Wednesday, November 17, 2010

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)).

Tuesday, November 16, 2010

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?

Thursday, October 28, 2010

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.

************************************************


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.

Saturday, October 23, 2010

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...)

Saturday, October 16, 2010

Spelling

P wrote me a note:
"I Like sgoL
MoMMy.
SbeshaLy
riting.
I Am Happy."

Once I realized that "sgoL" refers to school, the note made sense.
Although the spelling is not perfect, it shows progress in topics I haven't made an issue of. For example, she correctly used the silent e in "like" and the "ing" in "riting". Since she isn't reading fluently yet, I'm not expecting her to spell well, but it's fun to see that she's picking up some rules without being formally taught them.

I'm also glad that she likes school, and is happy. Given that she usually complains about copywork, I'm also strengthened in my resolve to make her do things that are good for her even if she doesn't appear to like them at the time.

Friday, October 1, 2010

Binary

I wasn't planning on teaching the kids about binary numbers yet, but Ari and I ended up doing it yesterday. It was Barry Simon's fault.

Here's how it happened. We were discussing CBS (Community Bible Study, which the kids and I attend on Thursday mornings) at lunch time. E is never able to remember the story he has heard at CBS - I'm not sure if he just isn't aware that they're telling a story, or if he's decided that forgetting the story is easier than telling us about it. In any case, this led to a discussion of good and bad teachers. And Ari and I started talking about Barry Simon.

When I was a frosh (insert quavery voice) at Caltech, Barry Simon taught Math 1a. He was brilliant, I'm told. So brilliant that there's no way he could stoop to teaching the elementary concept of epsilon-delta proofs in such a way that the average Caltech freshman could understand them. Instead, he found special cases and exceptions, and talked exclusively about those. At least, I think that's what he did. I never really understood anything in Barry Simon's class. I spent one evening determined to understand the topic of the next day's lecture before it happened, so I studied the subject over and over until I was sure I grasped it. I entered the class knowing how it worked; I left class hopelessly confused. The joke was that one day Barry Simon would teach us to breathe, and we'd all suffocate.

As Ari and I discussed his teaching style, I wondered aloud how he would teach a 6-year-old how to add with regrouping. I figured the first thing he would do would be to convert 28+37 into binary, without mentioning that he was doing anything of the sort, or explaining to the 6-year-old that such a thing as binary even existed. I was unsure of whether P was ready to learn binary, but when Ari was done laughing, he decided to prove me wrong.

This actually turned out to be a lot of fun. Ari labeled a piece of paper with columns for 8s, 4s, 2s, and 1s, and we explained that in binary you're only allowed to use 1s and 0s. Ari started by having P identify the values of 0000 (B's age), 0100 (E's age), 0110 (P's age), and 0111. E then wrote a few 1s and 0s at random, and it ended up being 00101. P's ability to easily figure out that that was 5 made me wonder if I really could show her how to add in binary without and with regrouping. We started out with 1+2=3 (01+10=11), and then I explained how 2+3 (10+11) had 2 in the 2s place, meaning 4, so we had to write a 1 in the 4s place instead: 10+11=101. She thought this was really neat - and I suspect that it'll help her grasp regrouping more easily when adding in base 10.

All of a sudden, I started wondering: What does the Fibonacci sequence look like in binary? What about skip counting - what patterns are there? How do you do long division in binary? I can imagine myself forgetting about what I'm trying to teach P and starting to explore this sort of question myself during our math lesson, leaving her hopelessly confused. Please say it ain't so: Could I ever turn into Barry Simon?

Thursday, September 23, 2010

Ancient mysteries solved!

Last Friday, I decided to introduce P to addition with regrouping (what you do if the sum of the ones digits is greater than 10, as in 27+64). I carefully laid out the problem, and explained each step thoroughly. As soon as I carried the 1, P cried out, "Oh! I've been wondering about that 1 for years!" Upon being questioned, she informed me that a big kid in our old church in PA (where we lived over a year ago) had demonstrated addition with regrouping, and P had not understood it then. Interestingly, I had tried to explain the same concept about 6 months ago, but P didn't catch on and I left it for later. Half a year's growth and a deeper understanding of place value has made a huge difference. Apparently, Math on the Level's maturation-based approach works!

Willpower!

We spent last weekend in St. Louis for Ari's uncle's wedding. Our plans were quite flexible, and since I didn't know how much time we'd be spending there, I packed most of our school books into the heavy-duty Sonlight tote and brought them along with us. All day Friday, my mother-in-law was preparing to host the rehearsal dinner, and school was a reasonable way to keep the kids occupied. We headed down to the finished basement and put their pencil cases on the ping-pong table. There were fewer toys around to distract everyone (though baby B found a box of rocks and corals to gnaw), so things went more smoothly and quickly than they usually do at home.

We've been using Home School Family Fitness as our PE program. The first step the author suggests is setting up a routine of strength and endurance exercises: sit-ups, push-ups, pull-ups, etc. We've been working on these for a few weeks now. Typically, E has been able to do about 7 sit-ups and 15 push-ups, and he can hang on the pull up bar for about 6 seconds. P has been doing about 15 sit-ups and 7 girl push-ups, and hanging on the pull up bar for more like 25 seconds (neither child can do a real pull-up, but then, nor can I). Before we left for St. Louis, P did 25 sit-ups and 15 girl push-ups. So I was skeptical when she announced on Friday, "I'm going to do a hundred sit-ups!"

I now have extra evidence that this child is related to me (though giving birth to her is pretty strong evidence already). I said, "There's no way you'll be able to do a hundred sit-ups!" She did 105. She then announced, "I'm going to do 70 push-ups." This time, I was even more sure it was impossible. After every 10 push-ups, I asked her if she wanted to quit yet. She did 72. I informed her that she would be in worlds of pain the next day. She wasn't (or, at least, if she was, she didn't say a word about it). She said, "I can feel myself getting stronger. I like being strong."

Motivation is an important factor in what one is able to do. Today, I didn't feel like sitting on P's feet for 10 minutes while she groaned her way through another 100-odd sit-ups, so I told her I'd count how many she could do in 3 minutes. She barely made it to 25 after 2 minutes, and quit. I'm sure if I'd okayed her to do another hundred, she'd have made it. I just have other things to do with our time.

Friday, September 10, 2010

Finding a New Groove With Math

At the end of last week, P complained, "Math isn't fun any more this year." I'd been giving her 5 review problems daily, same as last year, while working on a new concept. It may be that I wasn't approaching the concept of place value in a way that worked with her learning style, or that she had forgotten several of the review items, but I felt that the main problem was that I was requiring too much writing of her. We've been doing math at the end of the school day, right before lunch, and by that time, she has already done a page in her handwriting workbook, written a list of 10 spelling words, often done copywork for language arts, and frequently completed part of a science worksheet.

At the same time, I was busy reading this article. If you don't have time to read 25 pages of sometimes over-emotional diatribe about what ails math education, here's my summary: Math is actually an art form - finding the beauty of patterns in conceptual objects (numbers, triangles, etc). Math education has removed all the art and beauty from math, and turned it into a purely mechanical exercise requiring memorization without creativity. It would be better to teach no math at all than to ruin the subject the way it is ruined by teachers who don't know better because they've never seen math, either.

