Wednesdays with Words: For all the saints . . .

I'm currently reading Wilkie Collins' The Woman in White, which I'm really enjoying but I'm not ready to make a post of quotes -- it would take too long to get it together and I want to get back to my book.  Instead, here's a quote from a book I've never read (but which now has to go into my wish list!) that I found at Alan Jacobs' blog on Tumblr and is perfectly suited to this week in the Church year.

To those who know a little of christian history probably the most moving of all the reflections it brings is not the thought of the great events and the well-remembered saints, but of those innumerable millions of entirely obscure faithful men and women, every one with his or her own individual hopes and fears and joys and sorrows and loves — and sins and temptations and prayers — once every whit as vivid and alive as mine are now. They have left no slightest trace in this world, not even a name, but have passed to God utterly forgotten by men. Yet each one of them once believed and prayed as I believe and pray, and found it hard and grew slack and sinned and repented and fell again. Each of them worshipped at the eucharist, and found their thoughts wandering and tried again, and felt heavy and unresponsive and yet knew — just as really and pathetically as I do these things. There is a little ill-spelled ill-carved rustic epitaph of the fourth century from Asia Minor: — ‘Here sleeps the blessed Chione, who has found Jerusalem for she prayed much’. Not another word is known of Chione, some peasant woman who lived in that vanished world of christian Anatolia. But how lovely if all that should survive after sixteen centuries were that one had prayed much, so that the neighbours who saw all one’s life were sure one must have found Jerusalem! What did the Sunday eucharist in her village church every week for a life-time mean to the blessed Chione — and to the millions like her then, and every year since then? The sheer stupendous quantity of the love of God which this ever-repeated action has drawn from the obscure Christian multitudes through the centuries is in itself an overwhelming thought.

— Dom Gregory Dix, The Shape of the Liturgy (1945). One of my favorite paragraphs I’ve ever read. (via wesleyhill)

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Shelfie

Biographies, shelf 2 of 3

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Sunday, October the 26th, was the feast day of Alfred the Great.  Every year in October I read Chesterton's Ballad of the White Horse to remember him and to learn from him.  I've blogged about both the poem and the man several times over the years, so be sure to check out my Alfred the Great tag.  One of the posts includes lots of links to cool websites with history, music, and more.

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Current Reading
A History of Mathematics, Uta C. Merzbach and Carl B. Boyer
A History of Pi, Petr Beckmann
Introduction to Arithmetic, Nichomachus of Gerasa
The Code of the Warrior:  Exploring Warrior Values Past and Present, Shannon E. French
The Woman in White, Wilkie Collins
Onward and Upward in the Garden, Katharine S. White
A Book of Hours, Thomas Merton, ed. Kathleen Deignan

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Math Teachers at Play

Last week I submitted my post about our counting circle to the MTAP Math Carnival #79.  There are a lot of interesting contributions to the carnival, but here are two of my favorites.

"You just listened, so then I could figure it out."  I love reading math conversations between children and skilled adults.  Not only do I learn math, but I learn how to be a better teacher and parent.  In this post, five-year-old Daphne's mom asked her a hard question.  "There was a long pause while she thought, Maya waited, and I drove." After Daphne gave the correct answer, her mom asked her how she was able to figure out the answer.  What follows is a conversation where the little girls explains how much she likes thinking deeply about "tricksy" problems.

The Factor Game.  I haven't had a chance to try this out with my kids yet, but this teacher v. class game looks fun.  Strategy game that requires knowing the factors of numbers.

Be sure to check out the whole thing -- Math Teachers at Play Carnival #79.  There are several other links to math conversations with kids, plus lessons at all levels from beginning to advanced concepts, teaching tips, and more puzzles and games.

Nature Notebook -- trying again

Silvia's posts on her nature walks and pictures of her and her daughters' nature notebooks always inspire to make this a habit of my own.  I didn't like the way my pencil sketches were turning out, so I bought myself a set of watercolors.

