Friday, December 30, 2011
We returned to Texas for Christmas (a 2-day drive, but worth it to see family and friends again), and only just got back. It's nice not to be in the car any more, though all 3 kids did really well. Apart from the part where B found the box of his disposable diapers, and threw about 35 of them all over the car, and the older 2 then used the empty box as a projectile... aaaaah! And B developed a habit of yelling, over and over, "Please stop reading Hobbit, Mommy! Please stop reading Hobbit, Mommy!" But usually, he gave up after a few paragraphs to pages, and we successfully followed the adventurers all the way over the Misty Mountains, across Mirkwood, and to Smaug's demise. We have yet to see the results of the dwarves' gold lust, but we'll save that for after B's bedtime but before P and E's over the next few weeks.
I promised to blog about the Vibrant Dance conference Ari and I attended at the end of October (see my previous post). Being closely related to one of the organizers, we had the opportunity to attend the dinner for the speakers the night before the conference began. As the dinner was winding down, we joined a conversation with Bruce Waltke. I thought I'd start with something he said both at the dinner and in one of his talks, because it has important implications for Christian unity. He described his response to the question, "Who is my brother [or sister]?" To answer the question, he looked at how Abraham, Moses, or David might have seen it. God gave Abraham the covenant of circumcision - an external, physical sign of inclusion in the people of God. For Christians, that sign has been replaced by baptism. So if you have been baptized, you might be my brother or sister. The covenant God made with Moses involved the Law, of which the Ten Commandments are the most important part. So if you acknowledge your responsibility before God to follow the Ten Commandments, you might be my brother or sister. (Aside: no-one except Jesus has actually followed all ten commandments perfectly - I believe Bruce Waltke's point was simply that Christians acknowledge them as a standard to aim for; that we recognize the fact of God's righteousness as represented in the Ten Commandments). The covenant God made with David was that the kingdom would be his family's forever - a physical descendant of his would reign as king. So if you acknowledge Jesus, David's heir, as the king of your life, you might be my brother or sister. Finally, in the New Testament, we see Jesus' incarnation, death, and resurrection. So if you accept those historical realities, you might be my brother or sister.
To sum up, if I find myself asking whether someone is my brother or sister in Christ, I can ask: Are they willing to be publicly identified with him? Do they acknowledge God's perfect law and righteousness? Have they submitted to Jesus' kingship? Do they believe that Jesus was fully God as well as fully man, that he died, and that he returned to life?
Note, of course, that nowhere in this analysis does someone's position on the timespan of God's creation appear - we can be brothers and sisters in Christ no matter how we interpret those particular details. I think that having that perspective is an essential prerequisite for having a gracious dialogue: we start from the understanding that we are brothers and sisters in Christ, and dialogue on the details on which we differ knowing that we're all going to be around the same Thanksgiving table as part of God's family a million years from now.
I should say, I didn't take detailed notes of what Bruce Waltke had to say - the above summary is based on my memory, 2 months later, of what I heard him say. So I may have made some errors in representing him. If you're unhappy with any of the above, the fault is more likely to be mine than his.
Thursday, November 3, 2011
Last weekend, Ari and I attended a conference (Creation: Biblical Options) organized by my father-in-law. My mother-in-law watched the kids, so I was able to hear almost every talk. I also helped Ari sell a few books at his booth during free time, since Ari was filling the role of conference photographer. I don't often get to go to conferences like this (or like anything), and it was such a blessing to be challenged to think in completely different ways than I usually do. Being close to the conference organizer, I got to interact with several of the speakers more than most of the conference attendees - Ari and I were invited to the speakers' dinner, and we stayed in the same hotel as the speakers. I'm planning on composing a few posts on what different individuals had to say. But, given that we're in the middle of moving across the country, future posts may take a while to appear. For now, I'll just say that although I don't agree with all the speakers' perspectives, I was encouraged and challenged by every one of them, and impressed at the graciousness with which they related to one another despite their disagreements.
