Dorothy Sayers and TLTOL (part six)

Back to my slow digestion of this essay....

Another quotation from the same issue of the TLS comes in fittingly here to wind up this random collection of disquieting thoughts--this time from a review of Sir Richard Livingstone's "Some Tasks for Education": "More than once the reader is reminded of the value of an intensive study of at least one subject, so as to learn 'the meaning of knowledge' and what precision and persistence is needed to attain it. Yet there is elsewhere full recognition of the distressing fact that a man may be master in one field and show no better judgement than his neighbor anywhere else; he remembers what he has learnt, but forgets altogether how he learned it."

I would draw your attention particularly to that last sentence, which offers an explanation of what the writer rightly calls the "distressing fact" that the intellectual skills bestowed upon us by our education are not readily transferable to subjects other than those in which we acquired them: "he remembers what he has learnt, but forgets altogether how he learned it."

I've discussed before how I feel about constructivist math curricula--I don't like them, and I refuse to allow a school to use such a curriculum on my children.
There exist many people, including some math professors, who DO love such curricula, though. They say things like, "I was taught what to do and not why to do it. Isn't it wonderful that [Everyday Math, etc.] challenges a child to understand why a math principle is true instead of settles for 'rote learning'?" Maybe my traditional math education was different from theirs, but I was typically taught how and why to do an algorithm and then given so much practice that it became automatic. Since I had no need to remember afterward why something worked, I often didn't bother to remember the "why". Getting the right answer was my goal. That changed temporarily in my university math theory and proof classes, where the math professors were trying to make a mathematician out of me. They didn't succeed; I got my B.S. in Mathematics and then went into computer programming and finally law school. I'm still content to be an excellent calculator.
Taking humanity as a whole, very few people are going to be actual mathematicians. Yes, everyone should be able to calculate and have enough experience with math through pre-calculus that they can understand general statistics terms and do their own taxes and home improvement project purchases (e.g., vinyl flooring, paint, etc.) without relying on a calculator. However, this low-level math isn't intriguing like fractals and vigesimal Mayan math, and it certainly isn't what university math professors spend their time on.
Why do we listen to these professor-mathematicians when they speak in glowing terms of elementary math programs, especially constructivist curricula that cover lots of "cool" topics in "creative" ways? Basic math is a limited, rather boring thing--although one which the non-mathematician will use throughout life--and the university professors rarely teach that subject matter. In fact, the professors often were the kind of child that learned most basic math seemingly by osmosis and never had to do timed drills to remember the multiplication table. They are experts at posing problems in and teaching certain areas of mathematics that the average person has no need or interest in: set theory, number theory, topography, cryptology, game theory, etc. They are rarely experts in teaching calculation and very basic geometry. I don't think they are in a position to opine on the fitness of elementary math curricula. I would rather read curriculum evaluations from high school math teachers who have to teach students after they have been subjected to a given curricula for several years. They seem to me better positioned to be experts on the effectiveness of elementary math curricula.

Ow

Yesterday, I slipped and banged my right thumb. It's been quite sore, but since I'm not positive that it was fractured, I've just worn a homemade splint on and off.

This afternoon, dd4 was playing with a heavy plastic garbage can and dropped it on my foot, and the rim (of the opening, not the bottom) hit my right toe, smashing it and tearing the skin. Again, I don't know whether it's fractured, but it's quite sore.

I occasionally read about people with sons having to make lots of trips to the urgent care and emergency room. We, with three daughters and six years of parenthood, have thankfully found so far that our children are fairly cautious when it comes to their own safety. Instead, they injure us. Oh, well, better us than them.

Spring Is Icumen In

We are having lovely weather in Colorado today! Of course, we'll probably get hit with freezing rain in June for it, but that's the price we pay for living at the foot of these glorious mountains.

Dd6 and dd4 are contentedly listening to Magic Tree House audio books while they read along in the paper books. When they're done with that, we'll head outside to do yardwork. Actually, I'll do yardwork, and they'll dig holes and plant flags in piles of dirt.

