30 November 2012

5+ Picture Books for Girls

Mystie emailed me yesterday looking for ideas, and I think she made an important point. She said that there are lots of lists out there for boys. You know what? She's right! I think that some of this is because, while girls tend to like books on the "Boy Book" lists, the reverse isn't always true. My little girls love a good story about knights battling dragons, just like their brothers, but my sons aren't fond of books about pretty dresses, especially if said dresses are accompanied by crying or other forms of deeply felt emotions.

With that said, I don't own lots of books that are easily classified as "Boy Books" or "Girl Books" because, frankly, I am far more interested in owning good books, and if a book is a good one, usually anyone--male or female, young or old--will enjoy the reading of it.

But make a list I did, and I thought I'd share it here. I'm feeling rather list-y today, after all! Most of this list is actually featuring authors of sets of pictures books. Some of these authors produced more picture books than others, with, I think, Beskow {at the bottom} holding the most-published prize. My goal here was to pinpoint some lesser-known authors and books, which is why you won't find the über-famous {and rather obvious--like Barbara Cooney} here on this list.
  1. The Flicka, Ricka, Dicka books by Maj Lindman. We own four or five so far; there are seven altogether. These are easy to read, so they double as early readers later on. Detailing the adventures of young Swedish triplets {before there was much in the way of technology}, my girls laugh away at the folly of baking a cake {and forgetting the timer} or helping a neighbor {while trying to keep their new dresses clean}.
  2. Old Mother West Wind by Thornton Burgess and illustrated by Michael Hague. I am a huge Hague fan. Huge! This book of stories by Burgess is enjoyable as it is, but Hague makes it so, so beautiful. Mother West Wind is just gorgeous; very satisfying for little girls who like beautiful dresses.
  3. Jill Barklem's Brambly Hedge books. These are out of print, but easy to find in good used condition. Barklem's ornate illustrations are a feast for the eyes of any child, but are especial favorites of my little girls.
  4. The Maple Hill Farm book by the Provensons. I don't know about you, but my girls seem to enjoy animal stories more than my boys do. These books about farm life are also enjoyable for parents because, frankly, parts are hilarious. At least, I think they are.
  5. Books by Elsa Beskow. Elsa Beskow, not unlike Jill Barklem, has created a whole world in miniature, but while Barklem's is populated by talking mice, Beskow's is populated by tiny people and fairies. She also has a wider variety than Barklem, not limiting herself to this tiny world, but branching out into orphaned children, funny adoptive aunts, and various livestock and wild animals. Her illustrations are beautiful and her tales are interesting.
What about you? What are your family's favorite "girl" picture books?

29 November 2012

Book Club: Sayers' The Mind of the Maker
{Chapter 4}

Sayers commences her fourth chapter with a seeming paradox. Is the Creator equal to the sum of all His work? {She means here that there is nothing about Him but His works.} Or is He entirely detached from what He has made and therefore unknowable? I have heard something along these lines presented before, as if these were the only two possible options available to us, and Sayers does a wonderful job {using her analogical skill} to show us that a third option not only must exist, but must be true.

Sayers' Case Against Pantheism

I love the way Sayers makes her arguments because they aren't logical, but rather analogical. I am so accustomed to people needing their arguments to make sense--logically speaking--that it is striking to read someone who makes arguments by drawing parallel lines and showing these lines to be so much the same that a divergence stands out as untrue. It is fascinating, and I want to try to learn to do this. I think Doug Wilson does this often and that is why, love him or hate him, he is a delight to read in terms of his mastery of this art.

Her case against Pantheism is simply that it doesn't fit the analogy. She uses the example of Shakespeare. We know that Shakespeare was a real person who wrote real works, and there is a sense in which he incarnated himself in his works. He can be said to be Hamlet, for there is a part of himself that he put into Hamlet. {Of course, she points out that he puts himself into each character, so he is also Othello and also King Lear and so on and so forth.}

Even though we know that Shakespeare is "in" his works, it is nonsensical to us to think that his works are literally him and that nothing else but his works has ever or will ever exist--that there is no Shakespeare outside of his works.

Mathematically speaking, arguing for Pantheism is arguing that:
Shakespeare = his writings
In other words, it's an absurdity.

Sayers' Case Against Deism

I don't think she ever uses the term Deism, but when Sayers is talking about the idea of God-as-disconnected-clockmaker she simply must mean Deism. Her argument here again relies on analogies, but it is structured somewhat differently. She asserts that the progression of history refutes Deism. This system requires the universe to be a machine of some sort which the Creator made and then abandoned to run on its own according to its own laws.

Sayers reminds us that machines produce "unities," the same thing over and over. A toothbrush machine, if there is such a thing, makes only toothbrushes. But our world is full of diversity and, Sayers says,
we have no experience of machines that produce varieties of their own accord.
Therefore, the progression of history--the sense that it continues to unfold {in many ways, like a book}--proves or evidences God's continued involvement because this type of situation requires His continued expenditure of creative power.

To go back to her "writer's trinity," the nature of the universe requires Activity still.

Vital Power in Writing

I like to write, as I'm sure you can tell. For me, writing is a path to understanding. I have, however, tried my hand at writing as a creative expression--as an artist--and I've found that I'm weak. It is incredibly difficult for me, and I'm never satisfied. We could say that my problem is in the "idea" category, but there have been times that I had a very clear idea and yet my execution was weak {and, I might add, embarrassing}.

So what was the problem?

Well, I had a light bulb moment this past week, when Sayers taught me that the vital power of an imaginative work is to have diversity within unity. She mentioned that someone like Shakespeare would pour himself not only into his heroes, but also his villains. Even into his fools! The point was that he poured himself in to each and every character.

She contrasts this with the manufacturing of so many "dummies" upon the page. These are characters which exist only to dialog with the main character, throwing the ball back to him. TV shows do this so as to have characters to kill off. My husband and I joke about this when we watch Revolution. See that new guy? He's definitely going to die.

This week, I learned that a writer's energy must be active in the whole and not in only his favorite parts or favorite characters. He can--and must--incarnate himself even in his villains, if they are to be believed.

Most of my fiction attempts were done at very young ages, but I think I gave it up because I wasn't any good. And I don't mean that I needed practice. I think I instinctively knew that I was missing something, but what was missing was a mystery to me.

Of course, there is a good argument for me never being any good, just as you would likely never have cause to purchase a painting painted by me, but I think my weakness was here, in this very spot Sayers touches upon. I think I might have thought that it was good and noble to "incarnate myself" into my heroines, while leaving my villains to fend for themselves. It was sort of like constructing a straw man fallacy. I didn't realize it at the time, but I think I see this clearly now. I thought weak villains were "good" in the sense that we want to hate them, don't we? But they were never believable precisely because they were so weakly written. And I think that, because they were villains, I was afraid to pour myself into them. What would it say about me as I did? It wasn't just a failure of imagination. It was also an act of fear--I was afraid to pour myself into a villain.

I have a new resolve now to try and throw myself into something--into every piece of that something--to see what happens. I am curious to see if I can conjure something noble or, at the very least, worth reading, now that I understand this.

Even if I prove to myself that I am, in fact, deficient, I think it is useful to understand this concept of "diversity in unity"--that when I put my power into all parts, it strengthens the whole. If this makes sense. Does it?