We have a row of crape myrtles along the driveway and on my walk this morning, the patterns on the bark caught my attention, so this afternoon I attempted to paint the trunks of one of the trees.

This was mostly an exercise in mixing colors and trying get the general blotchiness of the bark.  I gave up trying to recreate it accurately.

I like this result a lot better than my pencils sketches of the Jerusalem Artichoke.

Learning together

We've gotten far enough along in our studies of Kittredge and Arnold's Our Mother Tongue that we've begun diagramming sentences.  This isn't actually taught in the book, so I'm using The Complete Book of Diagrams by Mary Daly, and I never learned how to diagram in school, so last week I had to ask my Facebook friends how to diagram two that I didn't know what to do with.  That was a fun conversation -- thank God for Facebook!



We're in Chapter IX now which focuses on complete and simple subjects and predicates, so for now, when I write a sentence on the white board, all I require the kids to do is to find the verb and circle it, then find and circle the simple subject, then draw a line to separate the subject from the predicate.  My 15yod is loving diagramming though, so after her younger siblings mark their sentences she likes to diagram them.

Grammar stuff
"Asterism" is a bonus word from the chapter of Life of Fred we read later.

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We had another fun counting circle.  These kids.  I tell them the counting circle is only supposed to take five or ten minutes but they're getting such a kick out of coming up with complicated ways of saying the next number that it's dragging out to quite a bit longer.  My 14yos isn't as fond of making up problems as his sisters are, so sometimes while he's waiting for one of them to figure out what to say next I'll ask him to go ahead and give me all the rest of his numbers at once.  In this case it means he was counting by 15s instead of 5s, and he enjoyed that extra bit of challenge.  And then he decided he wanted to turn his into problems too, so he thought about each one while his sisters were taking their turns.

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Quiet afternoon studies.  All of us sitting together is working out really well.

Tangling, October 7-12

Learn more:

• Zentangle.com
• TanglePatterns.com

Math activity: The Counting Circle

One of my math goals for my children is to build a strong number sense, which is, in part, "fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons. (Wikipedia)." The Counting Circle is one way to accomplish that, so a couple of weeks ago I added it to our Morning Time routine. It takes about ten minutes each day.

The basic procedure is to decide what your students will count by and what number they'll start on (e.g. counting by twos starting at zero), ask for a volunteer to start the count, and go around the room having each person say the next number in the sequence.  I have anywhere from three to six people including myself participating at any time, but it will work just as well even if it's only Mom and one child taking turns.

The very first time we did this, we started at one and counted by ones -- yes, that means 1, 2, 3, 4, 5, . . . .  I did it that way because my non-mathy kids looked a little wary about what we were going to be doing, and I wanted to start EASY so the drill would be a success.  The next time we counted the same way, but every so often after a child gave his answer I asked, "What number is [two or three siblings down] going to say?" and another time I asked the person who said 5, "Who's going to say 10?"  and then, when we got to 10, asked that person who was going to say fifteen.

After a few days I remembered that in the article I linked above, the teacher wrote the answers on a number line, so I incorporated that.  We moved on to counting by 2s starting at zero, and counting by 2s starting at one.

Today, I told them to count by halves, starting at zero.  And then I did something kind of dumb.  I asked them if it would be okay if I just wrote ".5" instead of "1/2" every time because it would easier for me.  They agreed because they're good-natured like that, and we started counting.

Actually, maybe it wasn't such a bad thing, because sometimes they said ". . . and a half," and sometimes they said, ". . . point five," so maybe writing ".5" every time helped reinforce the fact that they're both the same.  Hm.

Anyway, it got a little boring until my 15yod said, with a smirk on her face, "Eight and two-fourths," and I wrote down exactly what she said.

