Snippets

It's been a while since my last post, and I apologize. Too much life, too little computer - and that's not a bad thing.

B is walking well, and starting to talk. He says "Hi" to anything that moves, repeatedly. A few weeks ago, in the grocery store, I was wandering up and down the cereal aisle finding all the family favourites while an employee wandered up and down in the opposite direction restocking the shelves. Each time we passed each other, little B's face lit up, he waved his arms, and he exclaimed, "HI!" It made the guy's day.

B is also aware that books are important objects, and he explores them in every way he can. He loves the crinkly feel of his Daddy's Bible pages in his fist, so we've had a few ripped pages. He wants to turn pages by himself in books both board and paper, so we've had a few ripped pages. He knows that you have to take the book off the shelf before you can read it, so we've had a few empty shelves and crinkled pages, not to mention quite a clean-up job. I try to do as much school with P and E as I can while B is napping, because when I'm reading another book to them, I have no attention to spare for whatever havoc B is causing.

A month or two ago, I caught E paging through P's reader with a wistful look. At the end, there's a certificate stating, "I Did Read It!" When E got to that page, he looked at me and announced, "I did read it, just like P." I told him that he could start reading lessons right away. We started using The Reading Lesson, and he enjoyed the first few lessons, but started refusing to do the assignments in lesson 4 or so (they involved saying the sounds of about 25 letters on a page, mostly the same 3). I'm going to instead try some of the approaches suggested in Ruth Beechick's The Three R's, drilling new letters with actual words, which he finds more interesting, until we're ready for the Bob Books or Sonlight readers. He actually read Bob Book number 1 quite happily yesterday and the day before, but I remember with P feeling that they moved too quickly compared to the Sonlight readers. In any case, I intend to do a few days of drill with each new letter, creating words he can read, and then let him read a book containing letters he knows several times in a row. This is roughly the Sonlight K method, but I'm tossing the instructor's guide aside - I've gained confidence since teaching P to read.

Speaking of P's reading, she can now read anything you set in front of her (though I haven't tried her on Shakespeare yet) for about a minute or so, before the mental effort gets too exhausting. Halfway through the 3rd "I Can Read It" reader from Sonlight LA 1, she announced, "This is boring. I don't want to do this." So I let her choose one of the next readers, and she happily read One Fish Two Fish Red Fish Blue Fish and The Cat In The Hat. She's finishing up the rest of the Grade 1 readers quickly. We'd been having problems with her willingness to do the creative expression assignments, so, emboldened by Ruth Beechick and Charlotte Mason, I've replaced them all with copywork. Over the past several weeks, she copied the entirety of "What Bilbo Baggins Hates", which I mentioned in my last post. I've started taking spelling lessons from her copywork instead of from the lists in the instructor's guide. For example, if she copies "Chip the glasses and crack the plates", I have her spell plate, plates, gate, gates, hate, hates, etc. If she can do it well the first time, she doesn't have to do it again. If we come across a word that she'll need to memorize because it doesn't follow the rules (when, whole), I write it on the board, ask her to look at it until she knows it, and then erase it and ask her to spell it. If she makes a mistake, I simply repeat the process until she really does know it. This is working well for us, and I'm fighting a lot less during language arts time.

Although I haven't taught any formal multiplication yet, P can solve 56 x 4 mentally. I asked her how she did it (I had asked for the perimeter of a square, and expected her to line the numbers up on her paper and add them). She told me, "Two 50s is 100, two 6s is 12, and I need two 2s of each of them, so it's 200 and two 12s, so the answer is 224." That's the sort of answer I love! No fragile knowledge for my kids! I bought the Singapore Math book of Challenging Word Problems, which is another guard against fragile knowledge, and she's enjoying it.

In order to keep E from feeling left out, I've decided to give him 3 daily math experiences while P is working on her 5-a-day reviews. Typically, I'll have him write numbers on the board, play a RightStart game, and do some other fun activity - a dot-to-dot, playing with pattern blocks or Cuisenaire rods, playing with coins. He's enjoying getting more of my attention during school time.