Tuesday, October 11, 2011
I vividly remember P's verbal skills at 20 months, because that was when E was born. She could say single words, but they were typically hard to recognize ("bee" meant spoon, "na" meant towel, and several other items were "ba"). She never included more than one consonant in any word, using only vowel sounds to distinguish between "baby", "banana", "ball", and "book". I told Ari that we'd better not space subsequent kids that close together - having 2 little people who couldn't verbally communicate was just too difficult.
When E was 20 months old, he was starting to use 2-word sentences, and his pronunciation was leaps and bounds ahead of where P's had been at the same age. Of course, when P finally did learn to talk, she talked nonstop, and E was a convenient audience. He had at least double the live, personalized verbal interaction directed at him as P had had directed at her when she was that small.
Now that B is 20 months old, he has the benefit of 2 older siblings. They are both so much older than him that their pronunciation is practically perfect, as is their grammar. All morning long, they interact with letters and numbers, which B is able to observe but not really participate in. Like any small child, he is eager to catch up. So, at least a month ago, he started noticing words. He points at them and says, "E, O." When I read Goodnight Moon to him at bedtime, he takes my finger, points it to the words, and commands, "E! O!" Usually I satisfy this demand by telling him, slowly, what each word says. Sometimes he points to individual letters and I tell him what sound they make.
B has also become interested in numbers. Now, I remember that E was able to count to 10 by his second Christmas, when he was around 21 months old. Little B, however, has upped the ante by being able to recognize numerals from 1 to 8. He can recognize 9, but usually identifies it as a 6. (Of course, if you look at it upside down, they are the same thing - I'm not going to worry about my one-year-old's problems with reversals!) He'll take any counting book, open it entirely at random, and accurately identify the numeral while pointing at it: "Four! Seven! Eight!" While we were in the car waiting at a red light yesterday, I heard him announce, "One! Eight! Six!" I looked at the car beside us, and its license plate contained some letters and the numbers 98881. So, he thought the 9 was a 6, but other than that was exactly right. This afternoon, he started pointing out numbers on the box of disposable diapers in his room - a picture of a diaper is labeled from 1 to 6 describing all its fantastic features. The numbers are in no order at all, but he identified all of them correctly. The box informed us that it contained 140 diapers, and B pointed to those numerals and said, "One! Four! Round round round!" I told him that the round number was zero, and a minute later he correctly identified it.
I know, of course, that being able to say the name of a numeral has nothing to do with understanding that numbers have value. I'm working on helping him make the connection by holding up the right number of fingers each time he exclaims about a number, and I know it will come in time. But for now, I can at least brag that my 1-year-old is pre-reading: he understands that symbols stand for sounds or ideas. I'm pretty sure P and E are largely responsible for this early understanding. I'm already finding it easier to teach E to read than P - are the kids going to work me out of a job?
Wednesday, September 28, 2011
About 2 weeks ago, I stumbled across the Moebius Noodles group referenced on the Let's Play Math blog. Inspired by the idea of sharing cool math with my kids, we spent last Wednesday playing with Moebius noodles. For those of you who don't know, a Moebius noodle (also known as a Moebius band or strip) is a loop of a flat material (usually paper) that is twisted once before the ends are joined. Here, B demonstrates one.
Both P and E's fine motor skills are at a level where they can make their own, so they pasted together both regular loops and Moebius noodles. I had them each draw a line down the middle of "only one side" of each loop. One fascinating thing about Moebius noodles is that they only have one side. We then experimented with cutting our loops in half lengthwise. With a regular loop, of course, you get 2 loops. With a Moebius noodle, well... try it yourself if you've never done it. It's really fun, and surprising the first time.
Since we were still enjoying ourselves and it wasn't lunch time, I thought I'd try out another idea I stumbled upon. The gist is that you take two loops, glue them together, and then cut them both in half lengthwise. First, I took two regular loops and glued them at right angles. It looked like the beginnings of a chain you might put on a Christmas tree, only the connection was on the outside. I cut it in half down the middle of each loop, through the intersection point, and ended up with this:
P thought this was interesting, and tried it herself (by this time, E was busy attaching yellow loops to a piece of paper to make a "rocket", which seemed valuable in its own way). Meanwhile, I tried what happened when one of the loops is a Moebius noodle and one is a regular loop, which turns out to be the same as when both are regular loops. Finally, I tried both of the possible ways of joining two Moebius noodles: one when the loops are twisted the same direction, and one when they're twisted in opposite directions. I found it completely mind-bending! When the loops are twisted in the same direction, you get this:
But when they're twisted in opposite directions, this is what you get. (P tried this one as well, though I had to help her make the Moebius noodles so that they'd be even enough to cut in half neatly).
