Under contract

We are selling a house. It's the one we moved from a while back. It is stressful selling a house, even a starter home. Today we signed a contract with a buyer. Now maybe I can be less preoccupied about house-selling and spend fewer wakeful hours thinking about it when I'd much rather be asleep.

Homeschool Carnival

The Carnival of Homeschooling for the month of February is up here. The carnival recently switched from being weekly to being monthly, so there are a lot of submissions. Enjoy!

Fine line

My maternal grandmother died last week, and I was just at her funeral yesterday. She had a good, full life, and we celebrated it as a large extended family, glad that she could be reunited with my grandfather, who passed away 8 years ago.

Today my mother called to talk for a while. She started worrying aloud that the the workers at the hospice care had shortened her mother's life by giving her too much in the way of sedatives and pain killers.

Here's the thing. My grandmother was 96 years old and had severe Alzheimer's. She broke her hip in a very painful way a week before she died. She had been eating less and weighed approximately 75 lbs. when she died.

What could the hospice workers have done differently? She was clearly in decline and in great pain. I'm sure they knew that the pain killers would likely speed up the date of the my grandmother's passing, but is it humane to deny her the pain killers for that reason only?

I feel for hospice workers and family members who must make decisions about pain relief for someone near death. They walk a difficult path, treading a fine line between acting in a way that could shorten a life and permitting a person to suffer great pain. I pray they may always act with wisdom and charity, for even an ancient grandmother is valuable and worthy of thoughtful consideration.

Subtracting Negative Numbers

Dd10 and dd7 are starting to learn about negative numbers. Not because we've reached them in their math books. (Although, actually we have. Many of the "temperature" problems they do in their math worktexts require them to find differences between positive and negative numbers. It's sneaky, BJU Press, but I love it!) They overhear me talking about negative numbers during tutoring sessions with the teenage boy I tutor.

On Friday, I spent nearly an hour trying to help him see and internalize why subtracting a negative number is the same thing as adding the absolute value of that number. No matter how I approached it, he seemed to view it as some kind of mathematical black magic and not based on reason or reality. There are many ways of explaining why 3-(-2)=5 (this blog post has a few good ones), but nothing seemed to convince him. This is a big problem because he is currently working on line equations at school and has to be able to calculate the slope of a line when given two points on the line. It's difficult to correctly calculate "rise over run" if you can't properly find the differences between x- and y-coordinates that aren't all positive.

The last explanation I tried seemed to work. He is comfortable with the definition of zero and with the algebraic rule "If a = b, then a + c = b + c." So I showed him a brief version of this proof:
______________________________________________
x - x = 0                    (0 is always what we get if
                                 we subtract a number from itself)

(-x) - (-x) = 0            (ditto above)

                       Now add x to both sides of the second
                       equation, which we can do because of
                       the rule "if a = b, then a + c = b + c."

(-x) - (-x) + x = 0 + x

Which, because of the commutative property of addition (order of addition doesn't matter), is the same as...

x + (-x) - (-x) = 0 + x

Which simplifies to...

x - x - (-x) = 0 + x

Which simplifies to...

0 - (-x) = 0 + x

Which is the same as...

- (-x) = x
------------------------------------------------------------
And there you have it. Two negatives make a positive.

He now believes it and is properly applying it.

Boarding School Dragons

My children have been reading books about dragons recently. And sculpting and drawing dragons. Oh, and frequently dressing up like dragons.

A couple of weeks ago, I took the two oldest to a game store--the kind with D&D dice and books, little known board games from Germany (why do Germans make up so many board games?), and battle figurines--where we browsed for a long while. Then they started asking if they could play Dungeons and Dragons. They're a little young for such a complex game, so I found them a simpler role playing game instruction .pdf available for free. Dd10 read a bit of it, and then they stopped talking about playing D&D.

But the idea hadn't left them. They just didn't want to play someone else's game. They have now made up their own game. They call it Boarding School Dragons. It has a game board that began as only 6 pieces of paper that they had drawn on to form their playing surface. They have since expanded it to be double that size; I think they were influenced by this Horrible Histories video comparing Alexander the Great's military campaigns to an ever-growing Risk-like game. They have made their own game pieces, their own gold (paper) coins, and who knows what else. They made up all their rules*, and at the end of each session dd10 has to record what is going on in the game so they can pick it up again the next day.

Boarding School Dragons

It is amusing to see them--dd10, dd7, and dd5--so earnestly involved in creating and playing their game. It is also gratifying to me, for they happily entertain themselves after the schoolwork is done and when they could be watching videos instead.

* Dd7 hates to lose games. When they play store-bought games, she sometimes stops playing when she does poorly. I suspect she is tweaking the rules while they play to allow herself to get the outcomes she wants and the other two children let her because they are all having so much fun.

Partial Payback Time

I've been tutoring the son of a friend for a few months now. He has attention issues and lots of gaps in his algebra and fraction skills. For 4 days a week, my children have had to be super-quiet during after-school tutoring sessions so as not to distract him and dinner has frequently been delayed and a bit "thrown together." But I felt strongly that I should try to help this boy with math so it doesn't become a stumbling block to him in his eventual career. Both of his parents are health professionals. He wants to work in genetics and has a lot of curiosity and memory for the things that interest him. He has a lot to offer the world, but he'll never get there without overcoming his math woes.

He recently took a mid-year assessment test, and he has gone from "unsatisfactory" to "partially-proficient" in math since autumn. He's gone up 19 points on a scale that usually sees 5-10 points growth over the course of an entire school year. We still have a lot of work to do, but these are very encouraging test results. To quote Lina Lamont from Singing in the Rain, "our hard work ain't been in vain for nothin'."

It's at times been a sacrifice for my family, but I'm glad they've been part of this project this year. I expect they'll take from this 1) a great appreciation for not being behind in math themselves, 2) a conviction that service to others is worthwhile and rewarding, and 3) a realization that extra effort is required sometimes in life.

Scratch that bit about "toothless"

Last post I praised my baby's toothless grins. No longer. She has a tooth. Now she can actually bite into those bagels and pear slices that she has only mouthed and gummed up till now.

Isn't it amazing how the ability to wield even one sharp, hard item can change one's life? Teeth, knives, axes, scissors, etc. I really doubt that life--free of metal implements--was really less stressful 10,000 years ago as was recently claimed by a participant on a prehistoric times reality TV show.