question, I suppose, is then:  What is the equivalent in mathematics of making a two-year-old sit still for formal French grammar drills (which is not how they learn), and what is like surrounding the child with a linguistically rich, correct, and abundant exposure to the French language?  We must be careful not to give our children the equivalent in mathematics of a diet of French baby talk or street patois.

In everything we must be sensitive to our children.  Being a math major myself, I had no fear of the subject to pass on to my children, and they quickly came to understand that math and logic are delightful games.  (Better than me, in fact, since my initial mathematical experiences were those decried in the research you cited.  It wasn't until I discovered algebra that I realized math didn't have to be confusing and boring!  It wasn’t my age, but the subject matter that opened my eyes.  If I hadn’t been put into that advanced class in 8^th grade I’d have been miserable for yet another year.)

It's true that the one in our family who developed her mathematical skills the most was the one least exposed to stultifying school mathematics, but what I want to emphasize is this:  workbooks and worksheets were an important part of her preschool education—by her own choice.  She wanted "homework" like her older sister, and devoured every math workbook I could get my hands on (thanks to a helpful first grade teacher; there wasn't much available to the lay person in those days) and every worksheet I could invent for her.  Perhaps that did destroy her understanding of math, and we thus deprived the world of some brilliant mathematical discoveries, but somehow I doubt it.  Granted, her heart is in music, not math, but she “speaks” math and logic with ease, and she did get a math degree "along the way" in college whereas I had to struggle for mine.    As a young child she absorbed mathematics the way a Parisian child absorbs French, and workbooks were one of many contributors to her exposure.  They are not evil, nor are "formal" lessons, if one is sensitive to the individual child.