P is 12 - A Volcanic Birthday

There's nothing like keeping a secret for weeks, even months, and then revealing it to a person who is completely surprised. P12's birthday in mid-July was SO satisfying.

First, the cake. She wanted a volcano cake, and I had hoped to make it erupt using dry ice, but the only dry ice on Oahu turns out to be a 2-hour drive away (without traffic), which wasn't the best use of her birthday. So I "erupted" it using Jell-O.

I made two round cakes, stacked them on top of each other and cut them into the shape of a (steep) shield volcano. I cut out a caldera in the center. After icing the cake in brown, I made Jell-O using half the water called for. I put the cake in the fridge, and once the Jell-O was cool but not set, I spooned some of it into the caldera. I repeated the process every 5 minutes or so, resulting in a layered look to the "lava". Candles, of course, added to the "eruption" effect.

Next, presents. I know other people got her good gifts - there was a tessellations coloring book and some marvelous art supplies - but I was mainly waiting until she opened the gift from us. It didn't look fancy; it was just a few pieces of paper in an envelope.

 

She wasn't quite sure what it was all about, at first. "It says... Hilo? Someone is going to Hilo? Tomorrow?"

"Look at the names of the passengers," suggested Ari.

 

 

Realization slowly dawned...

 

 

 

"That's right. Just you and Mommy are going to leave Daddy and the boys behind and spend 5 days on the Big Island. You leave tomorrow morning, so let's work on packing!"

She and I had a marvelous time. We stayed with friends of friends, who were amazingly wonderful people and gave us great advice about what to see. And the volcano satisfied abundantly! P12 is a good hiker, so we were able to scramble all over and see all sorts of things that we wouldn't have been able to with the little guys in tow. I'll leave you with a sampling of photos.

On our first day, at Hawaii Volcanoes National Park. The crater with the main eruption is behind us. It's a pillar of cloud by day, and a pillar of fire by night:

 

The next day, we did some serious hiking.

 

 

We started out with the Thurston Lava Tube, then hiked all the way across Kilauea Iki caldera. The hill behind P12 was a fire fountain back in 1959, and the flat surface of the caldera was a lava lake.

 

Since a 4-mile hike in the morning only whetted the appetite of these two hard-core ladies, we decided we were still up for a 10-mile hike in the afternoon/evening, since it involved watching lava flow.

 

After a restful Sunday with our new friends, we drove around to the Hilo side of the island on Monday to see Pu'uhonua O Honaunau, also known as Place of Refuge. It's a place where the ancient Hawaiians were able to flee for safety if they had broken any of the kapu, or taboos. They had to swim or canoe in, likely with someone chasing them intending to kill them, but if they spent the night in the place of refuge, they were safe. I have heard the claim that many traditional cultures have elements that make it particularly easy for them to understand the good news about Jesus, and wondered if this might be such an element in Hawaiian culture: we have broken God's laws, and the natural consequence is spiritual as well as physical death, but if we run to Jesus, we will be saved.

 

In the afternoon, we drove to South Point and took turns being the southernmost person in the United States, and then hiked 3 miles round trip to a green sand beach. The sand isn't pure green, but there is a lot of olivine (a green mineral) in it, which gives it a greenish hue. The olivine erodes from the cliffs behind the beach.

 

On our last day, we spent the morning looking at lava trees (the structures left behind when a lava flow travels through a rainforest), and then went swimming in some gorgeous tide pools with more corals than I've seen anywhere in Oahu.

When we got back, the guys had managed fine without us, and we enjoyed being back with them - a good break helps you appreciate people more! I'm still amused that P12 asked for a volcano cake when she had no clue that the next day, she would get to see an erupting volcano.

E2 (almost 3 months later...)

It's been a few months... I guess I decided I had higher priorities than updating this blog. I really want to talk about P12's birthday, which was epic, but I realized I didn't post anything about poor little E2. So, here goes.