Read More:
-More posts linked at Ordo Amoris
-Buy the book and read along!
-Get Mind of the Maker for free from Willa's Readlist

28 November 2012

Did Geraldine McCaughrean Read Dorothy Sayers?

Since the Linky isn't up yet for the Mind of the Maker book club, I thought I'd do an extra entry for the previous chapter. We've already begun our Jesse Tree book because I only do this with the children on week days, so I need a full four weeks before Christmas. We've read this book at least two times before, but I suppose, since I hadn't yet read Sayers, I didn't recognize the connection.

Here is a copy of my summary of the "writer's trinity" that Sayers introduces in Chapter 3:
  1. Idea: this is the whole work, complete and at once, in the mind of the author. Something about this reminded me of the book Poetic Knowledge. It is as if she is saying that writers have a poetic grasp of their own work before they ever set pen to paper. This parallels the Father.
  2. Creative Energy/Activity: this is the actual act of writing, of putting in the work to make the idea a reality. This neatly parallels the Son.
  3. Creative Power: this is the meaning of the work, and the response in the soul. This parallels the Holy Spirit.
So guess how excited I was when I read this:
First there was the idea, complete and perfect: the beginning, the end, and everything in between. {God is a craftsman, you see, and a craftsman always plans before he begins work.} Then God flexed his fingers and began. He made light and with it warmth and beauty...


"But why the sun and the moon? Why didn't you carve Adam and Eve?"

"I told you, boy. These are symbols. They represent the time when God began his great plan. As it happens, Adam and Eve almost ruined everything...But people who come into this church will look at this sun, this moon, and remember how God created the world."

"And now you are creating it all over again," said the boy.

The old man was so angry that his fist tightened around his chisel and he shook it. "Don't talk wickedness, boy! I don't liken myself to God! that'd be falling into the sin of pride, that would!"

The boy looked startled. "Why? You said it yourself: there's a likeness. A family likeness. It's just that you're using wood, not clay..."
I don't see Creative Power, but I see the concepts of Idea and Creative Energy/Activity very strongly, as well as the idea that an artist reflects this. Wow!

Read More:
-More posts linked at Ordo Amoris
-Buy the book and read along!
-Get Mind of the Maker for free from Willa's Readlist

26 November 2012

Miscellaneous Musings on Monday

Good morning afternoon! I hope you all had a wonderful Thanksgiving. We sure did! We just ate the last of the mashed potatoes with lunch today. Yummy! We ate bread and mashed potatoes for the first time since September 1st, so this was a Big Deal.

In other news, the chicken pox are almost cleared up {and no longer contagious} and today was our first day of DecemberTerm. Like all first days, I had to run back and forth to bookshelves and the office because though I thought I was ready, I was sorely lacking the details. What can I say? I'm a big picture person and the details--the printing of important documents, for example--come at the last minute because that is when I remember them.


Here are today's links for Afterthinkers...

  • Giant Sun Eruption Captured in NASA Video from Space.com.
    On Tuesday and Wednesday (Nov. 13 and 14), space weather conditions sparked a geomagnetic storm that supercharged the Earth's auroras, creating spectacular northern lights displays for observers at high latitudes.
  • The Semi-Pelagian Narrower Catechism If you catechize, and you know who Pelgius was--and hence what semi-pelagianism is--then, and only then, will you think this is funny.
    9. Q: What is the assurance of thy salvation?
    A: The assurance of thy salvation is, that I know the date on which I prayed the Sinner's Prayer, and have duly written this date on an official Decision card.
  • Tyndale House wins mandate court battle from WORLD. If thou publisheth Christian books, thou legally qualifieth as a "Christian" for a religious exemption. At least, thou dost right this moment.
    Bible and Christian book publisher Tyndale House Publishers believes in the words it prints and sells to its customers. And on Friday a federal judge agreed the company has a right to conduct business according to those beliefs and without government interference.
  • FEDERAL JUDGE: HOBBY LOBBY MUST OFFER MORNING-AFTER PILL from The Blaze. But if thou art just a Christian that owneth a business--which happenest to sell books, on occasion, which belongest to the aforementioned Christian publishers--yea, verily, thou dost not qualify one bit.
    In a 28-page ruling, U.S. District Judge Joe Heaton denied a request by Hobby Lobby to prevent the government from enforcing portions of the health care law mandating insurance coverage for contraceptives the company’s Christian owners consider objectionable.
  • Senate bill rewrite lets feds read your e-mail without warrants from c|net. More good news.
    It's an abrupt departure from Leahy's earlier approach, which required police to obtain a search warrant backed by probable cause before they could read the contents of e-mail or other communications. The Vermont Democrat boasted last year that his bill "provides enhanced privacy protections for American consumers by... requiring that the government obtain a search warrant."
  • Obama's Southeast Asia Trip All Style, No Substance So basically this is just more of the same.
    But he also undermined his supposed democracy mission, first by telling the Burmese leaders that he too wished he could govern without opposition, calling into question whether he himself believed in the representative government he was advocating.
  • Hobby Lobby and Religious Liberty Under ObamaCare from Real Clear Politics. If you haven't figured it out already, this issue with contraception and abortion has nothing to do with contraception and abortion and everything to do with whether the State is allowed to rule the Church. It's an ancient story in new legal garb.
    It may be that the next major court decision regarding Obamacare will deal with how religious freedom rights apply to corporations - a Hobby Lobby case which follows with, or breaks from, the lessons of Citizens United could have enormous ramifications for religious business owners across the country. Americans will find out soon whether freedom of association matters or doesn’t under the Obama health insurance regime.
  • More Hard Thinking about Easy Reading from Living Books Library.
    It is possible that our children's leisure reading could be of higher caliber than it is. For example, I recently read an article by a gentleman who confessed to being a reluctant reader. He loved having his mother read aloud to him and really didn't want to have to do it for himself. When she made it clear it was time and he had no choice, she handed him three sets of books to begin with: the complete works of Nathaniel Hawthorne, James Fenimore Cooper, and Sir Walter Scott. He was seven years old. The choice of literature did not hinder him at all since these were the works he had been hearing for years and was completely comfortable with. You may remember that Charlotte Mason also cut her reading teeth on Defoe and Scott. Do you think we've slipped just a bit in what we expect of our children?
  • Homework: New Research Suggests It May Be an Unnecessary Evil from The Huffington Post. All our work is homework. I wonder what that means? He he...
    Let's start by reviewing what we know from earlier investigations.[1] First, no research has ever found a benefit to assigning homework (of any kind or in any amount) in elementary school. In fact, there isn't even a positive correlation between, on the one hand, having younger children do some homework (vs. none), or more (vs. less), and, on the other hand, any measure of achievement. If we're making 12-year-olds, much less five-year-olds, do homework, it's either because we're misinformed about what the evidence says or because we think kids ought to have to do homework despite what the evidence says.
  • TriHealth fires 150 employees for not getting flu shots from WLWT.com. Ah, the land of the free and home of the brave new world where abortions are elective, but flu shots, sadly, are not.
    One of Cincinnati’s largest employers fired approximately 150 employees Wednesday for failing to get a required flu shot.
And that's all for today. Have a good one, everybody! And a big thank you to those of you who emailed me link suggestions.

24 November 2012

Living California History: A Jed Smith Biography, and More!