In non-school-related recent events, we recently had to reiterate the rule of no playing with bricks when barefoot. E's big toe is quite sad, though not broken, and after I'd bandaged him and given him lots of sympathy, he spent an hour or so giving himself even more. He and P spend a lot of their free time building "flying machines" using ragweed stalks, bricks, leaves, and balloons. They fly to Catalina Island frequently (I don't believe either of them has been there in the flesh, but their grandparents have, and P & E see it as quite the destination).

Speaking of flying machines, I'm still plugging away at my flying lessons. I'm almost ready for the checkride! I passed my written exam with flying colours, I just got 2 questions wrong (and one was a stupid mistake). I need to do my maneuvers more precisely - I have to keep my altitude to within 100 feet of the goal, and my heading and airspeed within limits, which I find myself forgetting about as I think about other things. But I'm hoping the next lesson or two will be enough for my instructor to hand me over to the FAA examiner. I've actually interacted with the examiner - he's a really neat old guy, a WWII veteran, who loves explaining things to anyone who'll stand still and listen. I'm lucky in that I get to schedule 2 flights with him before the actual checkride, so I'll know more of what to expect. Once I pass the checkride (and oral exam preceding the checkride), hopefully on the first try, I'll officially be a private pilot! I'm looking forward to taking people for rides. I have a waiting list already!

Poetry

Recently, I've been having P and E memorize some poems. E has a ridiculously good memory, which I noticed as we review the Bible verses we've learned. P will say what she remembers, and E will fill in any words she stumbles on, in addition to flawlessly announcing the reference.

Over Christmas, Ari read Tolkien's original The Hobbit to the kids, and they fell in love with the poem "That's What Bilbo Baggins Hates". It is recited by the dwarves as they clean up after dinner, and goes as follows:

Chip the glasses and crack the plates!
Blunt the knives and bend the forks!
That’s what Bilbo Baggins hates –
Smash the bottles and burn the corks!

Cut the cloth and tread on the fat!
Pour the milk on the pantry floor!
Leave the bones on the bedroom mat!
Splash the wine on every door!

Dump the crocks in a boiling bowl;
Pound them up with a thumping pole;
And when you’ve finished, if any are whole,
Send them down the hall to roll!

That’s what Bilbo Baggins hates!
So, carefully! Carefully with the plates!

About a month ago, I started working on memorizing the poem with them. This has been a fairly effortless process with the following strategy. On the first day, I read the poem through 3 times on 3 separate occasions. Then, each day for 2 weeks, I read the poem through 3 times just once. Then, I started saying just the first word of each line and waiting for the kids to fill in the blanks for me. They're getting better at not needing me to say very many of the first words any more, and the entire process has been thoroughly enjoyable. We review the poem once daily now, with great relish.

This week, we've started in on another poem, which I first met in my Order of Magnitude Physics class at Caltech. When I first read it to the kids 2 years ago, they knew it was funny but didn't really get it. I had printed it out then, and somehow the printout surfaced again. When I read it to them a week ago, I knew this was another one they would love memorizing. It's written by Jack Prelutsky, who has written a wide variety of kids' poems.

The turkey shot out of the oven
and rocketed into the air,
it knocked every plate off the table
and partly demolished a chair.

It ricocheted into a corner
and burst with a deafening boom,
then splattered all over the kitchen,
completely obscuring the room.

It stuck to the walls and the windows,
it totally coated the floor,
there was turkey attached to the ceiling,
where there'd never been turkey before.

It blanketed every appliance,
it smeared every saucer and bowl,
there wasn't a way I could stop it,
that turkey was out of control.

I scraped and I scrubbed with displeasure,
and thought with chagrin as I mopped,
that I'd never again stuff a turkey
with popcorn that hadn't been popped.

(In case you're curious, in Order of Magnitude Physics, we had to calculate the approximate velocity of the turkey given only the information in the poem. This led to all sorts of experiments, including some classmates of mine stuffing Cornish hens with popcorn and discovering that the corn got too waterlogged to pop, and me stuffing an empty spice container with popcorn and putting it in the microwave, and discovering that the odor of melting plastic becomes offensive before any kind of explosion occurs.)