It's a bit hard to ask a small child what kind of cake he wants, since although he talks really well, he doesn't have enough concepts to communicate general areas of interest, but "butterfly" was one of his first words, and he always points with animation to pictures of butterflies. So this was the cake I made him:

 

I was pretty pleased with how it turned out. I used the last of that natural food colour, and threw in a bit of turmeric for good measure. E2 was particularly excited about the banana. When I turned 2, I was also given a butterfly birthday cake with a banana body, and I am quoted as saying, "Have a bit a nana?" So I thought the banana might be a hit, and it was.

 

 



I tend to be apprehensive about more presents for small people, since I know just who will be putting them away, but there were some fun ones, particularly the duck.

 

 



I think that's about all, but of course 2-year-olds can come up with some amusing things to say, and on the evening of P12's birthday he made me laugh too hard to discipline him. He walked up to me, looked me in the eye, said, "Mommy, I'm sorry I bit you," and before I could say that he hadn't, he grabbed my arm and bit me. I guess order of operations doesn't come automatically.

E10's birthday

I was going to post this back in March, but then I got sick. It isn’t the next boy’s birthday yet, so I’m not behind!

My parents had arrived the day before E10’s birthday, and we asked him which of the items on our must-see list he would like to do on his birthday. He picked swimming with sea turtles – not a bad choice! It was spring break, so the parking area and every other free parking area within half a mile were packed, but we finally found a place that wasn’t too exorbitant and hiked along the resorts and beaches until we got to the “hidden lagoon” (which isn’t as hidden as it apparently used to be when it was named). It did not disappoint: in addition to seeing sea turtles and a variety of pretty reef fish, there was an endangered Hawaiian monk seal napping on the beach, surrounded by caution tape which had been erected by a super informative volunteer. We went to Pizza Hut for a late lunch, and then my parents bought E10 a bike at Walmart while I went home and decorated his cake.

 

After he had figured out how to ride (it didn’t take long), it was time for the piñata. He and P11 had been planning this for months, and in the week before his birthday they made the entire thing by themselves. It was a great success!

Everyone (except little E1) got a turn.

Once the candy had been scooped up and partially consumed, it was time for him to open the rest of his presents. I really liked one with paper models of Escher’s artwork to assemble in 3-D. He was particularly excited by a new fishing reel.

After dinner, it was time for cake. I was really thrilled with his request this year: he had read a biography of the Wright Brothers in school, thought they were amazing, and wanted a Wright Brothers Flyer cake. This is the child who, 3 years ago, could not read two words together without doing a somersault in between them – it’s wonderful to see how he’s matured! My rendition of the Wright Flyer using white icing, pretzels, and chocolate icing for the propellers, was not as aerodynamic as theirs, but it was more delicious!

Natural born citizen?

I don’t generally blog about politics. But I am completely baffled on this one, and don’t really understand why it isn’t an enormous big deal: Why is someone who was born in Canada running for president of the United States?

As many of you know, I will never be president of the USA. I was born in South Africa, to parents who were both South African citizens, and only became a citizen of the USA 3 days before H4 was born. (They let me waddle to special seating where I could think about whether my practice contractions were likely to make the swearing-in ceremony even more memorable.) I certainly don’t fulfill the U.S. Constitution’s requirement that the president be a “natural born citizen” – clearly, for the first 32 years of my life, I was a natural born citizen of South Africa, and now am no more than a citizen of the USA.

My brother’s “natural born”-ness as a citizen of South Africa is a little more interesting. He is currently a South African citizen, and is officially South African by birth, as opposed to South African by descent. But my mom, talented woman that she is, managed to give birth in Israel to a son who was South African by birth. How did she achieve such a far-reaching accomplishment? At the time of my brother’s birth, my dad was serving in the South African Embassy in Israel. The only reason for our family’s presence in Israel was my dad’s service to the government of South Africa. This fact accounted for my brother’s status. Had we been in Israel on business or vacation when he was born, he would still have been South African, but by descent, not by birth.

