The Pointlessness of Precalculus

I know! Algebra is not used every day. People mock its pointlessness all the time. This showed up on Facebook the other day. You can spend your life escaping algebra! Woo hoo!

What we learned in history, science, and poetry is not useful either. When do you use a historical date? Recite Poe? Balance chemical equations? Calculate acceleration? But, I digress.

I was tutoring a senior (Jay) in precalculus while a junior in the same class (Kay) watched. The following conversation ensued.

Jay: "Mrs. Tammy, when am I ever going to use this?"

Me: "I used this sort of thing to learn high level statistics, and my husband did to learn engineering."

Jay: "I'm not going to major in any of that. This is useless!"

Kay: "My mom teaches math. She never uses this stuff."

So, I admitted what everyone knows. We'll never need to prove trigonometric equations in real life. I shared what I love about these problems. It's like the Gordian's knot. Tug at the right spot, and the whole thing unravels quickly. The same thing that drives Sherlock Holmes to solve mysteries drives me to prove equations. A puzzle. A mystery. A quest. How exciting when you find the right key (or two) and the knots disappear!

Jay had to prove the sides of the equation to be equal even though they look different. Many manipulations shows they are the same. This looks much scarier than it really is!

I ask students what to do first. If I hear a confident "cross multiply," we continue. If I hear a faltering "Cross multiply?" doubt arises. Some students speak jargon that confuses them. So, they launch a buzz word, hoping it's the right one. Then, I ask why cross multiplication. If the explanation makes sense, we move ahead. Otherwise, we linger.

I ask what they can do to make the equation easier. "I don't like fractions!" [That is why we cross multiply.} Then, I ask how to dump the fraction. Most know to multiply the fraction by its denominator (the bottom). I probe further to see if they know why you multiply both sides by the denominator.

The reason so many students falter in math is that they do not understand the why behind what they are doing!

Imagine the left side of the equation sits on the left side of a balance, and the right side on the other. Multiplying the left by a number greater than 1 increases its weight. Doing the same thing to each side keeps the balance. This applet shows this for simple equations! Some pre-algebra materials sow the idea of seeing equations on a physical scale and viewing them as puzzles.

The joy of math is found in unraveling complex mysteries.

Multiplying both sides of the equation by sec θ - 1 scares some students. Working with fractions, however, is scarier! We treat this ugly expression the same as any simple number. Including parenthesis avoids confusion.



We multiply by sec θ - 1 to create sec θ - 1 over sec θ - 1.



Why? Well, what is sec θ - 1 divided by sec θ - 1? Relax! Take deep breaths. What is 2 ÷ 2? One! What is 300 ÷ 300? One! What is a million ÷ a million? One! What is cheese ball ÷ cheese ball? One! So, what is (sec θ - 1) ÷ (sec θ - 1)?

ONE!

See that's not so hard even if the fraction looked ugly. Now, we have rid ourselves of fractions and all is well.



Some eye the right side of the equation nervously. Why would anyone want to times one number by the difference between two other numbers? Suppose you find your favorite microwave lunch on sale for $2.94 and you want to buy one for each day of the week. You have $20.50 cash on hand. Do you have enough money? While Pamela might be able to multiply 2.94 by 7 in her head, lesser minds like mine can alter the problem slightly and solve mentally, too. The product of 2.94 and 7 is really seven rows of 2.94 as illustrated below.



If we alter 2.94 a tad, we have something easier to manage mentally. What? How can 3.00 - 0.06 be easier than 2.94?



Mulitiplying 3.00 - 0.06 times 7 looks like this.



We can multiply in our head! Yes, 7 times 3 dollars is 21 dollars and 7 times 6 cents is 42 cents. Taking 42 cents away from 21 dollars yields $20.58. Alas, you can only buy six meals.



On the left is another way to illustrate the distributive property. This little rabbit trail has a point for those who do not like the look of cot Θ (sec Θ - 1). You can try to multiply vertically if horizontally worries you.



Sadly, the equation is still ugly. Do you see the next step? Take one step, and the equation looks prettier. Try to focus on what you can remove completely. Think about the analogy of the balance and what you can take off both sides.



Each side of the equation has - cot Θ. Are you stuck? Pretend it's something less scary like - 2. What can you do to - 2 to turn it into zero? Add two! What is - 2 + 2? Zero! What is - 300 + 300? Zero! What is negative million + positive million? Zero! What is negative cheese ball + positive cheese ball? Zero! So, what is negative cot θ + positive cot θ?

ZERO, zip, nada!



The new form of the equation looks almost friendly compared to the original rubbish. At this point in the game (to me, it is a game), I convert everything on the right side to sin θ or cos θ and let the chips fall where they may. These little identities are things that you memorize with use and can always look up if you aren't suffering through a test: csc θ = 1/sin θ and cot θ = cos θ/sin θ and sec θ = 1/cos θ. I simply plug and chug on the right side from here on out!

Patience Rewarded

Something funny happened on the way to blogging math. Pamela surprised me again, and several perfectly timed articles got me to thinking.

Right now, our readings address the end of the 19th century and the beginning of the 20th. I chose In My Father's House, the autobiography of Corrie ten Boom, as a bridge from the period to World War II. Before leaving for Kansas last week, we read about her encounter with a mentally-ill man named Thys. As a child, Corrie prayed for the alcoholics and homeless people living on the streets near her home. She and her sister Nollie came across a crowd of children picking on Thys. The passage we read began,

I was so full of pity for poor Thys and angry at the cruel children that I shouted, "You leave him alone, do you hear!"