Amazon links are affiliate links. I and my wallet love it when you click on those...so thanks!

I accidentally neglected California history last term. I really don't know what happened. I had various ideas written out, but for whatever reason, it all completely slipped my mind. And I mean completely. If this subject hadn't come up recently on the AO Forum, I'd probably still be in blissful ignorance!

So here's the deal. I never intend to do a "California Unit" like the schools around here. The main reason for this--beyond my natural aversion to such things--is that I remember zero from my California unit when I was in school. So my goal here is to design California history exactly as if it were part of Ambleside Online. This means I want living books--both assigned and for free reading--that match up with AO's chronological history.

Last year, we got our feet wet using Scott O'Dell's Cruise of the Arctic Star as a living geography book. It went fantastic.

This term, we're using a few books, though only one is assigned and scheduled out. Remember, Year Five is a year that lines up with a lot of major historical events in California--from Lewis and Clark first viewing the Pacific Ocean, to the Gold Rush, becoming a state, and so on. If we're ever going to really study California, Year Five is the time to do it!

I'm assigning two free reads this term, both of which take place during the Gold Rush era. First up is The Balloon Boy of San Francisco. This is a thin little volume, so E-Age-Ten is already halfway through it. He informs me it meets with his approval! The second is a bit better known, called By the Great Horn Spoon!

As actual assigned reading, I'm using a biography called Jed Smith: Trailblazer of the West. Jed Smith is mentioned in O'Dell's Cruise of the Arctic Star, but this will give us a lot more detail than we found there, plus we will learn about Jed's strong Christian faith.

Below is a 12-week schedule for reading this little biography. I am adding this to the AO schedule. I suppose that if you had trouble fitting it in, you could use it as your history biography. I hesitate to do that because it is a little bit light all on its own, but it is possible for those of you who need to do California history {it's required by law, remember} and feel like you cannot add any more to the schedule.

Jed Smith: Trailblazer of the West
by Frank Latham

{fits with AmblesideOnline, Year 5, Term 1}

Week 1: Jed Wins a Fight {Ch. 1} and Jed Hears of Faraway Lands {Ch. 2}
Week 2: Up the Missouri {Ch. 3}
Week 3: In the Land of the Sioux {Ch. 4} and On to the Yellowstone {Ch. 5}
Week 4: Jed Learns His Trade {Ch. 6}
Week 5: Fight with the Rees {Ch. 7} and Jed Takes a Message to Major Henry {Ch. 8}
Week 6: Ashley's New Idea {Ch. 9}
Week 7: Jed Whips a Grizzly {Ch. 10} and Jed Starts on His Big Adventure {Ch. 11}
Week 8: Jed Rides into the Unknown {Ch. 12}
Week 9: Jed Conquers Mountain and Desert {Ch. 13}
Week 10: Back to California {Ch. 14}
Week 11: Jed Meets the "White-Headed Eagle" {Ch. 15}
Week 12: "The Greatest of the Mountain Men" {Ch. 16}

I'm sure some of this could be done using a map--treating it more as a geography book. I'm choosing to use it as a simple biography, though having a big map on the wall means we'll often orient ourselves upon it whether it is assigned or not.

I'd love for you to share the titles of your favorite California books in the comments. I'm always updating my list!

21 November 2012

Five Favorite Christmas Picture Books

I was not going to do this. Tomorrow is Thanksgiving, after all. I try not to discuss our Christmas traditions much until after Thanksgiving. In addition to this, I have errands to run and things to {finally} help my mother with, now that my children's chicken pox is officially noncontagious. But you asked, you did! And I do so love to talk books.

So here's the deal.

I have a decent Christmas picture book collection, in my opinion. But some of them far outshine the others, and those are the titles I'm going to share this morning. At the bottom of this post, I'm going to put a Mr. Linky widget. I ask all of you to share the bestest of the best books from your Christmas collections. It's okay if some of yours are the same as mine, but what I'm really hoping is that we'll be able to introduce ourselves to titles we've not heard of before, with the ultimate aim of improving each of our collections.

Sound like fun?

Here's my contribution to the list. I'm doing this in reverse order, ending with my absolute, incontestable favorite.

  1. An Amish Christmas
    by Richard Ammon
    My children enjoy this story of simple joys on Christmas. I think it subtly teaches them that Christmas need not be elaborate to be rich.

  2. The Grumpy Shepherd
    by Paddie Devon
    I love the Christmas theme of grumpiness or sorrow turned to joy by the coming of the Christ Child. When Dickens wrote his classic Christmas story, he was playing upon the ancient theme!

  3. The Story of Christmas
    The text of this book is taken straight from the King James, which is common for a number of Christmas books. The reason this makes the list of favorites is the artwork, a wonderful example of Pennsylvania folk art style.

  4. The Christmas Miracle of Jonathan Toomey
    by Susan Wojciechowski
    The illustrations in this book are wonderful, and the story is priceless. It doesn't get better than this...except when it does, of course.

  5. The Year of the Perfect Christmas Tree
    by Gloria Houston
    You all know I'm a Barbara Cooney fan, right? This really is a beautiful book. But the reason why it is my number one favorite of all time is because it never fails to bring tears to my eyes. I do not tire of reading it, even though my little ones ask for it over and over. It is truly a timeless tale, I think, and the message of secret self-sacrifice is one that every mother can identify with, I think.

I'm going to leave the Linky live for a couple of weeks, so tell your friends that we're having a little pre-Christmas party and let's see if we can work up a list of seriously excellent Christmas picture books for ourselves. I mean...for our children. He he.

Someday I'll have to share with you my wishlist, which is equal in length {at least} to this list. I might like my collection, but there are also a number of wonderful Christmas tales I do not yet own. {Emphasis on yet.}

Happy Thanksgiving to you all!

20 November 2012

DecemberTerm 2012

Wow! It is hard to believe my plans are complete and ready to roll already, but what can I say? My new templates are working overtime to keep me from working overtime. It also helps that I now have years of plans from which to draw. I mean, tradition is tradition, right? I might switch things up a little, but I don't have to reinvent the wheel.

But first...what is DecemberTerm? I know that some of you are wondering. In brief, after years of living between sleep and awake {due to being pregnant--and nauseous all nine months, mind you--and nursing for years on end}, I awoke one Christmas to discover we had virtually no Christmas traditions of our own. DecemberTerm, which the children fondly call "Christmas School" or "Advent School" was my solution to this problem. I took what we normally do every morning--called Circle Time--and gave the whole thing an Advent twist.

Around here, DecemberTerm refers to all weeks of school between Thanksgiving and Christmas--even if they are technically in the month of November.

This year, I am especially ready for our Jesse Tree study. I am ready to walk through the Gospel once more, taking my children with me.

So here are the plans:

DecemberTerm 2012

Execution and Resources

As you can see, I'm sticking with my simple chart format that I used for Circle Time last term. This means I need a different resource than last year. First of all, I need my Memory Binder to be organized in such a way that it isn't a big deal that I didn't list out what we're doing on specific days. Lucky for me, I left it organized last year, so we'll just sing a couple songs each day and start back at the beginning when we reach the end. Luke 2 is easy enough--I've always just read it straight from the Bible when we work on it.

Here is a link to the Rossetti poem we will be memorizing.