Fast forward a generation, and let me take up the case of my utterly adorable niece, baby S. My brother married a US citizen while working on his Ph.D. in Toronto. My sister-in-law moved to Toronto after their marriage, and together they discovered that when it rains, it pours. My brother spent last fall celebrating his shiny new degree, welcoming baby S, and preparing to move to Israel. They applied for S’s U.S. passport right away, since it’s obviously easiest for Mom and Baby to travel on the same country’s passport. But at this point, it isn’t immediately obvious what S’s long-term citizenship will be. Here are 4 possible scenarios:

(1) They remain in Israel indefinitely. I suppose it could happen – they’re really happy there, and though they aren’t planning to stay, my brother’s current university might extend an offer he can’t refuse. Certainly baby S would retain her US citizenship, but as an adult she might be tempted to begin the arduous process of a non-Jewish person obtaining Israeli citizenship. I don’t think this is likely, but it’s not completely impossible. That way she’d end up with dual US and Israeli citizenship.

(2) This one is even less likely. But if a university in South Africa were to offer my brother an amazing position at the same time as a phenomenal design company in South Africa recruited my sister-in-law, they might be convinced to move to South Africa. Baby S would then be entitled to South African citizenship by descent, and could have dual South African and US citizenship.

(3) Here’s a more likely option than either of the previous two: my brother or sister-in-law accepts a job in Canada. In that case, if baby S grows up in Canada, I assume she would be eligible for Canadian citizenship on the basis of her birth. Would that make her a natural born Canadian? I don’t know, since neither parent is a Canadian. But in any case she could hold on to dual US and Canadian citizenship, or even abandon the US citizenship and be purely Canadian (if, say, Trump becomes president…).

(4) Another real possibility is that they move to the USA after the year in Israel, and baby S grows up there. She retains her US citizenship and never needs another. Once she reached adulthood, her citizenship would not be in doubt – she would have no reason to obtain the citizenship of any other nation.

Any of these 4 scenarios could happen – with varying degrees of likelihood based on my brother and sister-in-law’s inclinations and extended families’ locations. At this point, baby S’s ultimate citizenship status is in doubt in a way that none of my children’s is (mine were all born in the USA, two while both parents were citizens, and have lived here all their lives). Baby S is a born citizen of the USA, but I don’t think it’s reasonable to describe her as a natural born citizen when that level of doubt exists.

In case you missed it, the situation with presidential candidate Ted Cruz is very similar to that of baby S in scenario 4. He was born in Canada to a US citizen mother and non-US, non-Canadian father. They were not in Canada on official US government business, but with the oil industry. He returned to the USA as a child, grew up here, and once he reached adulthood his undivided US citizenship was not in doubt. But his situation as a baby mirrored that of baby S today. At that time, he was still in Canada, and could have followed scenario 3. Or what if his family had moved to Cuba – or, say, Venezuela, to follow the oil industry? Then he might have been more like baby S in scenarios 1 or 2. When he was a baby, his future citizenship was not clear-cut. This makes it hard for me to accept that he is a natural born citizen. Citizen, yes, and born citizen, but natural?

Can anyone help me understand why the Republican Party leadership is so certain he can get away with this? The only theory I can come up with is that most Americans have so little respect for Canada that they genuinely forget that it is a foreign country.

(In case you’re going to ask me, yes, I recognize that this post has a “the dwarves are for the dwarves” flavor about it – I’ve used my Facebook to argue that evangelicals shouldn’t support Trump, and here I’m attacking Cruz. But I’m hoping for a brokered convention, and voted for Kasich in that hope. It could happen – maybe Trump’s rage gives him a heart attack and Cruz’s run is declared unconstitutional or at least makes the party nervous about supporting him? Miracles do happen.)