Here's what happened next:

What I learned:

1. Slow down!  The point of the Counting Circle is to let the children think, not to get it done.
2. Write down exactly what they say -- don't take shortcuts just to make it easier on myself.  The excitement and creativity began when I wrote down 8 2/4 as my daughter said it instead of the faster 8.5.
3. Even when I think I've made a mistake it can turn out to be a good thing.
4. Definitely use the number line.  It makes it easier to keep track of where we are when I pause to ask a question, helps the children see and predict the patterns emerging, helps them learn different ways to write the same thing, and allows their responses to be more creative and complicated.

Today was a good day

Here's some New Math for you:

My husband's new job means he has a wonky schedule -- sometimes he has the usual daytime hours, but other times he has to work until nine or even eleven p.m.  On those days he either goes in at the usual time in the morning then comes home for a long afternoon before going back in around five, or he's home in the morning and goes in after lunch. 

+

I'm slow to adapt.

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We've had nothing but Morning Time since "starting back to school" (hah!) in August, and we're doing well if "Morning Time" (hah!!) happens before three in the afternoon.

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But today?  Today we managed not only to finish Morning Time in the actual morning, but to have our afternoon session as well.  :-D

For now, I only have the two youngest (14yos and 11yod) with me for an afternoon session as my 15yod completes her studies independently.  As I've mentioned before, she's taking an online Great Books course where she's currently reading Dante's Inferno and Dorothy Mills' History of the Middle Ages.  She also practices the violin for one or two hours, and she's using The Teaching Textbooks' pre-algebra curriculum, and Visual Latin.

So here's what I did with the younger two:

* First, I'm using the cursive handwriting program from The Logic of English, which I got a couple of years ago when it was a free download.  Today we had a quick review of the letters that begin with an upswing -- i, j, u, w, r, p, t, and s.  That took five minutes at most.

*  Then we moved on to Classical Composition I: Fable Stage.  When we left off I was doing the whole thing orally because these two students were barely reading, but their skill has really taken off on the past few months, so we'll be doing more of it in written form.  Today I began by reviewing the three parts of a story's plot (recognition, reversal, and suffering), then I read the fable and had one of them narrate, then they gave me examples of recognition, reversal, and suffering.  Tomorrow we'll review the variations they've learned so far, and continue with the next part of the lesson.  This took about twenty minutes.

*  Lastly, I gave them their books for independent reading and new composition books for written narration, which they've never done before.  Since we're just starting written narrations I didn't correct anything at all -- I just marked it to show that I'd read what they wrote.  Later on, after this has become a daily habit I'll start marking corrections they need to make.  When I did this with my older students I chose one area, or one kind of mistake they were making consistently, and then when that area improved I moved to another.  Generally I choose to correct grammatical mistakes over technical ones like spelling and punctuation, since the technical things tend to work themselves out over time and are far easier to correct, where grammatical errors tend to indicate sloppy thinking.  They spent about half an hour between reading and writing, but this time will increase as we go on -- I deliberately kept the work light for today.

One thing I did differently with these two than I've done before was to keep them at the table with me for their independent studies.  These are both pretty extroverted and are more successful when they're working around other people, even if they're not actively engaged with each other.  So they did their reading and writing while I did mine.  It was a pleasant setup for all of us.

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October is a gorgeous month in Virginia

Even the weeds are pretty

Math update: Struggling through a dry spell

I was working on  the third installment of my Squaring the Circle series, in which I’d intended to relate what I’d learned about the nature of pi – I said I was pretty excited about it, and I really was!  I only wish I’d written that section this spring when I was still glowing from that Eureka! moment.  It’s a lot harder to write about all these weeks later, so instead* I’m reading the whole chapter on the Ancient Greeks in A History of Mathematics – before I just read the sections dealing specifically with measuring a circle.

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But here’s something fascinating about this chapter – I met nearly all of these people when I read John Mark Reynolds’ When Athens Met Jerusalem this spring and summer.  Did you know that Thales, the first philosopher, was also the first mathematician?  I didn’t, which is why I was so surprised when I wrote this post on Math and Philosophy.

All the early mathematicians were philosophers.  In fact, it is said that Pythagoras is the one who coined the words philosophy, “love of wisdom,” and mathematics, “that which is learned.” 