There are many things to love about both of these poems. They have a steady meter and predictable rhyme patterns, which makes them easy to memorize. They are also full of delicious vocabulary words (ricocheted, chagrin), which, memorized in context, will be easy for my children to recognize when they encounter them in future. Most importantly, they are lots of fun. The kids have a great sense of accomplishment in memorizing and reciting long poems, and thoroughly enjoy the images created by the words. I intend to keep them memorizing poems throughout their education - I'm enjoying it too.

Disadvantages of fratricide...

It's been ages! Sorry...

At lunch on Friday, my sister-in-law Michelle was eating with us and we were discussing the joys of having a sister. P looked at us mournfully and announced that she only has brothers: Ari and I need to work on fixing this for her. I reminded her that, if another baby were to join our family, there's only about a 50% chance that it would be a sister, and if it were a brother, she'd be stuck with THREE. However, Michelle reminded P that when her brothers grow up, they will likely get married, and she'll get sisters that way - and appreciate them more, through not having fought with them throughout childhood. I think it was Ari who commented, tongue-in-cheek, "So, sisters-in-law might be the reward you get for not killing your brothers."

Without missing a beat, P replied, "I guess Abimelech missed out on his reward."

She's been paying attention during Bible reading.

FIRST SOLO!

There's nothing like finally doing something you've been dreaming of for half your life.

When my family lived in Jordan during my teens, I joined the Royal Jordanian Gliding Club. Gliding was an important part of my life for most of my time there, and I tried to fly every weekend. However, there were a number of aspects to the experience that failed to be awesome, despite the thrill of the actual gliding. There was no set curriculum or record keeping that I was aware of. I was given an exam in order to get my student pilot license, but during the exam, the other student in the room cheated flagrantly. If it was cheating at all. If the test question was, "What is the empty weight of the glider?", the student asked the adjudicator, "Excuse me, sir, but what is the empty weight of the glider?" He helpfully responded with the correct answer. Needless to say, I had little respect for the test. I was torn, ethically, over whether or not I should write down the answers I overheard if I couldn't remember them on my own. I was never told what my own results were, but I was given my license a few weeks later.

However, I never seemed to get any closer to the first major goal of a student pilot: the solo flight, when you get to be the sole occupant of the aircraft for an entire flight. On vacation in South Africa when I was 16, my parents got me a flight in a motor glider as a special treat. After handing me the controls and watching me fly, the pilot commented, "You must be just about to solo." Back in Jordan, a year later, with at least 50 more flights' worth of experience, I still had not. On one occasion, one of the instructors asked, seemingly in passing, "Do you think you might be able to come more than once a week?" I explained that the other days the club was in operation were school days, and no more was said on the subject. I thought nothing of it until the day my dad finally confronted them.

"We're only letting her fly because she's your daughter." That was the main result of my dad's request for some kind of time estimate on when I might expect to solo a glider. My dad, you see, was a VIP, a high official in the South African Embassy in Jordan. Having a diplomat associated with their club made them look good. My dad and I both got the impression that, had I been someone else's daughter, the mental deficiency that my gender implied would have prevented them from letting me get even this far. Needless to say, we were both angry. Trying to backpedal, one of the instructors said, "Besides, we already told her she needed to fly a lot more often."

Perhaps if I'd been more culturally savvy, I would have realized that the mild suggestion was actually a requirement. Then again, perhaps if I'd been more culturally savvy, I would have realized I had no chance in the first place. In any case, I stopped gliding. It took me a while before seeing an aircraft in flight didn't bring me close to tears. I thought, "When I move back to a 1st world country, I'll take this up again."

Time and money. Those are the two main obstacles to any number of pursuits, and flying is certainly one of them. However, Ari's parents have given us a number of financial gifts over the years, and now that he's working from home, our schedules are a lot more flexible. Last November, the two of us were hiking together when Ari suggested, "What would you think of taking flying lessons?" I believe I stopped in my tracks, dumbfounded. I had stopped thinking about flying at all, but with the realization that it was now possible, I started to dream again. It took him a good bit of effort to convince me to spend our money on something that, at least for the time being, would be purely for my enjoyment, but I finally acquiesced. On my 30th birthday, Ari got me a discovery flight at the West Houston Airport.