Neighbors

As you probably know, I am not a football fan. Last Sunday when I woke up, all I knew about the upcoming Super Bowl was that a team from North Carolina was competing for the first time: my parents live in North Carolina, and they had mentioned the fact. I figured that, for purposes of conversing intelligently with people I might encounter, I ought to at least ask Google the names of both teams, and which one won.

When we got home from church, it was easy to tell who one of the teams was. Every Sunday afternoon for the past several weeks, there have been roars of ecstasy intermittently erupting from the house across the street. A truck flying a “Broncos” flag has been parked in front of our house for ages, accumulating increasing amounts of bird dirt due to its positioning directly under the lamppost, but I had not realized it belonged to the across-the-street neighbors until I saw their décor. If the multiple Broncos flags flying from their dwelling, and the larger flag with which the truck’s original flag had been replaced, hadn’t tipped me off, I might have guessed they were Broncos fans by the football shirts every member of the family was wearing, or the Broncos chairs they were sitting in while they watched the large TV screen set up under their carport. Then again, the sign stating “Parking for Broncos Fans Only” might have served as a clue. I mused on what a study in contrast the two sides of the street provided: we do not even own a television, and my feelings toward ardent football fans range from amusement to bemusement.

We decided to spend Sunday afternoon investigating a portion of the windward side of the island. Shortly before we set off on our adventure, several men ran into the street shouting, and jumped up repeatedly to bump chests against each other. I was able to inform my mom, when I called her on the way to our destination, that the Broncos had scored at least one touchdown. She shares my passionate fascination with many non-football-related subjects: “Oh, dear – if they win, my colleagues will be depressed tomorrow morning.” Ari and I speculated on how our neighbors would respond when faced with either a win or a loss for their team. Ari figured beer would be involved along with either outcome, but fireworks would be included if the team won. I thought no more about it, because the afternoon provided plenty of interest. We started by exploring a coastline overgrown with mangroves, and moved on to a beach quite near to a smaller island to which Ari, P11, and E9 attempted to swim. For one of the first times since moving here, I wished I had brought a sweater to put over my swimsuit. We arrived home to the delicious odor of the dinner I’d placed in the crock pot before I left, and I started to wonder whether I ought to Google the result of the day’s sporting event. As I sat down at the computer and opened my web browser, I saw bright colors and heard and felt an explosion. Google was unnecessary: clearly, the Broncos had won!

I’ve heard complaints from other neighbors about the fireworks (they’ve been going off intermittently since Thanksgiving, to the consternation of the local dogs). And I’ve been irritated a few times at the neighbors in the cul-de-sac whose Friday night parties haven’t quieted down by 4am Saturday (though apparently the police came and chatted with them before Ari and I got around to figuring out how to build a sonic focuser to blast them with the Ride of the Valkyries if they kept making a habit of it). But I have to say, it’s really relaxing to live in a neighborhood where so many other people make occasional loud noises. I enjoy the freedom I have to allow my boys to be noisy, and the knowledge that, however weird we may be, we aren’t bothering the people around us any more than the average family in the neighborhood. We’re unusual in many ways, but I feel like we really fit in here in ways we didn’t anywhere we’ve lived since E9 was a toddler.

What sorts of interactions do you have with your neighbors? Do you feel that the personality of your neighborhood fits you?

 

Robot cake (H is 4)

As promised, I'm posting pictures of H4's robot cake. It was meant to be a pink robot cake, but I was using the all-natural food color I had bought at the health food store and the red color turned the icing brown. Not even reddish brown, mind you. It was supposed to be from beet juice, so I wonder if the package was just really old - it seems like fresh beet juice can't fail to redden whatever it touches. Next time, I'm buying the bad stuff, or using a beetroot. Fortunately, H4 was right there, and I immediately suggested adding cocoa powder to the icing to make it more brown. He likes chocolate (discerning lad), so the disappointment turned to joy fairly quickly. Apart from the failure to achieve the desired color, I'm pleased with the result.