An instant "I LOVE MATH" logo!
Monday, September 12, 2011
Our box of Raisin Bran proclaimed, in large letters, "$100 CASH CARD INSIDE". In smaller letters, one realizes that in truth, "you could find up to a..." If you read the fine print, you find that your odds of finding that $100 cash card are 1 in 24,800. There are other prizes, though: a $50 cash card (1 in 20,667), a $25 cash card (1 in 17,714), a $10 cash card (1 in 15,500), and a $5 cash card (1 in 12,400). So I read these statistics to the kids and solicited guesses on just how many boxes of Raisin Bran one would have to buy to be likely to get any cash card at all. Then I hauled out my calculator and did the math: the total odds, obtained by adding the odds of each value of cash card, are 1 in 3444. If you bought 3444 boxes, though, you still wouldn't be guaranteed to get a cash card (though you'd have better than even odds). We discussed how long it might take to eat 3444 boxes of cereal (about a decade, if the whole family only ate Raisin Bran for breakfast every single day - we could probably polish off a box a day between us). And if you bought 3444 boxes of cereal, you'd most likely only get one cash card, which would most likely be a $5 cash card.
P and E - mostly E - have invented a useful number, the gi (hard g, rhymes with pea). One gi is generally defined as "a number larger than the one you were just talking about by a considerable margin". So we find it helpful to suggest, "even if you tried gi times, you wouldn't be able to throw an apple all the way up to the moon," or "do I have to ask you gi times to clean your room?" E announced, "If you bought a gi of cereal boxes, you'd probably only find 1000 cash cards. That's how big a gi is."
Okay, I'm curious. How large does gi have to be in order for 1000 to be the most likely number of cash cards when the odds of finding one is 1 in 3444? I think all the probability and statistics I was taught at Caltech has fallen out of my head. Anyone care to remind me?
Saturday, September 3, 2011
"Your current account (email@example.com) does not have access to view this page."
What? I can't comment on my own blog? Does anyone who knows more about arguing with Blogger know how to fix this?
I mentioned that he was finding it hard to distinguish "b" and "d". So on Monday morning, having gleaned this idea from the Sonlight forums, I wrote the word "bed" in large lowercase letters. Then, I drew a stick figure lying horizontally on top of the word: "bed" looks a bit like a bed, with bedposts on either end. However, if you write "deb", there's no space for your stick figure to stretch out to sleep. So to figure out the difference, you find out if your letter would leave space for your stick figure to sleep if it was at the "B"eginning or at the en"D" of "bed". This seemed to work pretty well, and E started reading the first of his readers that contained both "b" and "d". After a few successful efforts at sounding out words, he looked up at me and said, "Do you know how I tell the difference?" I anticipated hearing something about how well my careful, clever explanation was working for him, but what he said was, "The 'b' doesn't have a tag at the bottom, and the 'd' does." In the font used in his readers, this is true. So it works reliably for him - he's had ZERO struggles since Monday morning when it comes to sounding out "b" and "d". I'm amused that he came up with something that didn't even occur to me, and it works great for him. Hopefully by the time he moves on to reading material that doesn't have that feature, he'll have internalized the other differences between the two letters.
The other great idea I had, which actually is working, was for helping E recognize and remember the word "the". Sounding it out each time was driving him nuts, and he really hated that he just had to remember that it didn't work that way. I'd just been telling him what the word was for over a week, when I had an idea. A while back, I heard a blonde joke (most of which I think are really stupid). A blonde is sitting on a bench with a book, and looking concerned, and saying, "ta-hee! ta-hee!" A brunette comes along, takes a look, and tells her, "'The', airhead!" Well, I didn't need to encumber E with the setup of the joke (both his siblings being blonde), but I told him, "When you sound out 'the', it sounds a bit like laughing: 'ta-hee!'." So now, whenever he encounters the word in his reader, he says "ta-hee...(giggle)...the!" What had been a roadblock for him is now something he finds amusing.