Here is an update on homeschooling:

1) We have reached 132 official days of an average of 4 hours of instruction; 40 more such days, and I don't have to keep records again until the 2011-2012 school year! I will keep some records just for my own purposes, of course.

2) Reading is going very well for both dd6 and dd4, who has benefited significantly from overhearing dd6's lessons. Both love to sit down with a book on their own and read (using a flexible definition of that word for the younger child).

3) Dd6 is over halfway through 1st grade math and understands all the math principles well. She still hasn't memorized her addition facts adequately, and it's slowing her down. Maybe I should make some silly poems for her to serve as memorization helps.

4) Dd6 initiates many crafts, art projects, and science experiments. Library videos and books have been invaluable resources for her.

5) We just started doing formal narration today. Inspired by a book on Charlotte Mason's education philosophy, I found an early reader volume of Aesop's fables and read the first fable, "The Wolf and the Goat", to dd6. She struggled a bit to retell the story in her own words, but seemed to enjoy doing it. I look forward to doing the entire book with her.

6) We just reached the Anansi the Spider stories in Volume 1 of The Story of the World. There are some very cute versions of Anansi stories on YouTube.

Dorothy Sayers and TLTOL (part five)

I don't have a lot to say about these next two paragraphs except that they demonstrate a level of education about logic that one rarely sees on display in modern writings (especially not in FB and blog comments):

Are you occasionally perturbed by the things written by adult men and women for adult men and women to read? We find a well-known biologist writing in a weekly paper to the effect that: "It is an argument against the existence of a Creator" (I think he put it more strongly; but since I have, most unfortunately, mislaid the reference, I will put his claim at its lowest)--"an argument against the existence of a Creator that the same kind of variations which are produced by natural selection can be produced at will by stock breeders." One might feel tempted to say that it is rather an argument for the existence of a Creator. Actually, of course, it is neither; all it proves is that the same material causes (recombination of the chromosomes, by crossbreeding, and so forth) are sufficient to account for all observed variations--just as the various combinations of the same dozen tones are materially sufficient to account for Beethoven's Moonlight Sonata and the noise the cat makes by walking on the keys. But the cat's performance neither proves nor disproves the existence of Beethoven; and all that is proved by the biologist's argument is that he was unable to distinguish between a material and a final cause.
Here is a sentence from no less academic a source than a front- page article in the Times Literary Supplement: "The Frenchman, Alfred Epinas, pointed out that certain species (e.g., ants and wasps) can only face the horrors of life and death in association." I do not know what the Frenchman actually did say; what the Englishman says he said is patently meaningless. We cannot know whether life holds any horror for the ant, nor in what sense the isolated wasp which you kill upon the window-pane can be said to "face" or not to "face" the horrors of death. The subject of the article is mass behavior in man; and the human motives have been unobtrusively transferred from the main proposition to the supporting instance. Thus the argument, in effect, assumes what it set out to prove--a fact which would become immediately apparent if it were presented in a formal syllogism. This is only a small and haphazard example of a vice which pervades whole books--particularly books written by men of science on metaphysical subjects.

Words I never learned in school that Sayers uses with ease: final and material causes, syllogism, and supporting instance. (To give my university its due, I did learn about final causes in my colloquium on Western civilization.) I can't wait to study formal logic in a few years with my children!

Chess Club

While I consider myself a homeschooler, I do send my daughter for a few hours each week to a local charter school. To do my part as a parent in the school's community, I volunteered myself and my dh to run a chess club after school. Today was the first day of the club. The children were great, plenty of adults showed up to help out, and there were nearly enough chessboards. I can see that flexibility and diplomacy will be key to this endeavor--flexibility to deal with shifting numbers and abilities as some beginners outstrip others, and diplomacy to gently correct children who are certain that pawns can move backwards.