So was he, which is always the goal. (But, as I said to a friend, if it looks like you tried and it contains sugar, it rarely disappoints).

Ari had been away from home since Tuesday morning - he had to observe remotely on Tuesday night and then travel to Mauna Loa to work on another telescope - but he got back around 6pm on H4's birthday. So he was able to be around while H4 opened presents, which means we have a few nice pictures of the festivities.

Ari's parents gave H4 a "crocodile dentist" game - you press down the croc's teeth until the mouth snaps shut on your fingers after a random number of teeth has been pressed.

Given B6's Lego obsession, it's not surprising H4 was pleased to be able to join the ranks of those able to play with "big kid Legos".

We gave him a flashlight which not only shines out the front, but can light up along the length of its body with a blue glow. He was thrilled. I'll have to haul out our "shine-a-light" book sometime...

Plateosaurus Cake (B is 6!)

As many of you reading this know, I have a tradition of baking my children birthday cakes following the theme of their choice. Sometimes these themes are easier to carry out than others! When I asked B what he wanted for his 6th birthday cake, he informed me that he wanted a Plateosaurus. I had never heard of the Plateosaurus before, not having memorized his Dinopedia the way he has, but he turned to the appropriate page and showed me what he hoped I could do for him:

 

He wanted just the head, with a leaf in its mouth, as shown in the picture. It actually turned out to be one of my more successful efforts. I baked a basic rectangular cake, and cut it out in the shape of the head using a paper stencil (so I could pencil in the shape before taking the knife to the cake):

 



I tried to get the 2 colors shown in the picture by coloring all the icing light brown with cocoa, and then adding blue to half of it, but it didn't work because I bought all-natural food color, which turned out not to affect the color of the icing strongly enough. It might have tinted pure white icing a light blue, but the effect of the cocoa completely overwhelmed it.

For the teeth, I had hoped to find yogurt raisins in the bulk section of the same health food store where I got the food color, but they were out of stock, so I used slivered almonds instead. And B insisted that both the eye and nostril should be made of raisins. The leaf was satisfyingly easy - I simply cut off a leaf from our cycad tree outside! Even if cycads weren't part of the Plateosaurus' diet, they were around in the time of the dinosaurs, so it felt quite authentic. Here's the finished product:

 

The young man was pleased with the result!

 

 



Next week, H will be 4, and he's requested a pink robot cake (yes, pink is still his favorite color). Tune back next week to see how that turns out!

Starting up math club

Math Club 1/15/16

A week ago I restarted an activity that my children and I really enjoyed in New York: an enrichment math club. I had planned to hold the club at a local park, but when I woke up that day it was wet and grey, so I changed the venue to my house. Given an enthusiastic response when I posted it on Facebook, I had been concerned that not everyone would fit, but as it turned out only 2 families were able to come. This was actually a good number to begin with – three 10-year-olds (including a set of twins) and one younger sibling, as well as my own children.

My idea for today’s lesson was to approach binary in a way that would be generally accessible, since I wasn’t sure how many younger children would be involved, and then to move to a more formal introduction. I was inspired by James Tanton’s “Exploding Dots” course (http://gdaymath.com/courses/exploding-dots/), and started with a physical activity based on the 1 <– 2 machine. Here’s how the activity went.

First, I placed a few sheets of paper on the floor in a line. I pointed out that a sheet of paper is fairly small; only one person can comfortably stand on it. So, if you ever have more than one person on a sheet of paper, the two EXPLODE! Only one “survives” the explosion, and that person is knocked to the next piece of paper in line. New people can only join the game by standing on the first sheet of paper in the line. So, after the first person joins the game, there is one person on the first piece of paper. Add in a second person, and they EXPLODE, and one of the two is left standing on the second piece, with the first piece empty. Add a third, and s/he can stand on the first piece without a problem: a person is on each of the first two places. Adding a fourth person is fun: the two on the first place EXPLODE, one joins the person on the second place, they EXPLODE, and one goes and stands on the third piece. If you’re familiar with binary, you can see where this is going; if not, try it out yourself (or click through to the Exploding Dots link). Some of the participants wanted to keep one person in the first place and explode the second person into the next place. I wish I’d thought of letting them play with that for a while – it would have been a base 1 system – but I just tried to re-explain that only one person can stay in the game after the explosion.