Oh, paperwork is another obstacle. Being an evil foreigner, the FAA had to make sure I wasn't just learning to fly in order to cause chaos and mayhem (of course, it makes sense for them to be concerned). They make sure you're not out to cause trouble by checking your fingerprints against those of known Bad People. This was harder for me than it sounds because almost every one of the 10 or so steps I had to follow produced its own glitch. However, I finally started lessons in June, 2 months after my discovery flight.

What a difference from my experience in Jordan! For one thing, there's the Ninety-Nines, an international organization of women pilots, the local chapter of which meets monthly at West Houston Airport. It's such an encouragement to enter a roomful of women who all have pilot certificates. More importantly, the entire outfit is so much more professional. It has been clear from the outset that each lesson has a purpose, and brings me closer to the goal, first of soloing and ultimately of getting my private pilot certificate.

The past month or two of lessons, I've mainly been working on landings. There are so many things to think about - making radio calls, making turns at exactly the right time, keeping the airspeed high enough but not too high, extending the flaps at the right time, keeping the nose pointed down the center line of the runway no matter what the wind is doing, starting the roundout and flare at the right moment and flaring enough to get the nose up but not so much that you stall too high and drop onto the runway, and deciding to go around if you know you forgot something and it's going to be a bad landing.

A month ago or so, my instructor gave me the required pre-solo exam, which I passed with an almost perfect score. (No, I didn't ask him for the answers - it was a take-home). He told me he was now just looking for me to make 3 good landings, preferably in a row, preferably the first 3 landings in the lesson, and he'd let me solo. For the next 6 lessons or so (I've been flying twice a week), I got increasinly frustrated at myself. I'd make a good landing, then a bad one, then a good one, then 2 bad ones, always bad in different ways. I'd think about what I'd done wrong last time, focus on fixing that, and let something else slip.

Last Wednesday, I almost had it. Every time, it seemed like the landing was just beautiful until the last second, when I would relax the pressure I was putting on the right rudder, and the nose would swing to the left, and I'd weave all over the runway. Then on Saturday, the wind was blowing from the opposite direction to what I'm used to, so we took off from the opposite end of the runway from usual. The change in scenery threw me off, and I was back to making different mistakes each landing (though I at least kept the right rudder in!). I counted up the flight hours and landings recorded in my logbook - over 30 hours, and over 100 landings. Surely I must be the slowest learner in the history of aviation! But I googled "taking a long time to solo," and came up with stories of other pilots who had taken a good bit longer than that, so I came to my lesson this morning feeling slightly happier about myself.



The wind was back to normal, the skies clear, the air chilly enough to justify wearing a sweatshirt. I did 2 landings with minor errors and was wondering if they counted as "good". As I was about to roundout for the 3rd landing, my instructor told me to go around. I thought, "That's odd. I thought it looked about perfect." But I increased throttle and lifted the flaps (forgetting to lift them incrementally, so the plane lost a lot of lift at once), went around the traffic pattern again, and brought it in for a reasonably good landing. I felt pretty good about them, but I wasn't sure what my instructor thought.

"Okay, I'm bored. Take me back to the ramp so I can take a nap. You take this thing up yourself." I broke into a huge grin. I grinned as I taxied back to the ramp, as he endorsed my logbook and student pilot certificate, as he told me to go around if I didn't think it was working out (that's why he had me practice it), as he jumped out of the airplane and asked me if I had any last words, and as he leaned in again to tell me to take it around the pattern 3 times.