Another link that might be helpful, if you are using some of these plans, is my document which coordinates The Jesse Tree book with applicable Scripture passages. Since I was not typing out daily plans this year, I needed something to organize our Jesse Tree readings, and this simple, one-page document is perfect. I plan to just keep it in the book and use it as a bookmark. Our Jesse Tree tradition is simple. We have a little felt tree, and paper ornament we made ourselves a couple years ago. We read the Scripture, and then the children narrate the Scripture. Then we read the chapter from The Jesse Tree, and then we hang the day's ornament on the tree. We just rotate children from youngest to oldest so there is no arguing over who gets to hang the ornaments.

Next year I hope to get a new Jesse Tree book {I like this one, but hope for even better--any suggestions?} and make a new set of ornaments as my children enjoy making them of course.

Perhaps you noticed that I didn't put Picture Study on the schedule? Well, we have studied these works two or three years in a row now. I plan to be a lot more casual this time around--I'll hang them where I always do, but we'll just chat about them a little. I don't know that we need to study them intensely every single year, even if they are masterpieces.

With that said, let me explain the weekly schedule. The children are really enjoying Pilgrim's Progress right now. I toyed with taking it off the schedule anyhow, but decided to not only keep it, but move it to two days per week. When you think about it, it really is a book that fits with the season, just not overtly. So I'm alternating Pilgrim's Progress with books from our Christmas collection. We have lots, and I'll probably let my preschooler do most of the choosing. The nice thing about having a good collection is never needing to say no. He can choose from the box and we'll do fine.

For other literature selections, I'm alternating Dickens' A Christmas Carol, which is the book we read every single year, with a new one, Marguerite de Angeli's The Lion in the Box. I am very excited about this. I scored a copy of The Lion in the Box on PBS. {I wonder if the previous owner realized even these cheap paperback copies are selling for over $40 a pop on Amazon? I did a little dance!} I try to have something new each year, and The Lion in the Box, along with our book for St. Nicholas Day, will be special treats.

Related Posts:
-DecemberTerm 2011
-DecemberTerm 2010, plus the Updated Version
-DecemberTerm 2009
-DecemberTerm 2008 {our very first DecemberTerm}

Book Club: Sayers' The Mind of the Maker
{Chapter 3}

I really thought I would never catch up. I still haven't been able to read all of the Chapter 2 entries, but I wanted to keep writing so as to stay on track, though obviously that didn't happen last week. But, conveniently enough, there is no posting scheduled for the club this week. This means I can post my entry and be all caught up for next week!

Barring all health drama, of course.

I took a bunch of notes on Idea, Energy, Power {aka, Chapter 3} because I didn't completely comprehend it the first time through. This post is a summary of where I went with my notes.

At least, I think it is.

Doctrine of the Trinity

Sayers begins by say that
the doctrine of the Trinity enjoys the greatest reputation for obscurity and remoteness from common experience.
Usually, when we read books like this, we see only how much further our culture has declined compared to the time at which the author was writing. I am so pleased to know that this a real area in which Christianity has progressed. I mean, yes, the basic defense of the Trinity was epitomized by Athanasius' defeat of the Arian heresy early in the 4th century AD. But Sayers is saying here that this doctrine was not connected to us practically. It was an abstraction. An accepted fact, yes, but still an abstract {and perhaps irrelevant} one?

The last few decades have seen huge leaps in Trinitarian theology. Theologians of many stripes have been pumping out Trinitarian-themed books over the recent years and months, among them The Deep Things of God: How the Trinity Changes Everything, Jesus in Trinitarian Perspective: An Introductory Christology, Our Triune God: Living in the Love of the Three-in-One, and {just two months ago} Delighting in the Trinity: An Introduction to the Christian Faith. It seems that thoughtful Christians everywhere are seeing what Sayers, who was often before her time, pointed out. She implied that there are minor trinities in abundance in this world.
We may perhaps go so far as to assert that the Trinitarian structure of activity is mysterious to us just because it is universal...

The Writer's Trinity

In this chapter, Sayers points out the minor trinity she calls the "writer's trinity" as an example of these sets of three-in-one that are all around us. It was very enlightening the way one metaphor deepened the other, and vice versa, though I suppose that is how metaphor works, is it not? Note that her example parallels the work of the members of the Trinity in creating the world. I was mixed up at first because I thought she meant this was a general parallel to the Persons qua persons, instead of specific to the work of creating. Here I thought I'd briefly summarize the writer's trinity so that I can remember it:
  1. Idea: this is the whole work, complete and at once, in the mind of the author. Something about this reminded me of the book Poetic Knowledge. It is as if she is saying that writers have a poetic grasp of their own work before they ever set pen to paper. This parallels the Father.
  2. Creative Energy/Activity: this is the actual act of writing, of putting in the work to make the idea a reality. This neatly parallels the Son.
  3. Creative Power: this is the meaning of the work, and the response in the soul. This parallels the Holy Spirit.

On Creative Power

Sayers writes:
Of these clauses, the one which gives the most trouble to the hearer is that dealing with the Creative Idea.
I fall short on this. It was on her final point--the parallel to the Spirit--that I had trouble staying with her. On the one hand, I understood when she wrote:
It is the thing which flows back to the writer from his own activity and makes him, as it were, the reader of his own book.
This, I understand and I see how it parallels the Spirit--not exactly, but at least loosely.

I have always been weak on pneumatology, so maybe it goes without saying that she promptly lost me when she said:
It is also, of course, the means by which the Activity is communicated to other readers and which produces a corresponding response in them.
Maybe I'll just throw out some questions and see what you all think. The reason I became lost is because the parallels are supposed to be according to the roles of the Persons in creating and yet here the parallel seems to have jumped to something more akin to God's relationship to His people. Did she have to jump because the work of the Spirit is not mentioned in the creation account? Am I just being too narrow? I already admitted that the Third Person baffles me.

Education is not a Lever?

She carries on:
The...suggestion is that, once an invention has been brought into being and made public by a creative act, the whole level of human understanding is raised to the level of that inventiveness. This is not true, even within its own sphere of application. The fact that every schoolboy can now use logarithms does not lift him to the intellectual level of the brain that first imagined the method of logarithmic calculation.
What I am trying to figure out is what Sayers thinks our response to this ought to be. Just give up and assume that Geniuses will be Geniuses and the rest of us will remain average, regardless? Of course, there is the situation we see today, which is the steady decline of the average. Surely, we must try to lift, whether the result is the next Shakespeare or not!

So what do we do?

I have spent a lot of time lately pondering the teaching of the Quadrivium using original sources and the work of historians as an educational tool. It is still very murky in my brain, but I will try to articulate this nonetheless. Let's take Sayers' example of logarithms. So we can teach our students to use logarithms, but their understanding does not parallel the understanding of the person who invented them. But what if we studied, along with our arithmetic proper, the history of the development of math. What if we saw math's limits at any one point in history, understood the necessity of the inventions which came along? What if we read Newton and understood that he invented calculus because he could not do physics without it? {Or was it mechanics?} I wonder if this would not provide some of the necessary lift.

Naturally, this will not produce Geniuses. Only the Good Lord can do such a thing. But it seems that something like this would provide a great assistance to our students, and lift them to a level of understanding that using the tools--like logarithms--alone would not do.