Sunday, August 28, 2011
Now that I’ve started school with P and E again, I’d better give an update on some of the highlights of this summer.
We’re expecting a fourth little someone! (I'll be calling him/her LS until we find out the gender and decide on a name). The official due date is February 12, 2012 – the other 3 were all early, so we’ll see. B’s 2nd birthday is January 27, so our plan of spacing them about 2 years apart seems to have worked. Thank you, Lord! So far I’m feeling great. I go running for a mile or so about half the mornings each week (if I don’t hear B’s sweet voice first). Every so often I think I feel LS moving; I'm 16 weeks along now so it likely isn't just my imagination.
How many women do you know who get their private pilot license while pregnant with their fourth child? I think I can be justifiably proud of this accomplishment, and of course grateful for all the resources - human and financial and even social (God bless America), all gifts from God - that made it possible. I took my checkride on June 18th, but hit a gust of wind while doing the soft field landing and failed. The second attempt, on June 25th, was successful, and I now have a shiny license with a picture of the Wright Brothers. I took Ari flying on our anniversary, and took the kids up a few weeks later. When my parents visited 2 weeks ago, I flew them to Fredericksburg and back, my longest cross-country ever. I'm so thrilled about being a real pilot!
Ari finished the Epic of Karolan! The final volume, Darkness Gathers Round, is now available from Hopewriter and from Amazon. It seems to be selling quite well although we haven't spent any money advertising - enough people were desperate to find out what happens next at the end of book 3 that they're buying it up at a good rate. We plan on spending our entire annual advertising budget in November, because that time of year generates so many more sales per advertising dollar.
We're still living in Houston. Ari, having finished his publishing project, is now looking anywhere and everywhere for any job in his field. We're open to anything that'll pay the bills and not hinder his chances of a further academic career.
I finally took the plunge and applied for U. S. citizenship. My parents will be spending the coming academic year in Jordan, so of course we're going to visit them after LS is born. The idea of Ari having to herd all 4 kids through one passport line on his own while I waited for another just made me shudder, so that's the main thing that triggered this decision. I had been concerned about the oath of allegiance, but I think seeing "foreign" as referring only to human kingdoms (because the Kingdom of God is for all people in all places) is justifiable. I submitted the paperwork a week ago, so hopefully it'll get processed before LS is born... I don't know how far I trust any bureaucracy...
P is now reading fluently, and attempts to read anything we leave lying around. E seems to feel that the fact that anything she can do, he can't do better, is quite unacceptable. So I started school with him in mid-July after we finished our school year in May, mainly to help him learn to read as quickly as possible. He's made it through the first 5 Level K readers from Sonlight, but is tripped up and intimidated by the difference between "b" and "d" - that's what we'll be working on this coming week. I started P on all subjects and E on Sonlight K core subjects this past Monday, so we're back to a full school schedule now. I'm trying to do school in the mornings, so that afternoons (when B naps) are free for me to relax. It helps to have toys that he can take out, spread all over, and put back again. It also helps to get the older 2 busy with seatwork and give him some undivided attention a few times during the morning, as well, so I'm trying to structure our school time that way. B likes sitting in my lap for a minute or two at a time while I read to the older two, and I'm hoping his attention span will gradually increase. He's started to be interested in looking at books (rather than chewing them or throwing them), so I'm planning on taking advantage of this interest as well. P can already read well enough to help read to him, and E is making steady progress, so I have hopes of eventually being able to ask each older child to read to B while I work with the other one.
In all, I'm glad to be back in a school routine - it's fun to spend the time with the older 2 kids and watch them learn. B takes up so much of my attention no matter what, that it's good to be able to plan to pay more individual attention to P and E as well.
Saturday, April 16, 2011
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!
Wednesday, March 2, 2011
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.
Sunday, February 20, 2011
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.