I don't fully agree with the author, but the article did make me think about how I'm going about teaching math to P. I decided to try to include more unguided discovery, as well as more guided discovery, into our lessons and our review. I started by revamping the 5-a-day review process. Instead of having her write anything with pencil and paper, I'm looking at what concepts we need to review and trying to find games to play that will require understanding of those concepts. Sometimes, failing to come up with anything creative, I simply have her do a problem on the chalkboard, which she at least prefers to pencil and paper.

I've been doing lesson prep for math on Tuesday nights, but Ari and I watched the first half of "Gone With the Wind" last Tuesday night instead, so I had no plan for Wednesday. Fortunately, the math video which once was lost now is found, so I simply let them watch that. "Professor Justin" reviews a number of concepts that we covered a while ago, and even E was really getting into shouting out the answers before Justin said them.

On Thursday, I used an idea gleaned from the Sonlight forums for our science experiment - demonstrating the water cycle. We put water in a pot (the "ocean") and heated it on the stove (the "sun") until it began to evaporate. I then held a bowl about 20cm above the pot and let the water vapour condense inside it ("clouds") until the droplets got big enough to "rain" back into the "ocean". Once the experiment was over, the kids begged to bake something with the boiled water. I had been planning on making bread (and, for vocabulary enrichment and additional science, discussing the differences between whole wheat flour and enriched unbleached flour). Our recipe calls for 3 cups of warm water and 1/2 cup of honey, so I added the 1/2 cup of honey to the boiled water to dissolve it easily. This turned into a lesson in adding fractions - "We have 1 1/2 cups of liquid in our measuring cup, and we need 3 1/2 cups of liquid. We've added all the honey we need, so how much water do we need to add?" P needed a bit of hand-holding, but she grasped it pretty well once I explained it in a couple of different ways. She easily remembered, while helping me make pizza dough this afternoon, that 2 1/2 cups of flour was the same as 5 half-cups of flour. Kitchen math is an excellent way to work with fractions - I plan to incorporate it into our days more often, since both big kids love baking with me. (B does too, if you count him sticking his hand into the dough when I'm not paying attention and then smearing it all over my recipe books).

Today's math lesson, I decided to introduce P to some patterns that I find fascinating. In the RightStart games package which we bought in May, there are games involving the "long chain" and "short chain". I had never heard of these, but they are patterns similar to Fibonacci in that they only require simple addition, but simpler because they only take into account the ones digit. Since we're working on place value and I'd like to help P get more comfortable with her addition facts, I thought they'd be valuable for her as well as enjoyable - she has a thing for patterns. For example, the one I started her out on is "4 2 6 8 4 2 6 8..." - the nth number is the ones digit of the sum of the (n-1)th and (n-2)th numbers. P loved this, and I had her figure out "0 5 5 0..." for herself. I also showed her the trivial case, "0 0 0...". She said, "That isn't a pattern. It's just zero." I neglected to introduce the vocabulary word "trivial", but she clearly grasps its concept. I then demonstrated, with some participation from her, the "long chain", which starts like Fibonacci (0 1 1 2 3 5 8) but, because it only contains the ones digit, repeats after 60 digits. She doesn't have the patience to do that much addition! But she liked the idea of a repeating pattern of numbers, so I imagine we'll play with that again.

Now, I'm off to figure out some hands-on, real-life activities for her 5-a-day reviews this coming week, and see if they lend themselves to any interesting patterns. I like this challenge - it's real mathematics.

Friday, September 3, 2010

So much activity, so little blogging time...

And we're back to a new year! Actually, we started 9 days ago, but I'm only getting around to blogging about it now. In case you were wondering, I'm not planning on blogging daily this year like I did last year, but I'll try for once a week.

This year, we're using Sonlight for just about everything except math. We're using Core K, Science K, and Language Arts 1, and continuing to use Math on the Level. Over the summer, P took violin lessons from a Ukrainian woman who came highly recommended by a friend at church. However, we decided that paying for both violin and ballet would be pushing it, so I'm going to continue teaching her using The Violin Book.

My general plan is to get through Language Arts 1 (and Handwriting Without Tears 1 for P and Pre-K for E) this academic year, but stretch Core K and Science K over 2 years. This is because K is labelled as appropriate for ages 5-7 and grades K-2, and E will be turning 5 and starting K next academic year, while P will be 7 and in grade 2. I'd like to keep P and E combined for Core (Bible, history, and read-alouds) and science, for simplicity's sake, so I don't want to move ahead of what E is ready for. I'll separate them for math and language arts, but try to do everything else together. This is working well so far - we do math and language arts daily, but alternate days for core and science. The only disadvantage is that P likes some of the books so much, it's hard for her to wait an extra day to read more. I'd say that's a good problem to have.

Wednesday, July 14, 2010

P's birthday

Last year, P announced that she wanted a house cake for her 6th birthday. As time went by, the request morphed into "Winnie-the-Pooh in a house," and finally, "Winnie-the-Pooh's house." I spent the past week or so mulling over how I could possibly make Winnie-the-Pooh's house out of flour, sugar, eggs, etc. I studied the illustration in the first chapter of the original Winnie-the-Pooh, which we recently finished reading, and then made my attempt.

I was fairly pleased with the result, which was achieved by delving into fondant-making. Fondant is a fascinating substance formed by heating a sugar syrup to 240 degrees F, spreading it out on a marble slab, and moving it around until it suddenly turns from clear and smooth to white and grainy. After kneading this, you have a glossy paste-like substance which can be coloured and turned into Winnie-the-Pooh and other accessories. Although it is made of pure sugar, it isn't as tasty as I would have guessed. I think next time, I'll use marzipan, which I know and trust more.





In any case, the birthday girl was perfectly happy.





We spent the day in College Station with Ari's grandparents, who have a swimming pool. In the morning, P worked hard at it and learned how to swim. She hasn't worked out how to breathe at the same time, which limits her range. Describing her accomplishment, she announced, "Now I have super powers."

As the next picture shows, we have a girly girl - she was thrilled to receive a dress, bead necklaces, clip-on earrings, and flowery flip-flops. After the presents were unwrapped, she enjoyed playing with her foam dollhouse and dolls and her Rush Hour logic puzzle, and looking at the poster of a "princess castle" we got her.


Saturday, July 10, 2010

Book Review: Through the Veil

When I clicked on a link my former pastor from Jordan posted on Facebook to an article his wife had written, I had no idea what a powerful writer she was. But I spent the next several days thinking about that article. When Lisa's book was available for pre-order, I knew I had to have it. It arrived 2 days ago, and I finished reading it this morning.