“Perhaps the most striking characteristic of the Pythagorean order was the confidence it maintained in the pursuit of philosophical and mathematical studies as a moral basis for the conduct of life.” (Merzbach and Boyer, p. 44)

More interesting passages from this chapter:

“ . . . mathematics was more closely related to a love of wisdom than to the exigencies of practical life.”

“Greek mathematics, in its earlier stages, frequently came closer to the ‘modern’ mathematics of today than to the ordinary arithmetic of a generation ago.”

“[T]he Pythagoreans not only established arithmetic as a branch of philosophy; they seem to have made it the basis of a unification of all aspects of the world around them.”

“The point of view of the Pythagoreans seems to have been so overwhelmingly philosophical and abstract that technical details in computation were related to a separate discipline, called logistic. This dealt with the number of things, rather than with the essence and properties of number as such, matter of concern in arithmetic. That is, the ancient Greeks made a clear distinction between mere calculation, on the one hand, and what today is known as the theory of numbers, on the other. . . .  [T]he early Ionian and Pythagorean mathematicians [have] the primary role in establishing mathematics as a rational and liberal discipline.”
That’s from the first half of the chapter.  There are sections coming up headed “Mathematics and the Liberal Arts,” and “The Academy,” so I’m looking forward to what else the authors have to say about that.

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I had a brief moment of elation today when one of my friends shared a math quiz on Facebook. 

There was one moment of panic involving multiplying a four-digit number by a two-digit one – the rest I was able to do in my head, but I had to pull out pen and paper for this one.  Oh, and there was one other that threw me, but my violin daughter was watching over my shoulder at that moment and said, “Think of it this way . . .” and then I was able to do it in my head.

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Here’s an interesting article you should read – Research on the Teaching of Math, which I think is a reprint of the appendix of the same name in Harvey and Laurie Bluedorn’s book Teaching the Trivium. They cover what they’ve learned of the history of teaching math, research on brain development, and suggestions for what to do with your own children.

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* Here’s a bonus article:  Why Writers Are the Worst Procrastinators.  I printed it out two days ago, but I’ve been avoiding reading it because I’m afraid it’ll be depressing.
:-p

Wednesdays with Words: Thirst

“I don’t have any excuses, Son,” he said to me. And it was odd to be called Son by a man I hadn’t seen in thirty years. It was odd to be anybody’s son. It felt right, but right for another time and another place and another story that never actually happened.

“I’m sorry,” he said. And he cried. A tear came down his cheek, and he put down his beer and reached his hand over the arm of his chair to the couch, and I took his hand. “I’m sorry,” he repeated, his voice breaking with emotion. “Do you forgive me?”

“I do,” I said. “I forgive you.” And I did, even though I didn’t know I needed to. I forgave him and haven’t felt anything against him since. He took a sip from his beer and thanked me. He put his hand on my knee and squeezed till I thought my leg would break. He reached over and picked up my book and smiled and shook his head. “You can write,” he said in a voice that seemed to come from before time. “I can’t believe how good your stories are.” I didn’t want his words to mean anything. I didn’t want to need his affirmation. But part of our selves is spirit, and our spirits are thirsty, and my father’s words went into my spirit like water.

[A Thousand Miles in a Million Years, by Dennis Miller]

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Shelfie

Books on education, books on books, and books on words

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Current Reading
A History of Mathematics, Uta C. Merzbach and Carl B. Boyer
A History of Pi, Petr Beckmann
Introduction to Arithmetic, Nichomachus of Gerasa
Our Magnificent Bastard Language, John McWhorter
Waldo, Robert Heinlein
Let There Be Light: A Book About Windows, James Cross Giblin
The Old Farmer's Almanac, 2015 edition
Onward and Upward in the Garden, Katharine S. White
Music of Silence: A Sacred Journey Through the Hours of the Day, David Steindl-Rast and Sharon Lebell



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