Of course, it all falls apart when we get to Shakespeare.
[T]he absurdity of the suggestion becomes glaringly obvious when we consider the arts. If a ruthless education in Shakespeare's language could produce a nation of Shakespeares, every Englishman would at this moment be a dramatic genius.
The arts are by their nature unnecessary. This is what makes them so human. Art can be Good and True and Beautiful and yet completely frivolous. We could survive without art, but our souls are better for it. This is the artist paradox. Sayers herself tells us that
there is no sense whatever in which we can say that Hamlet has "superseded the Agamemnan...
What this means is that there is no sense in which we could imitate what I was suggesting above with math and science. There was no necessity which led to Hamlet. There was no problem which only the Aeneid could solve. There is no parallel lever, I do not think, for the artistic side.

So how do we lift? Or do we lift at all? Or do we set the table, offer the feast, and know that each will take according to his need and ability? Shakespeare, for instance, had an understanding of the human heart that many believe cannot be duplicated. So the questions becomes: ought we to try?

Read More:
-More posts linked at Ordo Amoris
-Buy the book and read along!
-Get Mind of the Maker for free from Willa's Readlist

19 November 2012

Miscellaneous Musings on Monday

It's Monday! {As it is every week.} And, yes we still have chickenpox, thankyouverymuch. But I do believe we shall be noncontagious by Thanksgiving Day. Hip hip! In keeping with our recent theme of health emergencies, both of my girls had anaphylactic-type reactions to shrimp last night. Um. They have eaten shrimp before, but I'm sure it had to be that because they certainly weren't reacting like that to cauliflower and zucchini, which we eat all the time. Usually, Daughter A., especially, just picks at her shrimp. But the girls were both hungry all day yesterday, so being the genius I am, at dinner I said something smart like, "Eat your food, or else."

Well, they ate it.

And then I got to drive {in the wet and dark} to get Benadryl, give out high doses to two very swollen faces {and bodies covered in hives}, and get up by timer beep throughout the night to make sure they were still breathing.


When I said, "or else," I had no idea what I was getting myself into!

In the Real News...
    The nearly $29 million science experiment on the North Slope produced 1 million cubic feet of methane, according to the Associated Press. Now, researchers have begun the complex task of analyzing how the reservoir responded to extraction.
  • Antibiotics Are a Gift to Be Handled With Care from The New York Times. KM shared this in the comments, but I wanted to bump it up here. I am so thankfuly for antibiotics, but they were handed out to my generation "like candy," as they say, and many detrimental results followed.
    “When antibiotics were developed, they were miraculous for all the reasons that you know,” said Dr. Martin J. Blaser, the chairman of medicine at New York University School of Medicine. “With few exceptions, there was almost no long-term toxicity that was identifiable, and so everybody thought that if you took an antibiotic it could produce some immediate upset — it could produce a rash, loose bowels — and then everything would return to normal, bounce back to normal. But in fact there was no real exploration of that. It just became an article of faith.”

    Dr. Blaser has devoted himself to a study of what is now called the microbiome, the bacterial population that lives on us and in us, and the effects of perturbing that population by antibiotic use. He and other researchers are asking questions about whether alterations in the microbiome may be linked to many different patterns of health, growth and disease.
  • Beware: ObamaCare’s now reality from The New York Post. Yippee. I know too many people who thought they were getting a free lunch when indeed they may find they are getting no lunch at all.
    If you get your health insurance through a job, you might lose it as of Jan. 1, 2014. That’s when the new “employer mandate” kicks in, requiring employers with 50 or more full-time workers to provide the government-designed health plan or pay a fine. The government plan is so expensive, it adds $1.79 per hour to the cost of a full-time employee. That’s incidental if you're hiring neurosurgeons but a hefty increase for hiring busboys and sales clerks.
  • On Assigning Books from The American Conservative. Most books are purchased flippantly. But books? They change the landscape of the soul.
    As a Christian, I should be prayerful all the time, but it’s when I see those book order forms that prayerfulness (at least about my teaching) really kicks in. I believe that these are the most momentous decisions I make as a teacher: the questions about how I run my class sessions and what writing projects I assign are relatively minor in comparison. It’s what my students read that has the deepest and most lasting effect on their lives.
  • Why We Memorize Poetry by KM her very own self! You knew I would link this, didn't you?
    A memorized poem becomes an old friend. Many of the poems we have memorized are common, found in various anthologies. When we come across one we know in a book of poetry, the children are delighted. Their faces light up and they will often happily start singing or saying the poem along with me.
  • On Sons and Generals by Cindy Rollins. I wonder how long she has been waiting to use the sentence, "As the mother of a green beret..."
    We thought our General was honorable and we are surprised when is not. We want our sons to have honor and we don’t even know where to begin. We laugh and scorn and mock and deride and when our tree bears bad fruit we are shocked.
  • Fred's modern rite of passage from The Guardian. Interesting concept. Would you create a rite of passage for your sons? For all of your children? Discuss!
    Why not set him a 21st-century, western (pain-free) equivalent, I thought. Fred was just a few weeks away from his 13th birthday, which seemed like an important turning point. He was eager for more freedom and independence, pushing to go to bed later, have more pocket money, not have a babysitter, cycle to random far-off places and go to football matches without an adult. But did he have the maturity and worldiness to be granted these things? Let's put him to the test, I thought. Now seemed the perfect time to make sure he had the skills needed for a more grown-up life.
  • In Which I Rant About Something That Is Probably Nothing by Queen of Carrots. I must say I agreed with her.
    Maybe it's silly. I mean, nobody says a robot gets a till-death-do-us-part vow. But surely even a robot deserves a little more perseverance. Fight for your friend, little dog! Climb the fence! Borrow a boat! Don't just walk away and find someone new!
  • The Cod Liver Oil Song from The Healthy Home Economist. We've made our children take cod liver oil for years. I'm putting this song on a folk CD mix I'm making for their Christmas gift. They are going to love it!

And that is all for today, folks!

13 November 2012

Book Club: Sayers' The Mind of the Maker
{Chapter 2}

This post is a week overdue. In addition to Math Week, I also had the stomach flu last week. As proof of my good fortune, three of my children have come down with the chicken pox in the last 24 hours. I considered skipping this chapter, but decided I'd rather be behind than skipping an integral part of the conversation. After all, I don't really know what I think until I've written it down.


This whole chapter is really focusing on the idea of analogical knowledge. I could probably spend much time meditating upon the quote from Aquinas on the opening page, which include this striking idea:
[W]e arrive at the knowledge of God from other things.
He're referring here to analogy, and he uses as his example the names of God, which help us to know more about Him...by analogy.

A few years ago, Cindy somehow convinced me that analogy and metaphor {and thus, I assume, the dreaded simile} were important. Even though I didn't quite grasp why, I allowed them to gain ground in our schooling, and we even developed a bit of a family game in which we try to say that one thing is like another. Bonus points are earned for being funny.

I'm sure the it's as itchy as the chicken pox line is only a few days out.


So basically metaphor and analogy are important. They are how we come to know things. We rarely know things--especially important things--directly.

Oh. And I'm not exactly sure why. I hope to find out when I read the entries of the others, which I haven't done because I usually don't read until I've written my own post.