Through the Veil is a collection of essays, mainly about women Lisa met in Syria and Jordan. I love how she weaves the thread of their stories around her own childhood memories and experiences, drawing both into a unified whole. Many of the cultural features I encountered during my time in Jordan are addressed in these essays: the evil eye, modesty and propriety, hospitality, honour. But Lisa, who was then the age I am now, saw them differently from how I did, and integrates them into her understanding in a more complete, rational, adult way than I was able to as a teenager. I appreciate the depth and compassion of the stories she tells, looking honestly at herself as well as the friends and neighbours she writes about. Many people I've met in the West have flimsy cardboard ideas of what life in the Middle East is like - Lisa gives a well-rounded, fleshed out view. There aren't pat answers or stereotypes; instead she succeeds in fulfilling the promise of her first chapter:

"I write the Damascus I love, but sometimes her face blurs and I can’t make out details: both dreams and memories are tangled things. They twist themselves around smells and feelings and other memories of times and people far removed. They tumble to the page like a child at play, breathing hard. I calm and comb them, working out the catches and finding the story enmeshed in strands of memory. I write and rewrite, but some memories remain confused and tangled. I work the others, braiding them and tying the ends with reflection and sometimes also tying them with regret."

Tuesday, July 6, 2010

Here are a pile of pictures from a couple days before my brother Paul came to visit, until halfway through his visit. We haven't transferred the second half of the pictures from the camera to the computer yet.



Look who lost a tooth! We took bets on when it would come out. I lost badly - I said it would hang in there until after Paul left. Ari came closest - he guessed it would be on the way to pick Paul up from the airport, whereas it actually happened the night before he arrived.



We went to the zoo, and E enjoyed the Komodo dragon. We reconnected with one of my oldest friends, whose family always invited us over for Thanksgiving when we lived in Dallas. We had so much fun with Joy, we completely forgot to photograph her!

We headed to Galveston on the Sunday afternoon after Paul arrived, and had great fun splashing in the surf along with Ari's brother Dar and his little boy (Michelle was busy that afternoon).





When wading, what do you do if you see this?





The stingray came close to me (I jumped, it fluttered away), closer to Paul, and actually swam right over Dar's foot (Dar had the sense to hold completely still as the tail brushed by his ankle).

E had a blast in the waves.



B, on the other hand, thought it was much too big and splashy of a bathtub for his taste (though the temperature was about the same), and whimpered for almost an hour, continuously. Fortunately, this tired him out.



The next day, all of us (except Dar, who had to work) went to the aquarium at Moody Gardens. Paul enjoyed some quality time with his youngest nephew,



and P and E had a blast running from their uncle in front of a tankful of sharks.



That evening, Dar and Michelle opened their beehive for us. They wore their full bee suits, and Ari put on a spare hat of theirs and a sweatshirt and took pictures.



Everyone wearing bee protection got to see a bee in the process of being born (you can see her in the middle of this picture).



Michelle came over and showed the rest of us, who were protected by the screen porch, what they were doing.



If I were keeping track of educational experiences over the summer, this would certainly count - but of course, kids don't just learn during formal school time.

Thursday, June 24, 2010

End of school; Fredericksburg

The last few days. I got lazy about blogging daily toward the end there, didn't I? I'll probably cut back during the summer, but not completely. We studied South Africa and Antarctica during our last week of school. We looked at the photos from our family trip to South Africa in 2008 - P was almost 4 then, and E had just turned 2. He has some very vague memories of the trip, and P remembers it fairly well, but the photos helped. We'd taken a few videos on our digital camera, including one of E at the lion park. I'm explaining that the lion we're looking at is a lioness, a girl lion, because it doesn't have a mane, and E lisps, "No! It's a boy dion!" This was greatly enjoyed by both kids. I think E enjoys seeing that he was once little and cute, since baby B tends to have a premium on that these days. Of course, E still is little and cute, just not the littlest and cutest. We watched "March of the Penguins" to go along with our study of Antarctica, and marveled at what those birds go through to obtain babies. Pregnancy may have its frustrations, but it isn't months of starvation in blizzard conditions balancing an egg on one's feet. During our math time, we played a lot of RightStart games, including a modified beginners' version of "Corners" which P loved.

Fredericksburg. We spent last weekend in the small town of Fredericksburg, TX where my inlaws are considering buying some property. Our major task for the weekend was to use a ground conductivity meter (glorified metal detector, AKA The Beast) to search for hidden trash on the property. There is plenty of un-hidden trash in a ravine on the ranch, including historical refrigerators, cars, and at least one wild hog carcass. They just wanted to make sure that what they saw was the total of what they'd get. However, it turned into an enjoyable family weekend. Ari's brother and his family joined us on Saturday morning, and we all went swimming except baby B, who napped, and Ari, who read the manual for The Beast. That afternoon, we all hiked to the top of Enchanted Rock (except baby B and my nephew G, who were carried). We got our new digital SLR the day before leaving for Enchanted Rock, so we went wild taking pictures. Unfortunately, I haven't loaded any of them onto this computer yet, but I have the best of intentions. Once our hike was over, we met up with Ari's parents and grandparents, and drove out to the ranch, which is only a mile or so from Enchanted Rock. It was too late in the day to be worth hauling out The Beast, but we walked around the property and admired its beauty while being sobered by the ravine full of trash. We spend Sunday relaxing around Fredericksburg - swimming, of course, to the kids' immense satisfaction, and falling off a large inflatable swan into the swimming pool. On Monday, there was a lot of teamwork involved in putting up evenly spaced flags to systematically scan the field they were most concerned about, but taking care of 3 small children in a field full of grass burrs was complicated enough that I wasn't able to contribute to the cause. Instead, I headed back to the hotel with the kids. We met Ari's grandparents, who were about to head back to their home in College Station, and had lunch with them at the Rather Sweet Bakery. As the name would suggest, their emphasis is on dessert, and the children each got to order a confection as big as their heads. I split each child's dessert in half, so that I got a whole dessert, they each got half, and we all got way too much. But decadence is half the fun of being on vacation. On Tuesday morning before we left, I took the kids to a hand-carved candle store, where we bought $1 candles made of wax remnants for each kid, and on the way back we paid 51 cents for the privilege of turning a crank to squash a design onto a penny. A great time was had by all.

Our next major adventure will consist of my brother's visit. He postponed it for a week to spend time with a young lady he's fallen head over heels in love with (at least, that's how my mom describes it), but we fully expect to see him at the airport tomorrow afternoon, ready to be interrogated about his love life.

Wednesday, June 16, 2010

Success!



And I conclude that our first year of formally homeschooling has been successful in every way.

Thursday, June 10, 2010

Week 34/35, day 4

Thursday. P's violin teacher asked her to practice 3 times daily, playing each of 3 pieces (only 4 measures each, but still) 3 times through. She practiced twice today, but I'm already seeing significant progress. After I had P and E review memory verses and update the calendar, E wandered off while P read her reader and did her copywork. She did her 5-a-day math review all by herself. 2 of the questions were games. We played card games from the Right Start Math package I bought at the homeschool convention in San Antonio. We started with "Go to the Dump", which is a variation on "Go Fish" where instead of finding pairs of identical numbers, you find pairs whose sum is 10 (for example, if you have a 6, you ask for a 4). She did this easily, which surprised and pleased me. We then played a game with an empty clock face, on which each of us took turns placing number cards from 1 to 12 and :00 to :55. P enjoyed both of these games, so I suspect we'll end up playing them frequently in future. In the afternoon, after P's second practice, I had her make a book about Nigeria. She drew a flag, coloured a map, and drew a gorilla in a rain forest, a girl carrying a bowl on her head, cacao beans, a girl in a colourful dress, and an open-air spice market. She also spontaneously wrote a "poem": "runing in the praree/ the gros wavs/ in the wind/ and mi sgrt wavs/ in the wind." (gros = grass, sgrt = skirt). She illustrated it, too. It's fun to see her writing ability grow.

