Lift Up Your Hearts!

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.

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.

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

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.

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.

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 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.

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.

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.

High Tide in Tucson, by Barbara Kingsolver.  (HarperCollins, 1995)

This one was a little harder.  None of it was dull, but a great deal of it was maddening.  With a few exceptions, such as her love of nature and her attitude towards clothing and fashion, Barbara Kingsolver and I apparently stand at opposite poles on every issue.  Having read Animal, Vegetable, Miracle I know this is not entirely true, but High Tide in Tucson manages to flush out many areas of extreme disagreement.  One critical example: while we share a love of and respect for children, hers leads her to support passionately governmental programs and family situations that I think, with equal passion, are downright harmful to children.

What is most frustrating is that she can be so well-educated, so intelligent, and have obviously done much research, and yet be so blind.  I don't mean she's blind because she doesn't agree with me, but because she apparently can't see the humanity of her opponents.  The person who excuses tobacco farmers on the grounds that they are human beings who are supporting their families in the only way they know how, nonetheless sets up her enemies as straw men and proceeds to demolish them without taking the time to get to know the reality of their lives and logic.  For someone who clearly wishes to be liberal and accepting and open to new ideas, her world is curiously black and white.  One either accepts every aspect of evolutionary theory lock, stock, and barrel, or else believes the world was created in six 24-hour days back in 4004 BC.  One either embraces all possible combinations of people as equally legitimate forms of "family," or restricts that term to a husband and wife with two children, a boy and a girl, living isolated lives in suburbia with no room for a community of friends and neighbors or even grandparents.  In Kingsolver's mind, there is apparently no substantial difference between a mother working long hours in corporate America with her children in day care, and a mother working long hours on a farm with her children (and husband) close by.  And that women without "careers" have so much time on their hands they take cleaning and home decorating to unheard of heights just to keep themselves occupied!  All forms of religious belief are valuable, held by reasonable people, and have something to teach us—except Christianity.  Every group that calls itself a "family" is a blessing, unless that family happens to be a husband, wife, and two kids living in suburbia, with the mother working at home, in which case it's likely to be toxic and conceal child abuse and a woman on tranquilizers.  Every culture is beautiful, except for Western Europe's, every country admirable except America.  I'm exaggerating slightly with that last example—Iraq and Kuwait are also evil empires in her mind.

In the hands of a lesser writer, such sentiments would caused me to throw High Tide in Tucson across the room and miss the valuable parts of the book.  (Really, there are some.)  Fortunately, Barbara Kingsolver is not a lesser writer.  Her arguments are not convincing, even when I agree with her, because her ignorance about things of which I know does not give me confidence when she covers areas in which I am clueless.

Is it any wonder Americans are such poor money managers when you look at the behavior of our government? Or should I perhaps say that the other way around?

Only a few short years ago, the State of Florida was enjoying a large budget surplus, because tax revenues went through the roof thanks in part to all the rebuilding necessary after our four-hurricane year. Naturally (but stupidly), everyone clammored to spend the "excess." There were plenty of claimants for the money, but few indeed were the voices of reason, and they did not prevail. It should have been obvious to anyone with any sense at all that boom times don't last, and the years of plenty are when you put away your surplus to help you through the lean years.

Now the rebuilding is complete, and people are being more careful with their money, so Florida is hurting for sales tax revenue. Suddenly we are cutting programs, laying off public prosecutors, and—that whicih inspired this post—threatening to demolish the wonderful Road Ranger system that I wrote so enthusiastically about after I was stranded on the side of the highway, at night, in a non-functional car. If we had invested that surplus when we had it, we could be using it now to go along normally, and avoid the expense of restarted when economic conditions improve. Basic economics, Finance 101, just plain common sense.

It's true that Barack Obama scares me.  He has so much charisma that I'm afraid an Obama presidency would actually succeed in implementing his harmful agenda.  I'm not saying that Hilary Clinton's and John McCain's agenda's aren't harmful—just that I think they're less likely to succeed in bringing them to fruition.

Senator, the problem isn't the way you said it, but that you believe it.  But you are not alone in believing what Hillary Clinton, most of the Democratic Party elites, too many of the Republican Party elites, Hollywood, and much of the media "know is true."  Clinton, attempting to capitalize on Obama's gaffe, explained that "Americans who believe in the Second Amendment believe it's a matter of constitutional rights," and "Americans who believe in God believe it is a matter of personal faith."  Perhaps that's just another example of unfortunate phrasing, but the attitude seems equally elitist and out of touch with the real people who actually believe in God and in the Constitution of the United States.