I was expecting to feel more nervous than I really did. I sang as I taxied to the end of the runway, wiped the grin off my face long enough to radio my intentions, and took off. Apart from the plane climbing faster with only one occupant, it was just like what I've been doing multiple times a lesson twice a week for the past few months. There's enough to think about when flying that I didn't have attention to spare for anything other than a general sense of extreme happiness. Knowing that there was no-one to take over for me if I did anything wrong just helped me to focus harder. The second landing was the best I've ever done. By the 3rd landing, I was feeling a touch overconfident, came down hard, and bounced it. My instructor sat on a luggage cart on the side of the taxiway and watched me, waving to me each time around. When I had parked the airplane, he congratulated me and told me the second landing was beautiful.

There's a tradition that, after your first solo, the instructor cuts out the back of your t-shirt and signs it. Stacy, a fellow Ninety-Nine who works at the desk, told me the origin of this tradition. Back in ancient days of yore, when aircraft held only 2 people seated single file, radios were nonexistent, and the engine was too loud to yell over, the flight instructor would sit behind his student and communicate by tugging on his shirt to show him where to go. When the student was ready to solo, he no longer needed the instructor to tug on his shirt.



So, I now have a cut up t-shirt and a tremendous sense of accomplishment. It's a remarkable feeling, to lose a dream and receive it back better than before. Thank you, Lord!

(Photo credits: Aircraft in flight and on ground: Ant and Eva Greenham; Solo picture: Brian Padar (my instructor)).

Allegiance

It would be very convenient if I were to become a U. S. citizen. I've had my green card long enough, and we can spare the money, and I'm only mildly allergic to paperwork, so none of that is holding me back. What's holding me back is the Oath of Allegiance.

I've had difficulties with allegiance for quite a while. It actually started the summer between second and third grade. My family was living in Dallas, TX at the time, and the elementary school I attended had a tradition of making the children stand up and recite the Pledge of Allegiance every morning. This may be common nationwide; I only speak from my own experience. What happened that summer when I was 8 years old was that I learned the meanings of the words "pledge" and "allegiance". The first day of third grade, as we recited the pledge in the morning, I was horrified. Without knowing what I was doing, I had promised to align myself with a foreign country! The following day, I stood with my hand over my heart, facing the flag, and kept my mouth shut while my classmates recited the pledge. After a few days of this behaviour, my teacher confronted me. I struggled to express my feelings, stating only, "I don't think I should say it because I'm from South Africa." I don't remember anything of her response, only that the result was that during pledge time for the rest of my time in Dallas, I mouthed the words in unison with my classmates without making a sound.

When I started considering upgrading from green card holder to U. S. citizen, I read the Oath of Allegiance which all new citizens are required to take. It states,

I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law; that I will perform noncombatant service in the Armed Forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion; so help me God.

The part that gives me pause is not either of the ones that they allow an exception for (military service, or using the word "oath"). My problem is that, first and foremost, I am a citizen of the holy nation of God Almighty. As a global nomad, I'm not particularly attached to any earthly prince, potentate, state, or sovereignty - heck, there isn't a city on the planet I've spent a total of 6 years in. I'm interested in U. S. citizenship for its convenience - my husband and 3 children are citizens, and when we travel it'd be easier to stand in the same queues as them. I don't mind giving up my allegiance to South Africa. My problem is that I am absolutely and entirely the subject of the Creator of the Universe (including all the nation states on earth), the Prince of Peace, the Blessed and Only Sovereign. I will never renounce or abjure my allegiance or fidelity to him, but will remain subject to him all my life, a fellow citizen of all believers in Jesus.

I know, I know. They don't mean to involve God at all, except as a means to enforce compliance with the oath ("so help me God"). But if a situation ever arises where my allegiance to Christ and his Kingdom conflicts with my allegiance to the United States, I would not like to have sworn to ally myself with the United States. If the word "earthly" could be inserted in the oath ("...I absolutely and entirely renounce and abjure all allegiance and fidelity to any earthly prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen...") I would be quite happy with it. I just have no idea how to go about doing that - it's not a box you can check.

What would you do?

Exponential!

Every so often, you just let your 6-year-old do whatever she wants to during math time, and she ends up calculating 2^30.

I love homeschooling.

At breakfast time on Tuesday, P started with "Two ones is 2, two 2s is 4, two 4s is 8, and two 8s is 16." E then asked me, "What are two 100s?" I doubled for him until we got to 409 600, whereupon folding the laundry and feeding the baby took up too much of my attention.