Wednesday, June 9, 2010

Week 34/35, day 3

Tuesday: Sea World! We had a marvellous time at Sea World. We started out watching the dolphins. We happened to arrive at feeding time. Visitors may spend $6 for a tray of fish to feed to the dolphins. We felt that since we'd already paid over $200 for tickets and parking, we didn't need to pay to feed the animals as well, but we got to see the dolphins pretty well after they'd eaten their fill. They even splashed us!

We visited the reef and sharks exhibit next, which was similar to many other aquariums I'd been to. uShaka, a similar park in South Africa, cost about a fifth as much and the aquarium section was better. Ari explained to the kids how fishes' gills have the same function as our lungs, namely getting oxygen into the blood.

We ate lunch (like many places, once they have you trapped they can charge what they like for food, particularly given their "no outside food" rule), and went to see the orca show. That was impressive, though we were a bit annoyed by the TV screen with images competing with the leaping orcas. It was hard to tell when they wanted you to look at the animals, and when they wanted you to look at the screen. Perhaps people who own TVs are better at paying attention to both simultaneously, but I maintain that they can't do a very good job of either in that case. However, there was a baby orca (born this January) which accompanied its mother while she did her tricks. After the show we hung around for a few minutes to watch the orcas just swimming, until they kicked us out in order to clean the stadium.

The second show we went to changed my mind, and made me feel that the price we paid had been reasonable. It featured belugas, dolphins, macaws, and amazing humans. It was beautifully choreographed, something like a circus show but with more of a sense of beauty and wonder. Divers swept through the water, propelled by fast-moving belugas on whom their feet rested. Synchronized swimmers, divers, and trapeze artists in fancy costumes performed amazing tricks. As one performer climbed up and down long red sheets attached to a hoop in the ceiling, red-winged macaws swept past. I had never seen people do such amazing things, and the way they combined their act with the trained animals added to the sense of awe.

We next went to the sea lion show, which featured a mini-play featuring sea lions and an otter. It was amusing, but didn't really give you a sense of what sea lions or otters are like - just what they can be trained to do. However, after the show, we were able to see them swimming around their enclosure as people fed them (again, for $6 per dish of fish). There was a 2-day-old sea lion nursing from its mother, and we were able to get a good view of it. The area had a faint smell of fish, vaguely reminiscent of a seal-filled island near Cape Town that I saw when I was five, but it was clear that Sea World keeps its facilities much cleaner than seals in their natural habitats do.

After the sea lions, we gave the kids the option of watching the orca show again before looking at the penguins and heading home. We were glad that they chose to, because it meant they weren't burned out yet. The second show was quite different from the first. The animals decided not to cooperate, so we heard a lot more about how the animals are trained. The keepers reinforce positive behaviour, and ignore negative behaviour - they spent much of the show time ignoring the orcas. Ari commented that this wouldn't work with kids, because kids left to themselves will put themselves in dangerous situations and will cause destruction to property, unlike orcas in a tank. We enjoyed the second show more than the first, because we could see more of how the orcas naturally like to behave. We actually got a better view of the baby orca as well - when its mother felt like leaping from the water (not in response to a trainer's request), it leapt too - beautiful.

Since it's southern winter, the penguins' enclosure was kept dark. This made it hard to get a good view of them, though a few of them were swimming around in their near-freezing tank. The puffins, on the other hand, were fun to watch - they're northern hemisphere creatures. In all, it was a thoroughly enjoyable day, and I'm glad we did it, even though it was a total of about 7 hours in the car. San Antonio is about as far as one can reasonably go from Houston for a day trip.

Wednesday. After P and E got back from "Oma Day" and I got back from my flying lesson (which unfortunately didn't involve flying, due to extreme turbulence and low clouds), P went to her violin lesson. Her teacher is moving her fast and expecting a lot of her, and she is reluctantly rising to the challenge. I think it's good for me as her teacher to see how someone else interacts with her in a learning situation. Since I know her really well, I can understand her better than the violin teacher can, but it's good for me to see just how much the teacher is expecting of her - it makes me feel happier about my own high standards for her.

After the violin lesson, we did school. P read a new reader (the next to last one), did the day's copywork, and completed her math worksheet. We read a book about Nigeria, as well as a story from Stories from Africa about a Nigerian girl whose father made her live with the goats when she became a Christian and refused to steal the neighbours' hen. I plan on having P make her book about Nigeria tomorrow - I think spreading it over 2 days helps a lot.

Monday, June 7, 2010

The book is wrong! (Week 34/35, day 1)

Thursday and Friday. I got too busy to blog the last few days of last week. School went on as usual; I introduced another letter for which we made a letter sheet, and I tried to read to the kids about Egypt but they were too antsy to sit still for it. On Saturday we did a lot of walking - P and E badgered me to go for a walk with them in the late morning, and then in the evening we walked to dinner and back, so they probably covered a total of about 4 miles on foot without help over the course of the day. As Ari said, they're the children of hikers who are the children of hikers who are the children of hikers...

Monday. We looked at the letter X in language arts today. Of course, the number of words starting with X is limited, and the number of words starting with both X and the "ks" sound is zero, so we looked for words merely containing the "ks" sound spelled X: fox, six, ox, etc.

We did get to reading about Egypt. We had 2 library books, one written at the kids' level, so I read it to them almost verbatim. Whoever converted the fahrenheit measurements into celsius did not understand the standard formula. Quick poll: does this statement make you wince?

"Hot winds can cause the temperature to rise 68 degrees F (20 degrees C) in just two hours."

Choose one, please. Not both. I don't know for sure which figure is correct, and whether the original figure was given in degrees F or degrees C, though 68 degrees F is more impressive. The author then naively applied the standard conversion formula: Degrees C = (Degrees F - 32) * 5/9 (or the inverse, Degrees F = Degrees C * 9/5 + 32). It's the 32 that got him into trouble. When comparing an increase, you don't need to correct for a different zero point - the result should be that the temperature can rise by about 38 degrees C in just 2 hours (or by 36 degrees F, if the 20 degrees C was the original).

I'm going to write to Scholastic Publishing and alert them to this error (and ask them which figure is correct). I will explain it to them in more detail, using smaller words and bigger pictures, than I did above, because I assume my average blog reader to understand math more deeply than the average book publisher. I'll let you know if I can convince them.

My kids will understand math better than this, if I have anything to do with it. This is one of the joys of homeschooling - you observe the howling ignorance around you, and you say, "I have the power to help at least 3 little people grow up to not exhibit that particular type of howling ignorance." I won't let them just plug and chug into a formula they don't understand.

P enjoyed making her Egypt book, particularly once she realized she could write her name in hieroglyphics. She drew a flag, coloured a map (she coloured the area around the Nile green, and the rest yellow, adding little red "rooftops" clustered around the Nile delta to show that more people lived there), and drew the Sphinx, the Nile, her name in hieroglyphics (she asked me to write "hieroglyphics" for her - a bit intimidating for a 5-year-old), the pyramids, and the Sahara Desert. She then copied down all the hieroglyphics and their equivalents that were listed in the library book and that weren't too complicated-looking (she left the bird drawings alone). I suggested taking the book back to the library this afternoon, but she wanted to keep it in order to keep playing with hieroglyphics.