I spent a bit of time deciding if I agreed with Sayers on the imago dei referring mostly to our ability to make things. Her argument hangs on the fact that when we are told in Genesis that man is made in the image of God, the only thing we know about God up to that point is that He is Maker. So Sayers jumps to this conclusion:
The characteristic common to God and man is apparently that: the desire and the ability to make things.
I hesitate to question Sayers here because I know her brain is far superior to my brain, but the theologian in me wouldn't let it go. It seems like a sloppy hermeneutic. Since the Dominion Mandate follows directly after the assertion that man is made in God's image, it is more likely that it is the mandate itself that defines the image. Man is told to tend and keep, and we can consider this a reflection of the image. Later, we are also told that God breathed the breath of life into Man, and he became a living spirit. Again, we have the image of God, here seen in the idea that Man is a being much in the way that God is a being; though he appear physical, yet is he spiritual.

With all of that said, I found myself having come full circle because, you see, many theologians call the Dominion Mandate the Cultural Mandate. They extrapolate that tending and keeping necessarily lead to all the trappings of culture. Things like government...and even art...would be a logical consequence over time. So you see that I ended up where Sayers did, but by an indirect route.

This is proof that Sayers should be the one writing the book.

As if there was ever any doubt.


The really important part of this chapter is when Sayers tells us what her book is about:
[T]his book is an examination of metaphors about God...
Her intent, then, is to remind us of the limits of metaphor using the example of God-as-Father.
Our own common sense assures us that the metaphor is intended to be drawn from the best kind of father acting within a certain limited sphere of behavior, and is to be applied only to a well-defined number of the divine attributes.
And then she asks that heart stopping question:
[I]s the phrase "God the Creator" metaphorical in the same sense that "God the Father" is clearly metaphorical?
I adored her answer. She brings up that we cannot create ex nihilo but only rearrange matter. But then she explains how our artistic endeavors do verge upon creation out of nothing:
We spend our lives putting matter together in new patterns and so "creating" forms which were not there before. This is so intimate and universsal a function of nature that we scarcely ever think about it. In a sense, even this kind of creation is "creation out of nothing." Though we cannot create matter, we continually, by rearrangement, create new and unique entities...Nevertheless, we perceive that this is only a very poor and restricted kind of creation.


It is the artist who, more than other men, is able to create something out of nothing. A whole artistic work is immeasurably more than the sum of its parts.


The poet is not obliged, as it were, to destroy the material of a Hamlet in order to create a Falstaff, as a carpenter must destroy a tree-form to create a table-form. The components of the material world are fixed; those of the world of imagination increase by a continuous and irreversible process, without any destruction or rearrangement of what went before. This represents the nearest approach we experience to "creation out of nothing," and we conceive of the act of absolute creation as being an act analogous to that of the creative artist.
Fascinating, no?

Read More:
-More posts linked at Ordo Amoris
-Buy the book and read along!
-Get Mind of the Maker for free from Willa's Readlist

Afterthoughts was nominated for the Homeschool Blog Awards in the Best Homeschooling Methods Blog Category as well as the Best Current Events, Opinions or Politics Blog. Thank you kindly for the nominations, friends! Better head on over and vote. Please note that you can vote once per day, per computer. Have fun!

12 November 2012

Miscellaneous Musings on Monday

Si and I just got back from meeting our brand new {darling} nephew, and boy are my ovaries aching. Times like this make me sad that having babies is in the rear-view mirror for us. I look forward to grandchildren! And anyhow, there's nothing like babies to take your mind off terrible election results, even if I did turn on the TV momentarily in our hotel and learn that General Petraeus had resigned. I thought right then that something was rotten in the state of Denmark and all that, and I still think that.

Or something.

In the news...
  • Tips on Getting Children Interested in Hard Books from Higher Up and Further In. I suppose you should automatically expect a link from this blog every week. It is, after all, one of my favorites!
    For many of us, our first tendency is to look for something easier. Sometimes, that is what we should do. After all, children are unique. What works for one child may not work for another. But I have found that I shouldn’t be so quick to dismiss a work of literature simply because it's a hard read. I have often been able to help jump-start my children’s interests in books by trying various ideas.
  • Tomb of Ancient Egyptian Princess Discovered in Unusual Spot from LiveScience. Because archaeology is always interesting...
    A limestone staircase descends from north to south along the burial court; four limestone pillars that once supported roofing blocks hold carved hieroglyphic inscriptions reading: "King's daughter of his body, his beloved, revered in front of the Great God, Sheretnebty."
  • A Peek into a PNEU Type Teacher Student Relationship from All That's Good.
    Is it not delightful to hear how well she reads Stephen's appetite. She can sense when one chapter is enough. She does not force feed him when his appetite is gone. She doesn't do the same lesson every day. She is personal, winning him over to a new world of the joy of books, poetry, music, French, and Latin too it says later in the book.
  • California Voters Approve Higher Taxes from The Wall Street Journal. Alternate title: Californians Prove, Once Again, Their Low IQs. Oh, my poor, poor state. And my poor, poor wallet. The California Teacher's Assocation was out rallying for this one, threatening their employees with large class sizes and saying that it was only a "tax on the wealthy." I'm sorry. I am far, far from wealthy. This is one-part sales tax. Are we normal people assumed to not buy stuff??
    According to the California Secretary of State's website, 53.9% of voters backed the measure, Proposition 30, while 46.1% voted against it, with all votes counted except for provisional and some mailed-in ballots.
  • IF YOU GO SEE ‘THE HOBBIT’ AND WONDER WHY IT LOOKS WEIRD, HERE’S WHY from The Blaze. Inside of myself is a 90-year-old woman who hates change. I am convinced I won't like this style-change, but I will go see it anyhow because of my undying affection for Bilbo Baggins.
    Fritz noted in the L.A. Times that the format has gotten relatively negative reviews after it was shown at the CinemaCon convention in April. In May, Engadget reported director Peter Jackson saying it will be an adjustment for audiences.