Dorothy Sayers and TLTOL (part four)

These next paragraphs from Sayers' essay call to mind (they are full of questions, after all) far too many examples from my own life and family:

Do you ever find that young people, when they have left school, not only forget most of what they have learnt (that is only to be expected), but forget also, or betray that they have never really known, how to tackle a new subject for themselves? Are you often bothered by coming across grown-up men and women who seem unable to distinguish between a book that is sound, scholarly, and properly documented, and one that is, to any trained eye, very conspicuously none of these things? Or who cannot handle a library catalogue? Or who, when faced with a book of reference, betray a curious inability to extract from it the passages relevant to the particular question which interests them?
Do you often come across people for whom, all their lives, a "subject" remains a "subject," divided by watertight bulkheads from all other "subjects," so that they experience very great difficulty in making an immediate mental connection between let us say, algebra and detective fiction, sewage disposal and the price of salmon--or, more generally, between such spheres of knowledge as philosophy and economics, or chemistry and art?

In connection with the first paragraph, I immediately thought of relatives and friends who think some questionable websites on alternative medicine and sovereign citizenship are correctly informing them.
The second paragraph was illustrated recently. Two days ago, the Washington Post published an opinion piece entitled, "Our Superficial Scholars", discussing Rhodes Scholarship applicants and saying, "high-achieving students seem less able to grapple with issues that require them to think across disciplines or reflect on difficult questions about what matters and why." Isn't it interesting that the high-achieving students, the ones who learned to play and win at the "school game", are now being criticized for not making mental connections between different spheres of study?
I think such compartmentalization is a nearly unavoidable result of our grade 7-12 school structure. When we tell youth that they can only learn math in Algebra (for 53 minutes until the bell rings and they head out the classroom door to traverse the school hallways in a path that cleverly takes them by their latest crush's locker), then world history in World History Class, then music in Music, etc., it is nearly impossible for them in such an environment to see connections between these subjects, especially because they are rarely taught a correlated curriculum that makes apparent the connections between the disciplines.
A great strength of homeschooling is the time and study flexibility to permit children to make inquiries on subjects different from the one at hand. Whatever questions dd6 has about insects or watermelon seedcounts while we read a book about China can be answered quickly (thanks, Google!). Another strength is the ability to teach in a way that promotes making connections; for example, if we have just read a story (language arts) set in a bayou, I can assign a worksheet about Louisiana (geography), read to my daughter about swamp vegetation (biology), and watch The Princess and the Frog (art, jazz, and zydeco).

Sayers' TLTOL (part 3)

Sayers calls into question the discernment and debating abilities of those educated in modern times:

Has it ever struck you as odd, or unfortunate, that today, when the proportion of literacy throughout Western Europe is higher than it has ever been, people should have become susceptible to the influence of advertisement and mass propaganda to an extent hitherto unheard of and unimagined? Do you put this down to the mere mechanical fact that the press and the radio and so on have made propaganda much easier to distribute over a wide area? Or do you sometimes have an uneasy suspicion that the product of modern educational methods is less good than he or she might be at disentangling fact from opinion and the proven from the plausible?
Have you ever, in listening to a debate among adult and presumably responsible people, been fretted by the extraordinary inability of the average debater to speak to the question, or to meet and refute the arguments of speakers on the other side? Or have you ever pondered upon the extremely high incidence of irrelevant matter which crops up at committee meetings, and upon the very great rarity of persons capable of acting as chairmen of committees? And when you think of this, and think that most of our public affairs are settled by debates and committees, have you ever felt a certain sinking of the heart?
Have you ever followed a discussion in the newspapers or elsewhere and noticed how frequently writers fail to define the terms they use? Or how often, if one man does define his terms, another will assume in his reply that he was using the terms in precisely the opposite sense to that in which he has already defined them? Have you ever been faintly troubled by the amount of slipshod syntax going about? And, if so, are you troubled because it is inelegant or because it may lead to dangerous misunderstanding?