Tomorrow, we plan on driving to San Antonio to visit Sea World. Should be fun!

Wednesday, June 2, 2010

Week 32/33, days 2 and 3

Tuesday. Nothing much of note happened during our formal school time. Both P and E wanted to watch the math video, and half an hour's search failed to turn it up, so I let them watch another video instead. We then spent an hour or so looking at some of my dad's photos from Israel, Jordan, and the surrounding areas. Half the photos I couldn't identify, but there were a few featuring me in pigtails or my brother in a stroller (we lived in Israel when I was a preschooler), or my brother and I as teenagers (when we lived in Jordan), which held the kids' interest. We also looked at my dad's photos featuring the Garden of Gethsemane, Golgotha, and the Garden Tomb, retelling the Easter story with photos of where it happened.

Wednesday: Geography. This morning, inspired by my inability to find the math video yesterday, I did some serious clean-up in my room while Ari's mom took the kids out. I feel much happier now, even though the math video didn't turn up. P's violin lesson was right after the kids got back, so we only started school at about 3pm. Because P and E were tired, it took more pushing than usual to get through everything I wanted to. We were studying Israel today (which is why I showed them those pictures yesterday), and we spent some time looking at the children's atlas page. In addition to talking about various places where Biblical events happened, I gave a brief overview of the Israeli/Palestinian conflict. It was easy to frame in terms of P and E's everyday skirmishes. P looks at E wrong, so E says, "No, P!", so P roars at E, so E hits P, so P hits E harder, so E hits P harder while yelling at the top of his lungs, so P hits E yet harder while shrieking at the top of her lungs... by this time the kids were rolling on the floor laughing at my description. I explained that unfortunately, some grown-ups in charge of countries or large groups of people act like that, only worse, when they both want the same thing (namely, the land). Neither side can have all the land they want, so they scream and hit each other (or blow each other up) and unfortunately their mother doesn't come in and pull them to opposite sides of the room, because countries don't have mothers. Having lived on both sides (Jordan - whose population is more than half Palestinian - and Israel) I tend to be impatient with anyone who casts either side as the "good guys". I agree with my dad on this: in his "Christian Perspectives on the Modern Middle East" class, he informed his students that in his class, there was only one stupid question: "Who are the good guys?" There is only one good guy, and as it turns out he was born in Israel, roughly 2000 years ago. Jesus is the only one who can transform a hating heart into a forgiving one, and I personally am beyond thankful that he can and does.

In any case, we looked through the pictures from the library book I got about Israel. It was clearly written by someone who didn't care for Christianity (our atlas mentions Jesus twice in its 2-page spread on Israel, whereas this 62-page book only mentions him once in passing, skips straight from the Maccabees to the fall of Jerusalem in 70AD in the history section, and spends only 2 paragraphs talking about Christianity in Israel, listing it after the Baha'i and Druze and devoting more space to each of those as well). But it gave a relatively balanced view on the Palestinian conflict, and the pictures were worth looking at. P started making a book which I'll have her finish tomorrow. I made falafel for dinner, reminiscing about when we lived in Jordan and crossed the border, reaching Jerusalem somewhat after lunch time and thoroughly enjoying a falafel with my family outside the walls of the Old City.

Monday, May 31, 2010

Week 32, day 1

Monday: Language Arts. Having reviewed all our memory verses last week, this week's review went more smoothly. After finishing our catechism review and hymn and updating the calendar (I let P write the time on the calendar today), I asked P to read her reader. She picked it up, flipped it over, and started reading the parent information on the back. The format of the books is that each features a different animal (in this case, a newt). It is often hard to tell from the illustration just which animal the main character is supposed to be, and its actions are rarely consistent with what such an animal can do in real life. On the back of the book, there is a paragraph giving details on the true lifestyle of the featured animal, using vocabulary and phonics rules the child has not yet encountered. However, P made it through the first sentence without any help. I told her that if she read the entire back, we'd switch and I'd read the story - previously, the deal has been that I refuse to read the reader itself, because that's P's job. She needed help with words like "poisonous", and because the letters and spaces were smaller than she's used to, she struggled with keeping track of where she was on the page, but she ended up reading the entire thing, figuring out phonics rules by herself. She has gained so much confidence this year! When she was done, I told her, "Now, you can read anything you want!" As promised, I read her the story about Ned the Newt.

Both P and E did their writing assignments happily. E traced his name (all capitals) pretty well, but he preferred to continue each "big line down" about twice as far as necessary, so that the E looked like an F with an extra small line near the top, for example. He thought this was funny, and I let him get away with it for now. P has gotten so good at writing, she did her copywork with no trouble at all. P then dictated a friendly letter to my mom (yes, Mom, you'll get it in a few days or so) about starting violin lessons. She copied the entire thing and drew a picture of herself. It's so neat to see how much she's learned this year.

This afternoon, we went to the optometrist because I had broken my glasses and needed new ones, and it had been about 4 years since my last eye exam. I scheduled an exam for P as well, and she turned out to have 20/20 vision. Hopefully it stays that way. E wanted an exam too, but he can't recognize the letters individually though he can say them in order, and the optometrist wasn't set up for kids who can't name their letters yet. He was disappointed until the optometrist gave him a pair of sunglasses to match P's (after having her eyes dilated). Who knows? Perhaps he'll suddenly want to learn all his letter names and sounds as a result.

Friday, May 28, 2010

Week 31, days 4 and 5

Thursday: Bible. Last weekend, I went through all the verses we've memorized so far, put them on 3x5 note cards, and organized them in a card box. I filed some under "daily" review, some under "odd" or "even" (referring to the day of the month), and some under "Monday" through "Friday", based on how well I thought the kids knew them. We've been using this system all week, and it's helped to remind the kids of some of the verses they had almost forgotten. Once they're really down pat on some of the verses, I'll file them under "1" to "31" to be reviewed only once a month. Hopefully, this way many of these verses will end up in their long-term (lifelong) memory. This weekend, I intend to do the same for our catechism questions and the hymns we've learned so far. I introduced a new memory verse and catechism question, and we read 3 Bible stories: the stoning of Stephen, Philip and the Ethiopian, and the conversion of Saul/Paul. The remainder of the school day was a fairly uneventful set of our usual review exercises.

In the afternoon, we went to the library to pick up books for the next week and a half's worth of geography lessons. This ended up taking 3 times longer than I had planned, because my library card initially didn't work. A month or so ago, I had returned a pile of books from 2 different branches using their shiny new computerized return system. Unfortunately, computers being (fast, accurate, and) stupid, the system didn't acknowledge half of the books as being returned. (I had inserted them into the machine at a slight angle, you see). A week later, noticing that some of the books I had returned were listed as ovedue, I complained, and they tagged the books as "missing, claims returned". They found all but one of them, but apparently the search time had expired and I was now automatically charged for that book. If I hadn't had a distinct memory of putting that particular book into the machine, I might have been open to the possibility that it really was somewhere in our house, but I refused to pay a $30 fine for a book I had truly handed back. So this took a while to sort out, but eventually they cleared the fine and made my library card work again. I'm glad, because I rely pretty heavily on my library card.