After we’d added in 5 or so people, I got out the whiteboard, and we started over again, writing down what happened if we dumped on a whole bunch of people at once. Someone suggested trying to put 9 people on the first sheet of paper, which required all 5 of mine and all 3 ten-year-olds, plus myself (holding E1), but it didn’t work too well because several people (all mine) wandered off before being exploded and were hard to find again (and to keep track of). At this point we moved to using the whiteboard exclusively.

I drew 4 boxes, and we began making a chart, using what the children didn’t yet recognize as standard binary notation: 1 is 1, 2 is 10 (a person in the second place as a result of the 2 who exploded in the first place), 3 is 11 (a person in each of the first 2 places), 4 is 100 (only one person left on the 3^rd place, with the first 2 empty). I had them take turns drawing each subsequent number of dots in the first place, carrying out explosions and writing the resulting binary number in a somewhat organized chart. We went up to eleven or so (1011 in binary).

At that point, I got out the main manipulative I had prepared, a set of 5 cards containing 1, 2, 4, 8, and 16 dots respectively. I let them look at the cards and say what they noticed. “They’re all even!” “Except 1 isn’t.” “And 6 is missing.” “And 10.” Finally, “Oh, you have to double them.” Once that idea was mentioned, everyone agreed: it was a sequence of numbers you get by repeated doubling. Once they’d realized that, I asked them to make numbers using the available cards: 7 (1+2+4), 13 (1+4+8), 21 (1+4+16). Is there only one way of making each of these numbers, or could you find another way to do it? Well, all 4 children who were still engaged with the activity did it the same way, and no one could think of another way. “Unless we got into teams and had 2 of each card.” But with just one set of cards, we agreed that there was only one way to make each number.

The next step was to ask if there was any connection between the activity with the cards and the activity with the exploding dots. This puzzled them for a little while, so I set up a set of dot cards in order beneath one of the binary numbers we’d written on the board, with each card marking a place. They were able to see that, for example, 1010 was the same as 8 + 0 + 2 + 0.

Someone noticed that five in binary is 101, and ten is 1010. “What’s twenty?” They found it was 10100, which was an interesting pattern. I asked if anyone had any guesses about what forty might be, and there was general agreement that it should be 101000. We had to add another place, though, since our dot cards only went up to 16, but when we’d added the 32 place we noticed that 40 was indeed 32 + 8. I had thoughts at this point about doing some addition (with carrying) and subtraction (with borrowing), but I could tell that people had about reached the end of their interest with the activity, so we wound up and everyone left.

Things that went well: Letting them say what they noticed about the base 2 cards, noticing patterns of doubling and halving (5, 10, 20, 40 translates to 101, 1010, 10100, 101000), letting them hold the whiteboard markers, asking children to explain their reasoning whether the answer was right or wrong (which helped me see how my explanations were going awry).

Things that didn’t go as well: Whiteboard markers running out of ink (repeatedly), allowing some people to dominate the conversation and failing to include others, not explaining the rules of the game carefully enough for everyone to understand that one of the people in the explosion disappears completely, drawing 4 boxes on the whiteboard before we needed all of them (should have added boxes only as needed).

Plan for next time: I have no idea which of the same children and which new ones – of which ages – will come, but, weather permitting, I’m hoping to do it at the park. We’ll look at fractals – there’s a gorgeous, enormous tree there, so tree fractals will flow naturally. I’ll try giving each child a sheet protector with cardstock inside it, and a (new) whiteboard marker, so they can each explore without one child dominating. I’m particularly enamored with Sierpinski’s triangle and the Koch snowflake, so those will certainly feature. I’ll plan to post again with how it goes.