The interest both P and E had showed in doubling suggested to me that I abandon my original plans for math (which weren't anything special, anyway) and let P practice addition by doubling until she lost interest. She didn't. We started by writing the doubles on the chalkboard, but soon ran out of space. I copied the answers we had so far onto a piece of paper. P struggled to write neatly enough to line up the problems exactly, so I set up each subsequent problem for her on the chalkboard, she solved it, and I wrote it on the paper. By the time we got to 262 144, P was not only not losing interest, she was excited. "Mommy, math is so much fun!" I began to think of possible strategies for ever stopping her, because the boys were getting bored (B was trying to eat the chalk each time P put it down).

Half a year ago or so, we read a picture book in which a girl tricks a greedy king by asking for a grain of rice as a reward, doubled daily for a month. So I suggested that P calculate how much rice the king gave the girl on the 31st day, and then stop. She added excitedly, finally concluding that the total was 1 073 741 824 grains of rice. While P worked, E kept commenting, "That king must be getting worried!" I only pointed out 2 minor errors during the course of this monumental calculation, which P corrected herself.

While P was busy, I had been reflecting on the fact that Sonlight's Core K, which we're using this year, contains a longer book with the same basic storyline. So, once P was done, we read A Grain Of Rice and thoroughly enjoyed it. The story was well told and both P and E followed it with enthusiasm. We compared the amount of rice the emperor was having to give the peasant each day with P's calculations, and it was fun to see them line up perfectly.

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I'm convinced that a good teacher is always learning. Of course, I find math enough fun that I'm reading this book as my Sunday rest book (and at other times during the week too). I just read about a method of multiplying 2 numbers that requires only addition, doubling, and halving. (You can read about it here). We've covered addition and doubling already - when it comes time to teach P about multiplication (which she can already do, she just doesn't know it) this might be a neat thing to show her. I love that even with elementary math, there's something new for me to think about.

Finding Patterns

I noticed that P was having trouble with subtraction. Mainly, she was counting on her fingers inefficiently, and didn't seem to have realized that subtraction is simply the inverse of addition. So I decided to introduce that concept this week. I used Cuisenaire Rods to show her that if 4+2=6, then 2+4=6, 6-4=2, and 6-2=4. We worked on the concept for several consecutive days, and she really seemed to grasp it.

To reinforce this concept and others, on Friday I gave her a blank addition table: a 10x10 chart with the numbers from 1 to 10 on the top and left hand sides. She needed to fill in the sum at each intersection point. At first she just enjoyed the mechanics of pointing to a random space, figuring out which two numbers to add, and writing the sum in the space. Then, all of a sudden, she realized that diagonals had the same answer: 3+5 = 4+4 = 5+3 = 6+2 = 8. She looked up at me, bright-eyed, and said, "Mommy, I love this! There are so many patterns in this!" When the table was filled in, I showed her that if you want to subtract, you find the number you are subtracting (the smaller number) at the top, go down to the number you are taking it away from (the bigger number), and go left to find the answer. I promised that for all future math problems, she may use the table. Since she generated it all by herself, it isn't cheating, and using it will give her practice with the math facts.

While P was busy with her addition table, I got bored. I had been starting to teach her about perimeter, and she did great with measuring the sides of squares or rectangles and adding them together. But to mix it up, I wanted to make her some right triangles (so that I can get all 3 sides the right length - I can't draw a 60 degree angle by eye). So I wondered what the set of all possible integer side lengths for right triangles was (integer because she isn't measuring half inches yet, let alone whatever the square root of 2 is closest to on a ruler). This turned into a fun math problem, which I solved. E wanted me to use his pencil, because he would like to wear it down more quickly (he finds short pencils more attractive, I believe), so every time I stopped to think, he encouraged me with, "Do more math, Mommy!"

If you're wondering what my solution was, leave a comment and I'll give a summary of my reasoning and results. Or, have some fun with it yourself first! (Mwa-ha-ha... trying to infect the world with mathematical recreation...)