Friday: Geography. Today, we learned about Jordan. I went through a long decision-making process on which countries we're going to cover before the end of the school year, and I've narrowed the list down to Jordan, Israel, Egypt, Nigeria, and South Africa, possibly adding in Antarctica at the end. I skipped Turkey, Iran, and Kenya, which had been on my list, due to time considerations and the fact that I couldn't think of anything on my short list to remove in order to put one of them in. But then, my dad lived a perfectly happy life knowing nothing about how amazing Turkey was until he was my age, at which point he was incensed at his entire schooling experience for denying him an inkling of how phenomenal their art and architecture are. So my kids will be happy too, and I'll let them in on the wonders of Turkey (and other places) before they're 30.

My box of games from RightStart Math arrived yesterday, and I started teaching the kids the mnemonic rhyme "Yellow is the Sun" for how the numbers 6-10 relate to 5. I plan to include some RightStart games on P's 5-a-days for the rest of the year, and then just play occasional games throughout the summer, incorporating more of them in our math lessons in the fall.

For language arts, I had P describe how to play a favourite game. She chose Uno, and ended up being able to summarize the rules quite effectively. She wanted to play it as well, but it was getting on towards lunch time and I wanted to make hummus. Given the choice between playing Uno and helping in the kitchen, both children chose the latter. We enjoyed our lunch of fresh-baked pita bread (such fun to watch them puff up!) and hummus as well as zaatar.

After lunch and P's violin practice, we started our study of Jordan by looking at a book about the Nabatean city of Petra that I found on my brother-in-law's bookshelf (he's in the Caribbean, so he won't mind me borrowing it). I loved explaining the pictures based on my memory of the place, trying to give a fuller sense of the place by my descriptions than the pictures alone could give. Living in Jordan for 4 1/2 years in my teens gave me the chance to visit Petra a number of times, and I fell in love with the place. One day, of course, our whole family will have to go there and probably spend a full week exploring it and the surrounding areas.

We marked Jordan on the Markable Map (there was only space to label it "J"), and discussed how, though it was hard to see on the map, Jordan did have a tiny coastline on the Red Sea - at only 16 miles long, you wouldn't expect it to look impressive on a world map. We then looked through a library book on Jordan. This took ages, I confess, because I was able to tell so many stories about the different pictures. The kids saw a picture of King Hussein and heard how I sang a solo at a school concert he came to (his daughters went to our school) - the choir teacher only told us on the day of the concert that he was expected to come, which didn't exactly make me less nervous. We looked at pictures of Jerash, and I told how my high school graduation was held at the main amphitheatre there, and how Queen Noor, our speaker, flew in by helicopter. We read about mensaf (the national dish, consisting of lamb meat cooked in yogurt on a bed of rice and pine nuts), and I told how my dad had once been the guest of honour and was served the tongue - pulled by our host out of the lamb skull in the middle of the platter. Looking at the pictures in the book made me homesick. A picture of a shepherd on a donkey with his sheep could have been taken from our back yard. Okay, Lord, when do I get to move back to the Middle East?

Wednesday, May 26, 2010

Week 30/31, day 3

Wednesday: Geography. I'm shuffling our weekly schedule a bit here, in order to get through 2 weeks' worth of geography and language arts per week for the next 3 weeks - so that we can be done before my brother comes to visit. We followed the same review and language arts pattern as yesterday, which went well. On P's math 5-a-day, I had as one of the items "Play with MeasureUp! Cups". These are a set of 12numbered stacking cups which are volumetrically correct; that is, it takes 5 "1" cups to fill the "5" cup, or a "2" and a "3" cup to fill the "5" cup. So I hauled out a large bowl, a bag of rice, and the cups, and we worked on finding combinations that would fill different cups. P enjoyed using the "2" cup to fill various larger cups, so I explained how the ones that could be exactly filled using a "2" cup were even numbers and those that had too little or overflowed were odd. This will be useful when we get to multiplication and division, too.

Our geography lesson covered India. We traced and labelled it on the Markable Map, and talked about its proximity to the Himalayas on one end and the Indian Ocean on the other end. We read the atlas pages and a children's book on India, and P made a book featuring the flag, a map, and pictures of a Bengal tiger, the Taj Mahal, an elephant decorated with gold and blue, someone growing tea, and a monsoon flood. I cooked a kidney bean curry recipe I got from Jeannette ages back as well as an "aloo paratha" (bread stuffed with potatoes and peas) from my "Healthy Bread in 5 minutes a day" book. The kids liked the aloo paratha, but they object to curry. More for Ari and me!

Today was also P's first violin lesson. Ari stayed home with B while he napped, but E came along and was unusually well-behaved, looking at the pictures in books I brought for that purpose while P had her lesson. She learned the parts of the violin, how to hold it in position, the "music alphabet" (letters A-G, which she is to practice saying in reverse order) and whole, half, and quarter notes and rests. Her 1/8 size violin is too small for her, so we need to rent a 1/4 size one. Since her teacher gave her specific things to practice, it should be fairly easy to enforce a daily practice habit. The teacher seems, at least on a first impression, to be completely worthy of the high recommendation I heard about her. She has patience, a good way of explaining things, and a good rappor with P. What a blessing!

Tuesday, May 25, 2010

Week 30/31, day 2

Tuesday: Science. In addition to our regular review items, I had both kids write: E his name, and P the second half of this week's copywork and a vowel worksheet. We played "rhyme jump-up": I gave the kids a word, and then said other words. When they heard a word that rhymed with the first one, they jumped up. Both of them loved this game - the physical aspect of it appealed to E, in particular. I'm confident that we'll get through 2 weeks' worth of language arts this week, and I'm hoping to do geography tomorrow as well as Friday.

For our science experiments, we investigated some of the properties of air. We took 2paper towels, crumpled one of them up, and weighed them on the balance. Having determined that they weighed the same, we took turns dropping them simultaneously from the same height. Air resistance caused the uncrumpled one to fall more slowly, so we discussed how the air had more surface area to push on for the uncrumpled paper towel than for the crumpled one. We then filled a basin with water, and put the crumpled paper towel at the bottom of a clear plastic cup. We turned the cup upside down and put it in the water. The paper towel stayed dry, because the air in the cup took up space and the water couldn't come in. Then we tipped the cup sideways, and the kids saw the air bubbling out and the water coming in to wet the paper towel. After that, we looked at the effect on the water level of filling the cup with water and pulling it out of the basin inverted (the level of the remaining water went down, until the cup came all the way out, whereupon the water returned to its original level), and pushing the cup underwater inverted, so that it, filled with air, displaced some of the water, raising the water level. I let E do some independent play, during which he discovered that if you just put the cup in the water, it tips over and sinks, but if you put a bit of water in the bottom, that stabilizes it and it floats. Eventually, of course, letting a 4-year-old do independent water play makes the kitchen rather wet, so we mopped up and declared school over for the day.