I shy away from conflict. Just a small Facebook quarrel via comments can ruin my day because it's all words with no conciliatory faces to show that no hard feelings are accompanying the disagreement. I don't waste time watching Presidential debates because they're mostly performing for cameras and trying to make the other person look stupid to the projected demographic makeup of the audience. Don't misunderstand me: debate is incredibly important to our republic. But I don't see it well done, so I try not to waste my time or emotions watching useless debate. Ad hominem attacks, incomplete facts, and utter failure to understand the other side's point of view characterize much of "public debate" these days (go ahead and throw in some corruption, too, of course, for Americans aren't magically immune to it). I wish we had an Abraham Lincoln who could write his own eloquent and thought-out speeches, but we don't. Inspiring demeanor or folksy down-to-earthness don't make an argument valid or convincing. Is the solution teaching Latin to kids? Of course not, but there's a lot more to the education that Sayers is proposing in this essay.

Sayers' TLTOL (part 2)

Today I wearily consider these paragraphs:

Before you dismiss me with the appropriate phrase--reactionary, romantic, mediaevalist, laudator temporis acti (praiser of times past), or whatever tag comes first to hand--I will ask you to consider one or two miscellaneous questions that hang about at the back, perhaps, of all our minds, and occasionally pop out to worry us.
When we think about the remarkably early age at which the young men went up to university in, let us say, Tudor times, and thereafter were held fit to assume responsibility for the conduct of their own affairs, are we altogether comfortable about that artificial prolongation of intellectual childhood and adolescence into the years of physical maturity which is so marked in our own day? To postpone the acceptance of responsibility to a late date brings with it a number of psychological complications which, while they may interest the psychiatrist, are scarcely beneficial either to the individual or to society. The stock argument in favor of postponing the school-leaving age and prolonging the period of education generally is there there is now so much more to learn than there was in the Middle Ages. This is partly true, but not wholly. The modern boy and girl are certainly taught more subjects--but does that always mean that they actually know more?

Last night at 2:45 a.m. (a school night, mind you), I had to go ask the college student neighbors to turn down their music so that I and my baby could sleep. The house party included girls dancing in bras and a suspicious-smelling smoke. Is this "the modern boy and girl"? Their parents are paying for them to engage in substance-abusing revelry in the middle of a school night as part of a college education? Truly this is a marked prolongation of adolescence.
My own story is quite different. I moved into on-campus housing and started as a full-time university student just before turning 17. I attended BYU where there is little in the way of drinking or drugs, and I studied a lot. Sunday nights, I went to bed early so I could be ready for the week's coming classes and assignments, and I don't think I was too different from most other BYU students in that respect. We were occasionally reminded that much of BYU's operation budget came from donations by LDS church members and that we were accountable for how we used our opportunities at BYU. While the student body fell short of perfection, it was still very hardworking. Also, I never lacked for opportunities for legal recreation (especially dances, which I loved).
Based on my own experience, I believe that it is perfectly realistic to expect a majority of college students to engage in responsible behavior and that we do them a disservice by acting as though they're incapable of doing so. We also don't help them any by setting low educational standards for them. I enjoy Sayers' essay because she imparts a vision of a higher, attainable standard of education than that which now prevails in mainstream US culture.

Dorothy Sayers and TLTOL (part one)

In preparing to homeschool my children, I have read several books that reference an essay by Dorothy Sayers, "The Lost Tools of Learning", and it can be found online here. To help myself better understand the essay, I think I'll review it bit by bit here on my blog. The first two paragraphs are as follows:

That I, whose experience of teaching is extremely limited, should presume to discuss education is a matter, surely, that calls for no apology. It is a kind of behavior to which the present climate of opinion is wholly favorable. Bishops air their opinions about economics; biologists, about metaphysics; inorganic chemists, about theology; the most irrelevant people are appointed to highly technical ministries; and plain, blunt men write to the papers to say that Epstein and Picasso do not know how to draw. Up to a certain point, and provided the the criticisms are made with a reasonable modesty, these activities are commendable. Too much specialization is not a good thing. There is also one excellent reason why the veriest amateur may feel entitled to have an opinion about education. For if we are not all professional teachers, we have all, at some time or another, been taught. Even if we learnt nothing--perhaps in particular if we learnt nothing--our contribution to the discussion may have a potential value.
However, it is in the highest degree improbable that the reforms I propose will ever be carried into effect. Neither the parents, nor the training colleges, nor the examination boards, nor the boards of governors, nor the ministries of education, would countenance them for a moment. For they amount to this: that if we are to produce a society of educated people, fitted to preserve their intellectual freedom amid the complex pressures of our modern society, we must turn back the wheel of progress some four or five hundred years, to the point at which education began to lose sight of its true object, towards the end of the Middle Ages.

She starts off by saying that she, as a nonprofessional teacher, can critique teaching methodologies just as well as a bishop can discuss economics or plain men criticize Picasso's drawing ability. Frankly, I don't think that bishops are in a position to spout opinions on economics or that one could rationally claim that Picasso couldn't draw, so her first point falls flat. However, her second point is valid: we have all been taught in our lives, be it poorly or well, thus we can hold opinions on teaching obtained from our own experience. I read tonight that Sayers' father began teaching her Latin when she was six years old, so she certainly has a basis in her own early life for understanding classical education. There is a third point that she could have made in her introduction: that everyone can be a teacher, professional or not (Socrates preferred "not", and he is recognized as a great teacher).
Her second paragraph has been shown false. Many people have been influenced by her essay to "turn back the wheel of progress" to promote classical educations (e.g., The Well-Trained Mind and Designing Your Own Classical Curriculum). Progress originally meant "moving forward", not "moving in a better direction". The latter definition of "progress" as gradual betterment seems reflective of the optimism and/or arrogance of modern humans who think they are wiser than their ancestors. Taller, yes, but wiser? I'm not convinced of that. I'm OK with discarding some newer pedagogical ideas if it means my children are better taught due to use of older methods. Where's my hornbook? :)

Thanksgiving

As this wonderful holiday of family and tasty autumn food approaches, I'm going to take a little cyberspace to say 100 things I'm grateful for: my family, the Bill of Rights, the internet, my husband's job, our house, libraries, friends, a working car, heat for our house, our refrigerator, freedom to homeschool, health, my life experiences thus far, plastic dishes, the rule of law, books, computers, the Bible, the Book of Mormon, beautiful scenery, four seasons, pumpkins, telephones, safe public parks, jet planes, imported bananas, disposable diapers, wipes, thrift stores, ultrasound machines, kissable babies, AP tests, BYU, generous people, smiles, falling leaves, DVDs, Stare Dobre Malzenstwo, raising our children to be bilingual, free educational websites, skin moisturizer, vaccines, clean tap water, the Rosetta Stone, popcorn, going for walks, toothbrushes, wall-to-wall carpeting, good teachers, charter schools, temples, LDS General Conference, telescopes, stars, the sun, bees, classical radio stations, playdates, legal research assignments, politeness, apologies, listening ears, skin, eyes, ears, sugar, cocoa, Facebook, pianos, violins, orchestras, dictionaries, forgiveness, others' patience with me, my crockpot, pay-at-the-pump gas stations, Louisa May Alcott's books, ice skating, dancing, laughter, hair, my bed, holidays, peace, good health insurance, warm showers, good architecture, insulation, lawns, completed craft projects, emails from loved ones, flowers, trees, red rock canyons, the local zoo, ballpoint pens, key fob car locks, coral reefs, and the atonement and resurrection of Jesus Christ.

Homeschooling Carnival

The homeschooling carnival is up here at The HomeSpun Life. It's so nice of blog writers to host the carnivals. I've learned a lot from them over the past couple of years.