One of my frustrations in talking with people from other countries is running into comments that begin, "Americans..." followed by some statement of belief, action, or attitude that supposedly represents all or at least most of my countrymen.  More often than not, my insistence that "I am not that way, and neither is anyone I know" will not budge them from their certainty that what they see in our movies and television shows, hear from our politicans, and learn from our news media is the real America, while I and my family, friends, and neighbors must be some aberration.  That Americans tend to make the same mistake about people from other countries does not excuse such stereotyping.

I don't agree with John Stackhouse on everything—no surprise to those who know me; I'm not sure I even agree wtih myself on everything—but greatly appreciate the way he can take a controversial subject and shake it out with clarity and common sense.  I have little patience with the whole "postmodernist" idea that there's no such thing as real, absolute truth,  but at best only a useless, mealy-mouthed "true for you" or "true for me."  But equally frustrating are those whose claim to know the truth about something leaves no room for doubt, and what is worse, no room for the possibility that they might, in fact, be wrong.  Stackhouse addresses the latter situation with refreshing rationality in I'm Certain that There Are Two Kinds of Certainty.

As dictated, unedited, while Mom, Dad, and Noah were napping.

Then a wolf came.  And the wolf started tackling, too.  And the wolf started jumping wildly, too.  And the wolf was scratching the bear, too.  And then some tigers came. Then the tigers started jumping wildly and scratching wildly, too.   And then they began trying to bite at the bear.  And then they started jumping on the bear and kicking the bear.  And they all started jumping up to its head.

Then the bear was being so beaten up, it decided to go away.  And then the tigers and the wolf and the fox started following him.  And then the bear was even more frustrated with them that he climbed a tree, and then they climbed the tree with him.  And then he started trying to fling himself to the sky, and at last he was in space.

Then the tigers, the wolf, and the fox flinged themselves into space with the bear.  Then the bear was even way more frustrated that he flinged himself into Jupiter!  And the tiger, the wolf, and the fox flinged themselves into Jupiter, too.

And then they went back into earth, got a big long wire, and attached it to one end of a pole in the earth, and they dragged it out into space and sparked the bear.  And then they went back to earth, got some metal, and threw it at the bear.  So the bear stayed in space while the tiger, the wolf, and the fox kept springing up and down to have a way to kill the bear.

Then they took a sparkling, killing fire and threw it at the bear.  Then they took some snow and buried it in the bear’s eyes.  Then the bear was so angry that he took a tree, and the tigers, the fox, and the wolf got hold of the tree so the bear couldn’t whack them with the tree, and then they whacked the bear with the tree and then he started flinging them into earth, but then they went into space and started whacking the bear to earth.

That's what we did this morning.  We arrived at the Pittsburgh Zoo with a crab and left with a jellyfish, but in between Jonathan was a perfect little boy, just the right age to delight in all the exhibits.  He could identify many of the fish as well as the animals, and explained to me—thanks to a Magic Schoolbus book that's currently one of his favorites—that the clownfish can live inside the sea anemone because it's covered with mucus which protects it from the anemone's sting.

John C. Wright is one of the latest entries in my feedreader, and frankly I've forgotten whom to credit and am too busy/lazy to try to figure it out.  But thanks, whoever you are.  John's entries are almost always well-written and interesting, and often give me a fresh perspective on issues.  His latest is too rich for me to give it more than a quick read at this point, but I'm posting it here so I won't lose it, and for the benefit of others.

And when the Laws of England Are Flat, and the Devil Turns on You? 

Fans of A Man for All Seasons may recognize the title; if not, there's a YouTube link to refresh your memory.  If you're told "this video is no longer available," try again; it worked the first time for me, and not the second, but the next time I had no trouble.

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.

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

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!

I suppose it's one way of dealing with the complications of housing homosexual and lesbian students, but I'd prefer colleges just get rid of the archaic roommate idea and provide single rooms for everyone who wants one.  They could solve the subsequent housing crunch by instituting very stringent and strictly-enforced visitation policies that would drive off campus everyone who thinks he's in college for sex rather than studies.

The article reminded me of a story I heard back when co-ed dorms were first being proposed.  One college dean—I have no idea who, or where—after listening patiently to the case as presented to him by a couple of student representatives, turned them down.

"You don't trust us," they complained.

"No, I don't," he replied.

"Why not?"

Our newly-found Smith Genealogy manuscript, which I mentioned in a previous post, is proving a treasure not only of facts but of stories.  Here's one about my great-great-great grandmother, Margery Irwin, who was the author's grandmother.

Grandmother was born east of the mountains we think, in Lancaster County, Pa.  She was brought west of the mountains when five years old, packed in a wallet on a pack saddle.  Grandmother on one side and her sister on the other and a bottle of milk and skillet with them.