Monday, May 24, 2010

Week 29, day 5 and Week 30, day 1

Friday: Geography. We studied Australia on Friday. Both P and E were already able to identify Australia on a world map, but we labelled it on our Markable Map and looked at our kids' atlas page. We also read 2 books about Australia as well as a couple of chapters of "How to Scratch a Wombat". According to this book, wombats can sleep so soundly as to appear dead. The author found a favourite wombat of hers conked out on the doormat. Its heartbeat and breathing were undetectable, and it was rigid, so she sadly dug a grave, lowered the wombat into it, and it woke up and ran off. P and E enjoyed this story. P made a book on Australia, featuring the flag and map, and pictures of a kangaroo, the Sydney opera house, a boomerang, Uluru (Ayers Rock), and the Great Barrier Reef.

When we were done with school, the kids went outside and started digging a hole. I was stripping our basil and parsley plants of leaves in order to make (delicious) pesto, and they got tired of helping me and used E's digging tool that my parents gave him to get through the wood chips behind the garage and into the clay. They made a fairly deep hole, about as long as P's forearm. Then on Saturday Ari helped them to expand and deepen the hole, and they filled it with water - 6 buckets full. The water is sloooooooowly draining out; the clay soil is not very porous and there's still a lot in there.

Monday: Language Arts. I'm going to try to get through 2 weeks' worth of Language Arts this week and another 2 next week, in order to have time for a proper summer break. So we'll probably be doing some language arts every day in addition to what we usually do. We did the rest of our review items first. Before P read her reader, I had E trace his name on a dry-erase stencil I made for him by writing his name on a piece of paper, gluing it to cardboard, and covering it in clear self-adhesive plastic. P's math 5-a-day consisted of 3 problems and 2 games: Subtraction War and experimenting with our balance. We weighed a variety of small toys, and the kids grasped the idea of starting by adding the biggest weights and then adding smaller ones as the bigger ones overbalance the scale.

Once we got to language arts, we made a letter page with pictures we found online - an activity that both children enjoy. P was quite reluctant to do her copywork, so I decided we would do only a little more than was on the schedule for one day, and do more of it each day this week. I gave her the choice between the reader I had her start at the end of last week and a new one, and she chose the old one, feeling that the practice was good for her. Finally, she was to write a story based on a drawing of a pilot encountering a flying windmill. Her story turned out pretty well, I thought. I introduced her to the idea of a "point of view character" - the character through whose eyes the story is told. Ari has focused on this while editing his novels, so I've thought about it quite a bit as well. It seemed to me that P grasped the idea well and it helped her know where to start.

Speaking of Ari's novels, Ashes of our Joy is ready to purchase. Now you can find out what the Norkaths have been up to.

Thursday, May 20, 2010

Week 29, day 4

Thursday: Bible. We introduced a new memory verse - one I might end up reminding both P and E of quite a bit in future - and catechism question. We've been working on the hymn "To God Be the Glory" all week, but I forgot to review it today. We read the story of Pentecost in their children's Bible storybook.

P found her old handwriting workbook that she finished near the beginning of the year. It's neat to see how her handwriting has improved since she finished the book, and certainly since she started. She insisted on looking at every page, and she and E acted out the animals that represented some of the letters and numbers (Z for zebra, 6 bears, etc). Once they were done, I gave P the choice of reading the same reader we've been working on, and reading next week's reader. She chose next week's, which was what I expected, and did well with it. My plan is to try to do 2 or 3 weeks' worth of language arts next week, since it's introducing the letter E and there are 2 review weeks after that letter. P already knows her letter sounds very well, so I don't feel we need the review, and I'm getting antsy for a proper summer vacation. I'll try to fit in 4 or 5 weeks' worth of geography in the next 2 weeks, doing a country every 2-3 days instead of once a week, to keep pace with language arts. Now that all our outside activities are done for the summer, we have more time that I can devote to moving us along in school. I'd like to be done altogether before July so we can completely relax on our planned road trip and still have some unstructured time at home before starting first grade for P and Pre-K for E.

I put 2 games on P's math 5-a-day this time. I'm glad I started doing this, and not always having her solve 5 pencil and paper problems. She solved her 3 problems and then we played Subtraction War (played like War, but with 2 cards at a time, and the biggest difference wins) and Uno. I started teaching the kids Rummikub, but they're really too young for it and I did most of the thinking for each child's turn. I noticed after we were already playing it that it's recommended for ages 8 and older. Ah, well, there's good family tradition for doing that kind of thing. I remember my dad starting me on Monopoly when we were in Durban when I had just turned 6.

After lunch, P wanted to do a project from her new sewing book. I showed her the lazy daisy stitch, but we didn't really have good materials for embroidery around the house, so we went to JoAnn and picked up basic cross-stitch materials. She made one 4-petaled flower shape using lazy daisy, and it looks pretty good. I'll help her do another one tomorrow. I noticed while teaching her that, since I haven't really thought about how to teach sewing the way I've thought about teaching lots of other things, I don't have a good idea of what sorts of things are likely to trip her up. Learning to sew involves a lot of separate, complex skills: threading a needle, keeping the needle threaded instead of pulling it off the thread each stitch, figuring out where to put the needle in, tying a knot in the end of the thread so it doesn't come out of the fabric, etc. Of course P wants to be able to start and finish a project in an afternoon, so she needs me to pay attention and help her with each of these skills. With a baby to look after and dinner to cook, I'm not as helpful as she might wish. She did manage to thread the needle by herself, so hopefully she won't need me for that as often in future.

A child is constantly working on learning so many complex tasks! It's no wonder they sleep so much. I need to try to remember how much is being asked of them in just learning to navigate the world, so I can be more patient with all 3 of them.

Week 29, day 3

Wednesday: Math. I decided to continue working on the idea of the "math way" of saying numbers (five-ten eight instead of fifty-eight). This is basically a lesson on place value, a good concept for the kids to internalize. Even with reviewing what I taught both kids yesterday, our entire formal school only took half an hour. We looked at our experiment from yesterday, but there didn't seem to be any difference in the amount of water evaporated from the light-coloured metal pan or the dark-coloured silicone pan. I wish I had a setup where both containers were made of the same substance, but I don't. In any case, the idea of evaporation and condensation was effectively communicated. Later in the afternoon, we went to the library. I found books on Australia (which I plan on studying with the kids on Friday), including a book called "How to Scratch a Wombat", which was written by a woman who has spent 30 years interacting with wombats. It's heaps of fun, and she tells fascinating stories as well as giving basic information about wombats. I didn't realize how big or strong they were. I certainly don't want a pet wombat - it sounds like they are untrainable and have very strong opinions on what they want you to give them Right Now.

Tuesday, May 18, 2010

Week 29, day 2

Tuesday: Science We're back after roughly a week off. We spent Thursday through Monday in San Antonio for a homeschool convention where Ari sold his book, and a bit of a vacation. At the convention, I picked up a box of math games (actually, just placed an order, but got free shipping by doing it at the convention), some educational toys including a balance with varying sizes of hexagonal gram weights, books on Biblical character training, and a sewing instruction book with patterns for P, who has recently demanded to be taught to sew. I also stopped by the Sonlight booth to drool over the curriculum I plan to use next year (Core K, Language Arts 1, and Science K for P, with E listening in as he has ability and interest). We're going to have heaps of fun! We are already, of course. We went to the Alamo on Sunday, and it seemed like the kids got a lot out of it. It helped that I checked out 3 kids' books on the Alamo before we left for San Antonio, and read them to the kids on the way.