    “It does take you a while to get used to,” Jackson said.
  • Is GAPS for Everyone? Jennie’s Story from GNOWFGLINS. Since I write about our GAPS experiences positively, I try to highlight some negatives now and then to keep it fair and balanced. Special diets are not for everyone, and all special diets do not work for all people.
    It’s something of a testimony to my commitment (or stubbornness) that I stuck with the diet as long as I did. I really wanted to believe that if I did the diet perfectly, it would work. And I did do it perfectly, without a single cheat, for 16 months. During that entire time, I was never able to move past the 4th stage of Intro and, even then, was unable to tolerate many of the foods allowed on the previous 3 stages.
  • How to turn any Recipe into a Real Food recipe from Homemade Mommy. This includes a nice substitution cheat-sheet.
    How do I turn my old favorite recipes into Real Food recipes? With a few simple purchasing changes and a little elbow grease on some homemade items, you can make your favorite recipes and I guarantee they will taste even better!
  • FORWARD! TO MASS LAYOFFS! from Human Events. Shock. Now that the election is over, we can see what's really going on with the economy. Of course, if you know how economics works, you already knew this was going to happen.
    Schnatter also predicted ObamaCare would add between $5 million and $8 million to his business costs (which is fine, because he’s an evil rich guy who supported Mitt Romney for president, and we all know that truly patriotic job creators happily pay for increased business costs out of their own pockets) and that it would add 10 to 14 cents to the cost of his pizzas, which is a bummer, but under Obamanomics theory is totally unrelated to the process of extracting that “fair share” from idle plutocrats. Then he headed off to help out with a telethon for Hurricane Sandy victims and write the Red Cross a million-dollar check, but we all know that private charity is irrelevant, as only Big Government can save us from big storms.
  • Gut-Brain Connection? Leaky Gut? No longer “Crazy Talk” says AAP from TACA. Looks like my special diet experiments aren't as far-fetched as they once seemed!
    By the time I finished reading, the cynical frame of mind with which I usually read mainstream articles about autism treatment was replaced with optimism. Finally, mainstream research is planning to look at the gastrointestinal and nutritional aspects of biomedical treatment for autism. For twenty years or more, biomedical physicians have been treating GI problems in autism without much support from thorough mainstream research, and we’ve endured much criticism for doing so. Even worse, parents of children with autism have been begging pediatricians for help, will little acknowledgement that there is any possibility of a gut-brain connection in autism. The tide began to turn in January 2010 with Dr. Tim Buie’s consensus report on GI problems in autism (Pediatrics. 2010;125(suppl 1):S1-S18). And now the tide is actually surging in our favor.
  • Congress’ questions for Petraeus will have to wait from The Washington Times. I told you something was suspicious. On Friday I told Si how convenient it was, seeing as Petraeus was a key witness--if not the key witness--when it comes to the investigation of the assassination of the Syrian Ambassador on the anniversary of September 11th, and explaining why exactly the White House told the military to stand down.
    “I don’t see how in the world you can find out what happened in Benghazi before, during and after the attack if Gen. Petraeus doesn’t testify,” Sen. Lindsey Graham, South Carolina Republican and a member of the Senate Armed Services Committee, said on CBS’ “Face the Nation.”
  • Plutarch Does it Again from the CiRCE Blog. Sigh. I adore Plutarch, I really do. We have experiences like this all the time, too.
    The first bit of encouragement came as my daughter could not pull herself away from the Facebook and Twitter statuses of people who had voted for Obama. Over and over again she read of people praising Obama for the ‘stuff’ that was coming their way. I had never seen my calm daughter so upset. I encouraged her to stop reading the statuses and I picked up the Bible to read the verses we are memorizing and suddenly they became very real to us all.
  • Ask Andrew from CiRCE TV. I really loved this answer, and it wasn't just because he mentioned Ambleside.

Afterthoughts was nominated for the Homeschool Blog Awards in the Best Homeschooling Methods Blog Category as well as the Best Current Events, Opinions or Politics Blog. Thank you kindly for the nominations, friends! Better head on over and vote. Please note that you can vote once per day, per computer. Have fun!

09 November 2012

Teaching Euclid in the Homeschool, Part II {by Willa}

This is the last in our series of guest posts for Math Week on Afterthoughts. I broke Willa's original post up into two parts, the first focusing on the more philosophical and historical aspects of teaching Euclid, today's focusing on more practical matters. You may want to read the preceding posts first. Here is the series Table of Contents:

Willa is the wife of a computer game designer and mother to six sons and one daughter, currently ages 9 to 26. Her family has been homeschooling for 18 years. She currently blogs at Take Up and Read and has contributed chapters for Literature Alive! and A Little Way of Homeschooling.

There are many resources available for studying Euclid. The Google Books repository has the classic Heath-Heiberg annotated version of Euclid in three volumes {Books 1-2, Books 3-9, Books 10-13}. An interactive {Java-enabled} online version of this definitive work is available. Personally, I find Heath confusing because the commentary is so extensive, though the Dover facsimile edition is the one both my high school son and daughter used. The Green Lion edition in one volume is recommended at the college where they studied.

Another route might be to use one of the several Euclid textbook editions in public domain. This one arranged by HS Hall covers books 1-6 and 11-12 of Euclid and is targeted towards secondary schools.

Though it only covers the first two books of the Elements, I like the Class Lessons on Euclid which I mentioned in my previous post, because it explains the significance of some of the Euclidean ideas and words. For someone like me whose degree is in literature and who was not taught math using Euclidean methods {to say the least}, this provides extremely helpful context.

There are video demonstrations of the first 26 Euclid props on Youtube. These were not available when my older children were in the homeschool, but I plan to use these or similar ones with my current high schooler.

In the late 1800's, when Charlotte Mason was still alive,the PNEU schools founded by her used Euclid in the curriculum, but by the 1920's A School Geometry by HS Hall was being used in Form III {grades 7-8}. It is very Euclidean in format, with some adaptations in arrangement and method.

For younger students in Form II {grades 4-6} a book called Practical Exercises in Geometry was in use in the PNEU schools. Also, for younger students, Sam Blumenfeld has recommended a book called First Lessons in Geometry, which is from the 1850's and has a simple, conversational format.

Put Euclid in the weekly/daily schedule

There are close to 500 propositions in the 13 books of the Elements, plus sundry definitions. However, not many courses I have seen cover the whole 13 books. More commonly, high schools in the past couple of centuries focused on the first six books, which cover Plane Geometry and have not been outdated by advances in mathematics, and sometimes on only the first two. The first six books have only 171 propositions and 72 definitions. If you tackled only the first two books, that would be 61 propositions and 25 definitions. That seems doable for 1-2 lessons a week.

From looking at the PNEU Timetables, which used the methods of Charlotte Mason, I see that in 1908 there was a Euclid lesson 2-3 times a week, while Arithmetic or Algebra was studied 4-6 times a week.

My two highschoolers, who were seniors when they read Euclid, simply spent a few weeks on it alongside their ordinary work in a math textbook. My son carried the book around with him and did the demonstrations in his head {being that type of thinker}. My daughter used a whiteboard and colored pens and sometimes corralled a younger brother to teach the prop to in order to help her retention and memory.

Alternately, a student could work on Euclid while studying Algebra 1 as a sort of introduction to geometry before taking geometry as a course. That might be valuable in getting the student introduced to proofs and logical reasoning before embarking on the infamous double columns of the standard US proof.

I plan to work with Euclid once or twice a week with my present high schooler. We plan to review the proposition from the preceding week or two, then read the new one, discuss, and work through on the whiteboard. Since he is in the middle of Jacob's Geometry right now, we can use Euclid just to deepen understanding and contrast the older method with the newer one.

"Deliberate Practice" takes time

...They say that Ptolemy once asked {Euclid} if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry.

“some one who had begun to read geometry with Euclid, when he had learned the first theorem, asked Euclid, ‘But what shall I get by learning these things?’ Euclid called his slave and said, ‘Give him threepence, since he must make gain out of what he learns.’ ”

The importance of Euclid’s elements was recognised by the Greek philosophers, who posted on the doors of their schools: “Let no one enter here who is unacquainted with Euclid.” {Science-History of the Universe}

Looking through the Google Book repository and through the Parent's Review magazine archives at Ambleside Online, I found that around the turn of the 20th century, there was quite a bit of criticism leveled at the use of Euclid in middle and high schools. If you are interested, you can look at these articles from Parents' Review. The criticism is targeted as much towards poor, mechanical teaching as towards the propositions themselves, and brings to my mind Charlotte Mason's quote of Ruskin in regard to students:
'they cram to pass and not to know; they do pass and they don't know,'

We are fortunate not to have our kids tested on Euclid, but exams and hurry are characteristics of modern education, and if we are going to study a work like Euclid's, we should keep in mind that it should be something we do liberally, for the sake of becoming better, not just to get through it. It would probably be better to cover less, and do it thoughtfully and conversationally, perhaps with lots of drawing of lines and circles, even including a kindergarten sibling in the lessons as my daughter did, rather than memorize huge sections in a rush.