Stuck

Over a month ago, I optimistically posted that our math project for the next week or two was learning the addition facts. Here are the things I have done since then to facilitate dd6 in learning her addition facts:

1) Online games - turns out she's not much of a gamer (online puzzles, mazes, coloring games, etc. are liked, but not shoot-em-up, kill-the-alien-sum type games), so the free games on http://www.arcademicskillbuilders.com/ and other education game websites didn't do the job.

2) Addition fact songs scattered strategically throughout a newly-burned CD for car listening - dd3 now knows most of the addition facts, but dd6 must have already passed the stage where she memorizes every little thing she hears in passing. Most unfortunate.

3) Flashcards - moderately effective at reinforcing the sums she already knows and at giving me a chance to explain how to figure out other sums from the known ones, but kind of boring for both of us and so used only a few times.

4) We made 100 paper cutouts for the 0-9 sums in 10 different colors. I taped these on the kitchen wall and periodically ask her some of them. If she can answer one quickly, then I take it down. Over half are still hanging on the wall. Dd3 keeps answering my little pop quiz questions before dd6, which annoys me and probably frustrates dd6.

5) Cuisenaire rods - I pulled these out today and let her use them to show all the different ways to make sums up through 10. She enjoyed it, so maybe we'll use them again.

6) Addition Bingo game - dd6 enjoyed our Addition Bingo board game, but dd3 became temperamental and didn't want to play the game correctly, so I hesitate to get it out again. Same goes for Chutes and Ladders. (Ah, board game strife. When do they learn to cope with losing? Come to think of it, I still won't play Risk because I don't like that I never win....)

7) Various worksheets printed off from the internet and pages from sundry math workbooks - rather randomly chosen to keep her writing down math and reinforcing all the math that she has learned thus far.

We are stuck in our math worktext at the first page of double digit addition. I told dd6 a month ago that she needed to know her addition facts in order for her to learn double digit addition. She believed me, and now she absolutely refuses to work on double digit addition until she has memorized her sums. To tell the truth, I'm bored of working on 0-9 sums. But we'll keep at the task until it's mastered because it's truly fundamental. And because she won't let me move on.

What else to give them?

Dh and I were discussing this morning how middle class college students generally have received so many material benefits growing up in the USA. He asked as he left for work what they will want to give their children "to give them what they didn't have growing up"? My immediate response was "homeschooling"! Once we've made sure children have food, shelter, health care, clothes and toys (I think American children are usually inundated with toys these days), what's left? A good education and time with parents. Put those together, and what do you have? Education by mom or dad. Happily, with the internet and the public library, even lower economic class families can give their children good educations once their basic material needs are met. How equalizing!

Because we can't afford private school, homeschooling is the only way for me to give my children a really good education, not just one that makes them "proficient" in "standards". If my children reach 18 without reading some Plato, learning calculus, or being able to write essays in a couple of languages, then I haven't given them an education even as good as mine was. Based on the results I see from non-charter public schools, there is no way for the current public school system to give my children this education, so I am grateful every day for the freedom to homeschool.

Homeschool update

Dd6 just finished Chapter 11 (out of 21) of her first grade math book. She and I have less than 20 pages of Reading with Phonics left to go through with each other. Her writing is slowly getting better, she is pronouncing her r's better, and we have started reading a little in the scriptures each day. With the help of a $1 workbook from Target, we have learned about several countries (e.g., Kenya, Ireland, Australia, Egypt, Israel, France, China, etc.)

We started reading Volume 1 of Story of the World, putting a lot of focus on Egypt since we were planning a trip to the King Tut exhibit at the Denver Art Museum. Now that we've seen the exhibit, we should be moving on to Mesopotamian cultures, but I've hesitated to do so because dd6's class at her charter school (she attends about 7 hours a week) is currently studying ancient Egypt. It seems best to let her knowledge of ancient Egypt get reinforced at school for now. We can always cover Babylon later.