Today we resumed the week's worth of school where we left off. P remembered her memory work remarkably well. I decided to spend more time paying attention to E, and this helped a good deal. I had P read her reader to him specifically, which he liked, and I gave both of them a math lesson of sorts before I had P do her 5-a-day. From a session on RightStart Math at the convention I had picked up the idea of counting "the math way". Basically, English doesn't make place value transparent the way some Asian languages do, with numbers like "twelve" bearing no obvious connection to "ten plus two", so you instead teach the child to call that number "ten two", and to call 27 "two-ten seven". Even E was able to catch onto this pretty quickly, and I reviewed it with P on her 5-a-day. Once that was over, we played addition war (I let E help me add my cards) and Uno. We then set up the evaporation experiment from a week ago again, this time using 2 colours of container. I used a light metal bread pan and a navy blue silicone bread pan to hold the "dirty water" and same-sized ramekins to catch the "rain". We'll look at them tomorrow to see if there's any difference. In the afternoon, the kids played with the balance. It comes with containers that are marked in mL, so we weighed and found that 200 mL of water weighs 200 grams. I accidentally rediscovered Archimedes' principle (which I only fully grasped for the first time in sophomore geology at Caltech) when reaching into the water to retrieve a weight one of the kids had dropped in. The balance had been perfectly level, and as soon as my fingers entered the water, it dipped down on that side, even though my fingers weren't touching the bottom, because my fingers displaced a certain mass of water. I let P experiment and she found the same result. When we were done with the water, we weighed a banana, an apple, and a clementine. E then wanted to know what weighed less than a clementine, and we found that a playsilk weighed less even though it had a larger volume. This led logically to a discussion on density. Once we were done playing with the toy, the kids neatly put it away without being asked. WOW! I thanked them profusely - it was a very pleasant surprise.

Tuesday, May 11, 2010

Better

We didn't do any formal school today, because I hoped that a day spent without rigid expectations would help us all get back on a more even keel. It seemed to work. We went to Titmouse Club in the morning. It was the last session of the year, and the theme was pond ecosystems. The kids got to fish around in the pond with nets, and someone had caught a crawfish (crayfish? crawdad?) for the kids to look at. They also got to touch a box turtle and a stick insect (gently), and they painted plaster figurines of frogs and turtles. Once home, I gave E a badly needed haircut, and read lots of books to both of them. One of the books I read was What's So Special About Planet Earth?, which we checked out from the library because we enjoy the author's other books, How Do You Lift a Lion?, What's Bigger than a Blue Whale?, and What's Smaller than a Pygmy Shrew?. This one discusses why none of the other planets in the solar system would be a good place for humans to live, and goes on to describe the water cycle, among other things. I came up with a fun experiment to do: E and I poured some water into a medium-sized bowl and added salt and food colour (to represent dirty sea water). In the middle of the bowl I placed a small ramekin, empty at the beginning of the experiment. I covered the entire bowl assembly with cling wrap, using a rubber band to hold it in place, and put a marble in the middle to create a slope on the cling wrap. We put the experiment outside. Several hours later, some of the "dirty sea water" had evaporated, condensed on the cling wrap, and dripped down into the ramekin underneath the marble. We noted that the water in the ramekin was completely clear. There wasn't enough for us to taste it, but hopefully by tomorrow we will be able to investigate the effectiveness of our small solar desalination plant. Later on, next time we go to Galveston, I'd like to get some real sea water and redo the experiment. I'd also like to see what difference the bowl colour makes - we have a navy blue bowl as well as a white one, and I imagine the darker one would be more effective. When we were in Bahrain, the tap water was clearly desalinated ocean water, and tasted distinctly odd. I don't know what desalination method they use there, and I'm curious to see how our water will taste.

I guess I'm such a geek, even on days we don't "do school" I'm still educating the kids in some way or another...

Monday, May 10, 2010

Week 29, day 1

Monday: Language Arts. The first part of the school day went quite smoothly. P and E both happily participated in reviewing our memory verse, catechism, and hymn, and in updating the calendar. However, when it was time for P to read her new reader for the week, E found a plastic grocery bag, which he wanted me to tie shut so that the air would stay inside. Plastic grocery bags are never airtight, even when thoroughly tied, and they are also noisy, so after a few iterations of the rustling grocery bag deflating and E demanding that I reinflate and retie it, I sent him downstairs. He then returned upstairs to ask me to sort out the bag again, twice. I refused, twice, on the basis that P was completely unable to concentrate on her reader, and he finally stayed downstairs long enough for her to get through the reader.

When P started her math worksheet, E returned upstairs and asked to have a story read to him. We compromised by having P do one problem on her math for each story I read to the two of them. The last two "problems" were games: a hundred chart game they both completed, and playing Uno (which P asked to play dos times, and then laughed about her Spanglish). Although E is intellectually capable of playing Uno, he is emotionally incapable, at least at times. He doesn't want to put his blue 8 on a blue 4 because he feels that he should be allowed to play his red pick-up-2 card whenever he wants, and he throws his blue 8 across the room, picks it up, and bends it by holding it too firmly. Fortunately, after that outburst he willingly played by the rules, and even won the second round.

Both kids were compliant and pleasant when we introduced a new letter and made the letter sheet. However, P was thoroughly reluctant to do her copywork, and I had to be sneaky and manipulative to get her to finish each segment. We didn't get around to the creative expression assignment (we just barely finished 1 day's worth of language arts), and I hoped to do it after lunch. At that time, however, both kids decided they wanted to hand-wash the dishes and vacuum and mop the floors. It's hard to argue with that kind of industriousness, so I decided against pushing any more school on them.

When they were done cleaning they hauled out some colouring pages, which they worked on together. I heard yelling from their room, and when I came in they were sitting with their heads about 6 inches apart, yelling at each other at the tops of their lungs. I physically separated them, and asked P (the first one to regain her capacity for human speech) what had happened. The substance of her story was that she had coloured more of the fish on her own colouring page than E had wanted her to, so he hit her in the mouth. I asked E what had happened, and he refused to talk, so I asked him if P's summary of the events was correct. He said that it was. I wanted to have him apologize to P and have them reconcile and go back to colouring, so I asked him to stand up. He refused, and I gave him a small warning spank. I asked him a second time to stand, and his refusal earned him a proper spanking. I tried a third time, and he raised himself to a kneeling position and then slumped back down. Since the spanking wasn't working, I carried him downstairs, strapped him to his chair, and let him sit facing the corner for 5 minutes. When his time-out was over, I leaned over him to unsnap his straps. He jumped up so quickly that his head knocked my lip against my teeth, drawing blood. It did hurt his head somewhat as well. He was quick to apologize to me when I told him he'd really hurt me, and by that time he was willing to apologize to P as well.

Does this portend a continuation of a difficult week? Perhaps I should just ignore school for the next few days, since we're going to a homeschool convention starting Thursday morning. If I just spend 2 days reading to the kids all day long, perhaps they'll feel happier in general.