Back to blogging?

It's been a while since my last post. A LONG while. We've been in Hawaii for almost half a year now, and we're feeling more and more settled. Additionally, it's that time of year when people boldly state that they will do good things, go forth in the excitement of their resolution and do them twice, then quit. So, I thought I'd let you in on some of my resolutions for the new year - not necessarily in order.

1) Eat local eggs. So far, I've been doing much of my grocery shopping at Costco, over 14 miles away from our house, where the prices tend to be more reasonable than at many local grocery stores. Costco, of course, carries large quantities but less selection, and in the egg department, you can choose between conventional mainland eggs and organic mainland eggs. But when I think about how much space 3 dozen eggs a week takes up, shipping them from the mainland is pretty much equivalent to sending our entire family back to the mainland several times a year. That's not ecologically responsible, so I've resolved to prefer even conventional Hawaii eggs over mainland eggs. This idea extends to noble plans to seek out CSAs and maybe even a local dairy (I believe there is precisely one on Oahu), but as I haven't made good on those yet, they don't count as "resolutions."

2) Blog more regularly. I've had P11 and E9 post on private, non-searchable blogs on a weekly basis with the exclusive goal of allowing them to share their school writing assignments with their grandparents, aunts and uncles. This allows them to receive feedback from someone other than me, but doesn't expose them to the risks of posting things that can be googled. So my plan is to blog as often as they do. I didn't do this during our first week back of school, but starting with the second week is better than not starting at all!

3) Build a beehive. This one is pure fun. The children are studying insects this year, and ever since I decided that we'd be focusing on that topic, I've been toying with the idea. Ari's brother and sister-in-law have kept bees for years, and the honey they've given us has been utterly scrumptious. And there are always flowers in bloom in Hawaii! In addition, this gives me the opportunity to give E9 some hands-on experience with using math to solve real-world problems.* We're planning to build a top-bar hive (loosely based on BackYardHive.com's plans), so he'll have the opportunity to build skills in scale drawing, measuring, geometry, estimating budgets and amounts of wood needed, and other skills I probably haven't even thought of. And of course, we're hoping to reap rewards, not only in terms of honey, but in terms of understanding more about these amazing insects. So far, I've changed E9's daily math assignment format from 5 review problems a day plus instruction, to 2
harder problems a day plus some time working on the hive.

*I saw a compelling argument that essential math skills consist of 4 stages: clearly stating a problem, translating it into mathematics, calculating, and translating the answer back into a solution to the problem. Traditional instruction focuses almost exclusively on the third stage, calculation, which is the only stage that can easily be automated (computers, calculators, etc.), but what students really need is practice with stages 1, 2, and 4 - then they can teach a computer to do stage 3 for them. I want my children to be able to calculate, but if they can code a solution, that'll show that they understand the problem without having to suffer through pages of grunge. We might make coding a part of next year's course of study.

4) Get to bed at a decent time. This is the one I have the hardest time with. Ari's long commute means that he gets home late, and the children need to see their Daddy which translates to a fairly late bedtime. Once they're asleep, it's so relaxing to sit still for many consecutive minutes without needing to jump up (as I did at least 12 times while typing this up) to solve a child-related disaster, that I frequently give in to the temptation to keep reading, playing piano, or working on the computer until much later than is healthy. So I've resolved to be off the computer by 10, and ideally on my way to bed by then. This hasn't always happened so far this year, but I'm trying to form new habits. I know it's a blessing to Ari when he's sleep deprived from his long hours to know that I'm not and he can depend more on me. This is one I've been praying about for a while, and given previous answers to prayer, I know I'm going to do better this year: "This is the will of God, your sanctification" (1 Thessalonians 4:3a).