Speaking of school, she now attends Saturday School in German. It's only three hours and costs us, but it's worth it: she is finally starting to speak in German.

Our big task for the next week or two is to memorize addition facts up to 12+12 in order to prepare for math Chapter 12: Double Digit Addition. I looked at several different toys, games, and programs to help her learn her addition facts. In the end, I bought a set of addition flashcards ("Princess" cards because she likes them) from the dollar store and told her I'll give her five dollars to spend at the dollar store however she wants once she has all the addition facts memorized. She has a very good memory, so I don't think I'm expecting too much of her. She's already put in around an hour going over the flashcards by herself. I look forward to her reaching her goal of memorizing them all.

Fun with Liquid Measures

Today we are learning about pints and cups. I let dd6 play around with cups and a pint (2-cup) measure. Then I asked her whether she could drink a whole pint of water. She managed about a cup, but she had fun watching the water line go down slowly. I kept hearing in my head the line from The Fellowship of the Rings: "You mean it comes in pints!" I live in Hobbiton. :)

New School Year

We officially started the new school year two weeks ago. Dd5 is being homeschooled most of the time, but I have her in a local charter school for about 8 hours each week. I'm thrilled to have a school nearby that is flexible enough to be able to accommodate her need for social growth and group extracurriculars. I continue to take responsibility for her learning math, reading, writing, spelling, history (following the Story of the World books), and German; at school she makes friends, learns to get along with others, and does some history, science, art, music, and Spanish.

This year I am starting to keep records. It's a little nervewracking sometimes making sure that I've entered at least 4 hours of educational time per school day, as is required by Colorado law for children aged 7 and up. It's not that she's not learning enough. Rather, I'm too strict with myself when it comes to timekeeping. One reason I choose not to be a practicing lawyer is that I would have a hard time recording enough billable hours ("Oh, no, I can't count that as a solid hour because I got up to fill my water bottle...", etc.). It's a good thing I'm getting into the habit of timekeeping now while I'm still not legally subject to the 4-hour-per-day requirement.

"Stereotype threat" avoidance

In this article, Negative stereotypes shown to affect learning, not just performance, study finds, it describes how women informed of negative stereotypes about women's math-related abilities had their ability to learn negatively impacted. The women apparently spent more energy trying to prove the stereotypes wrong than they did actually learning.

"(The present study) points to the importance of creating environments that reduce the impact of stereotype threat during mathematical skill acquisition by women," the authors concluded in their PNAS article. "If creating such an environment is not done, the learning deficits that result could well be cumulative, causing problems that continually worsen as development proceeds."

It seems to me that an effective way of avoiding stereotype threat is to create a learning environment where children are isolated from each other and from adults who express negative stereotypes. They have to be isolated from each other because children are always trying to categorize each other: "Herbert is good at math and he's a boy. I'm not a boy, so I'm not good at math." They need to be isolated from adults who can't keep from expressing negative stereotypes because the adults will hamper both their learning and their performance. Children also need to be shielded from media that will teach negative stereotypes.

Maybe robot tutors are the way to go....

In the meantime, I will strive to be the positive-thinking homeschooling mom that my girls need. Not that any of them will ever think that girls are "bad at math"...too many females with math degrees in the extended family. :) (That said, I do think that the male brain tends do better when one looks at the extreme high end of mathematics achievement. I don't consider that a stereotype because it's actually true. See my previous blog post.)

"Gender gap persists at highest levels of math and science testing, 30-year study finds"

Here's a study result I find completely unsurprising. Girls in my family are very good at math; three of us have degrees in math. Yet none of us are ambitious to be great mathematicians or even stay in math careers.