Euclid's Elements are part of a liberal, philosophical education. Such an education cannot take place in haste, though timeliness certainly has a place.

Recently I read a book that discussed the concept of Deliberate Practice.

“When you practice deliberately, you identify the tasks or knowledge that are just out of your reach, strive to upgrade your performance, monitor your progress, and revise accordingly. Deliberate Practice...takes intense concentration...requires deep motivation, often self-generated....involves working on the task that’s most challenging to you personally. The book mentioned that this best takes place with some time and space to think and work. I think that freedom from too many media distractions and activities on the schedule helps with the kind of thinking required for Euclid and other "great books".

08 November 2012

Teaching Euclid in the Homeschool, Part I {by Willa}

This is the third in our series of guest posts for Math Week on Afterthoughts. I broke Willa's original post up into two parts, one focusing on the more philosophical and historical aspects of teaching Euclid, the other on more practical matters. You may want to read the preceding posts first. Here is the series Table of Contents:

Willa is the wife of a computer game designer and mother to six sons and one daughter, currently ages 9 to 26. Her family has been homeschooling for 18 years. She currently blogs at Take Up and Read and has contributed chapters for Literature Alive! and A Little Way of Homeschooling.

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.

The Autobiography of Bertrand Russell
Why would a student of today want to learn Euclid--not just about him, but from him and his ideas? And if a student did want to do this, how would he or she start? And how would a homeschool parent guide this study?

Euclid's Elements of Geometry was the core math text for close to 2000 years. Abraham Lincoln studied Euclid's books, as did Albert Einstein. Bertrand Russell was dazzled by Euclid, though he became disillusioned later in life. Anne of Green Gables was glad to be "done with geometry, learning or teaching it," as she "thumped a somewhat battered volume of Euclid into a big chest of books, banged the lid in triumph, and sat down upon it". The men of the Scientific Revolution, though they discarded most of Aristotle and Galen and other ancient scientists, kept the format and much of the substance of Euclid for their new physical models of the universe and its workings. Even some living today remember studying Euclid. In spite of the advances of the modern world, if Euclid looked in the Plane Geometry of a modern high school geometry textbook he would find much familiar to him, albeit ordered differently and somewhat altered in format.

Geometrical proofs are according to some reports slowly dropping out of the high school curriculum, perhaps because they can't easily be put on standardized tests. But something similar to the Euclidean method of constructing proofs is still employed by mathematicians today, so this de-emphasis may be a matter for concern. Some have proposed that Euclid, because of its emphasis on close reasoning and precise formulation, is a good bridge to college mathematics both for mathematics-oriented students and for those who major in the humanities.

Recently, the Great Books and classical education revival has led to a return to Euclid by some high school programs--Great Books Tutorial is one, Regina Coeli is another, The Lyceum is a third--and some colleges--St John's College is one, Thomas Aquinas College is another. The University of Denver offers Greek for Euclid.

If you are reading this, you probably have some interest in the idea of studying Euclid. Perhaps you have heard that the children in Charlotte Mason's PNEU schools studied Euclid in middle and high school, and want to follow that example; perhaps you prefer to focus on Great Books and avoid textbooks, especially modern ones; or perhaps you are a classical homeschooler who wants to prepare your child to tackle Euclid, Descartes and Newton in a liberal arts college.

My family is sort of a combination of the above. I have four grown children and three still in the homeschool. We use a classical/Charlotte Mason blend in our homeschool, and try to include a fair quantity of great books and a minimum of textbooks in our studies. But the immediate practical motivation for two of my older children to read Euclid was their admission into a liberal arts college. Both of them wanted to get some familiarity with the Euclidean method before actually studying him formally in a college environment. I would like to do some Euclid with the three remaining students at home before they graduate. That's where I am now.

From that perspective, here are some steps I think are important in teaching Euclid in the homeschool, especially since Euclid is not a standard textbook, and most of us {I, for one} were not taught mathematics in this way during our school years.

Know your goals.

The traditional goal of studying Euclid was to learn to reason well. A proof-oriented geometry course is a course in basic reasoning. There is a useful {and short} booklet in public domain: On Teaching Geometry. It makes the point that proofs are extended syllogisms. Given the premises, the result must follow, if the reasoning is valid.

Abraham Lincoln apparently used Euclid's system of logic in order to build his arguments in speeches and debates throughout his life, and recounted of his earlier days:
I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof? ... I consulted all the dictionaries and books of reference I could find, but with no better results. At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies.

One of Euclid's excellences is that every word and detail is chosen for a reason and so those words and details matter. They are not interchangeable. My son who studied Euclid in college said that he found that if he could not demonstrate a proposition in precise words, it usually meant that there was an error in his thinking -- he had taken something for granted, or made a shortcut in his reasoning. Since geometry is simpler than, say, political or philosophical argumentation, it is a suitable training ground for younger people.
One aim of education is to enable us to articulate what we see, and Euclid is superb at occasioning this activity. Euclid begins with simple geometrical objects that are presented to the mind in three ways: through canonical depictions on paper, through images readily held before the mind’s eye, and through careful language.

--Even the Flaws are Perfections {PDF}

One more reason for studying Euclid's ideas is that they are part of our intellectual heritage. The school math curriculum of today is often not only disassociated from its logical underpinnings, let alone its real-life applications, but from its place in the history of thought.

Start reasoning before Euclid.

This article makes the point that informal "proving" or justification of arguments should start before high school, and this sequel gives some ideas of how to do so.

This doesn't have to be complicated. If you are educating your child in a Charlotte Mason or classical Great Books style, hopefully you are already hearing narrations, discussing books and ideas with your child, observing the world around you and talking about it. This is a precursor for the kind of thinking done in mathematical reasoning, because you are already modeling and allowing time to observe, distinguish, trace cause and effect, etc.

Also, I think it's important that the children get real-life {or at least visual and interactive} geometrical experience. Montessorian manipulatives can be helpful. There are various geometry games and visuals online. Some practice in drawing shapes also seems like a good precursor to formal demonstrating of propositions. Playing with blocks certainly can't hurt, either.

Understand the Euclidean method and structure of argumentation.

When I first looked at an edition of Euclid, I had trouble seeing it as a math book. After all, there were no "problems," no arithmetic or even algebraic equations. Perhaps that is an advantage for modern students, who become accustomed to using their brains as calculators. This kind of mathematics uses the part of the brain that thinks and wonders and puzzles. But reading the Elements is not the same as reading a work of literature or history. You have to read carefully, and understand the structure of the arguments, and keep your mind active as you read. Perhaps you might even want a notebook or slate next to you as you read.

A book called Class Lessons on Euclid, in public domain, has given me some of the background I felt I was missing. The first 3 chapters give some reasons for studying Euclid {along with some information about his life}, discuss the definitions and axioms that precede the propositions, and tell about the structure of a Euclidean proposition. Even if a student or parent got no further than this, it would not be time wasted, because the logical paradigm of defining terms, listing presuppositions, and building syllogistic arguments is used in many Great Books. These are useful habits or skills for deciding any kind of serious issue in life, as well.

{...to be continued...}