Financial Decisions

My husband and I are bookish. (Big surprising confession, that one.) We don't pay a lot of attention to things like the stock market. However, we have been unable to ignore that our Roth IRA accounts, modest as they are, have no gains (actually some losses, sigh), and almost equal the amount left on our house mortgage. So basically we have a net worth of zero! We hate debt and live well within our means. The only debt we have is our mortgage. (Well, OK, we feel a debt to society to live well and raise our children right and a debt to our parents for life itself and a debt to the Lord for everything. I meant a money debt.) We are considering closing out the Roth IRA accounts (no penalties unless you take out earnings, and we don't have any earnings) and paying off our mortgage.

It's interesting researching the pros and cons of such an action. The major pros seem to be 1) a guaranteed cut in living expenses (especially mortgage interest), and 2) peace of mind. The major cons seem to be 1) loss of mortgage interest tax deduction (not applicable for us because we don't itemize deductions), and 2) no longer having the Roth IRA accounts for retirement later on, when they are likely to have increased in value. This second con requires an optimism about our economy that I do not possess. Any readers out there willing to give me reasons to be optimistic about my retirement account mutual funds before I unload them?

Explora

We just got back from a mini-vacation to New Mexico. While there, we had the chance to go to the Explora! center in Albuquerque. It was one of the most interesting science museums I have ever been to. It is full of hands-on inquiry exhibits. My children and I did some basic animation (computer and drawing frames), played with water and air and light and weight and color and bubbles, and saw a chemistry demonstration on density. Did you know that a Coca-Cola can will float in water, but a Diet Coke can will not? I didn't. (It's the missing sugar that causes it to have an average density less than that of water.) We had a great time!

Darwininan Garden

I like this lady's approach to building up her garden. Still, it doesn't sound like landscaping my children would enjoy playing amongst. Yucca? Not with my little ones' eyeballs at risk, thank you. I guess I'll have to keep trying to get some sort of grass growing.

Update on Home Learning

Now that dd5 has been out for summer from official school, part-time though it was, for a whole month, here's a list of what we do to keep educating her:

1) Nearly every weekday morning, we do 30-45 minutes of formal schooling. It includes 5 minutes of writing practice (copy one short sentence), 20-30 minutes of math (usually 2 pages from her math workbook), and 5-15 minutes of reading instruction from Reading with Phonics.
2) Much watching of Sid the Science Kid has been happening. I like the song that goes "I love my mom, my mom is cool."
3) We have occasional music lessons and went to a children's concert.
4) She is done with the library's summer reading program, and it did indeed jumpstart her reading on her own.
5) She doesn't let a day go by without doing something crafty: coloring, painting, paper plate masks, etc. Often her crafts are inspired by a book we've just read, such as the swans she painted today after we read The Ugly Duckling.

We also just play games, garden, visit friends and family, and go to parks. Summer is hot, and life is good.

Post Kindergarten

Last month dd5 officially finished kindergarten. Her school district enrichment program ended, and she finished her kindergarten level math book. She is 2/3 of the way through her Hay-Wingo Reading with Phonics, and her handwriting is (very) gradually improving. She and dd3 are already working on winning prizes in the local library's summer reading program. We'll be doing school through the summer, taking breaks when traveling or doing special family activities. I think we would all be very bored if we just put away the books for 2 months.

Please just immunize!

According to this article, "Doctors report alarming increase in mumps-related testicle problems among young males", parents who feared the MMR vaccine might cause autism and so had their sons go without the vaccine appear to have increased their sons' chances of fertility problems in the future. Not a good thing, especially since the alleged MMR-autism link just hasn't been proven. I immunize my children (late, sometimes, but what's the point in rushing all those shots when babies are still breastfeeding?) because vaccines prevent certain harm.

Weather

I didn't post for a while because I just didn't have anything to say. However, today I have something to say about the weather.

It TOTALLED my brother's house yesterday in Oklahoma. Stinkin' tornadoes. At least my brother and his family are safe.

Things we have learned: have storm shelters or friends close by with storm shelters, and do an inventory (with a copy stored at someone else's house or on the internet) of the belongings in your house BEFORE disasters hit.