The children stopped at my bold challenge. They looked for his defender and saw a little girl, less than half his size. Suddenly he walked toward me and stooped down. I could smell the unpleasant odor of his unwashed clothes and matted beard. He put his hand under my chin and kissed me on both cheeks.

Corrie went on to say that her sister Nollie, appalled at the kiss, whisked Corrie home. After hearing about what happened, their aunt scrubbed her face. At bedtime, their mama noted that Jesus was the source of her pity and kindness and that praying for street people might be a safer thing for little girls to do.

Yesterday—about a week later—Pamela read the next section. First, she narrated our last reading. Her retelling of the heated emotion of the scene came out in a burst of loud, angry words. "Corrie sees bullies. ANGRY! Leave him alone! Go away! Went to bed. Mom said obey. That's citizenship." Many things struck me about her account in that Pamela:

• Clearly felt Corrie's passion.
• Accurately labeled the children as bullies, a word not used in the passage.
• Recognized what Corrie did as a good deed even though her mother was worried.
• Picked a perfect word to describe Corrie's behavior: citizenship.

We do not work on vocabulary directly. Children glean word meaning from context. They do not need to copy the definition and use the word in three sentences. Is that how you taught babies new words? Is that how you beef up your vocabulary?

Pamela enjoys looking up words in the red discovery book (dictionary) and encyclopedia for fun. Curious about her knowledge of citizenship, I asked her where she read about it. She said, "In encyclopedia." I asked why she thought Corrie was doing citizenship. She explained, "Citizenship stop the war. Corrie stop the fighting." Then, I began to wonder. She reads my planning spreadsheets where I loosely categorize her school books as subjects. I had this book listed as World History, not Citizenship! Her summation of Corrie's action was truly an original thought!

Many students with autism prefer textbooks. Expectations are predictable. Having to answer the questions of others means more black-and-white thinking. Much of the work required is mindless busywork. Even though Pamela would find textbooks easier, I think going the living book route promotes more flexible thinking and more experience sharing.

Several articles that appeared in my Facebook feed yesterday affirm the elements of our approach to education:

• Reading Aloud to Older Children Is Valuable - Pamela and I read books in the manner described in the article, "And they read the Bard’s plays together, divvying up the parts, because 'that's how they are meant to be experienced.'" (We are reading aloud Macbeth right now!) Reading aloud to older children offers academic and emotional benefits. It broadens the menu by adding more challenging books. One mom describes how more pleasurable reading becomes for her daughter with dyslexia, "Reading together–with her watching the words as I read, and then her reading to me–is a way to be together, to experience the world, to enjoy a common pleasure." Retired teachers who reconnect with former students online find the most memorable thing they did as a class was reading aloud.


• Multi-Tasking Equals Failure to Filter - The jury is out on whether inattentive folks are born that way or are the product of chronic media multitasking. When several modes of data stream in, heavy multitaskers cannot ignore the irrelevant. They find organizing and storing information into memory difficult. They do not even switch attention faster. In a nutshell, information overload slows down their ability to process. That sounds a lot like autism!


• The Mind Is Made for Story - Modern textbooks promote multitasking. My son switched to public school as a junior. I was appalled at his precalculus textbook. The math book looked like it had ADHD: graphics, sidebars, pop-ups, font variability, etc. When looking up information to help David with his questions about math, I found it hard to follow a train of thought. Living books embed the information contained in graphics and sidebars into a narrative account. We can follow the train of thought in living books because our minds respond to stories.


• Lingering a Living Book in a Term or Year Supports Long-Term Memory - Modern students have to pack a textbook into one semester, and their classes can take up to ninety minutes. Packing in information over a short, intense period of time is called massed studying. Science backs up common thinking that cramming is ineffective. Yet, students today have to learn that way thanks to block scheduling. My high school spread out a math textbook over two semesters in five fifty-minute periods five times a week. Distributed study is far more effective. My husband's high school offered one math class. It weaved algebra, geometry, trigonometry, statistics, etc. over the course of four years. He never took long breaks from algebra in order to learn geometry. He aced his math classes in college!


• The Real Issue Might Not Be Inattention! - Students today have so many entertainment choices they can avoid boredom. When something loses their attention, they tune into something else. Having no other option forces you to stick with what you are doing. Jennifer Roberts, professor of art and architecture history, assigned her students to write an in-depth research paper based upon a three hour study of any painting in a nearby museum. Continued looking at one thing revealed something new. The longer students the painting, the more they discovered. Patience was rewarded. Living books are another way to encourage sustained attention, and the joy of reading them is the reward.

And, folks, I am not the only person not giving up teaching an adult person in the autism spectrum to communicate! "the neuroplasticity necessary for new language learning that was not supposed to exist in this population, did exist. Many of the students desperately wanted to crack the code of conventional communication, and their brains were capable."

Amen!

Instead

In case you haven't noticed, I've had a three-week hiatus from blogging. A situation that has been percolating for a long time has boiled over and spent my mental energy. I have several blog posts on the back burner. I kept replaying the situation, imagining new scenarios, and rehearsing my response instead of living. Last Friday, I started reading the text for next week's Charlotte Mason Blog Carnival and suddenly an idea hit me! I needed to apply "the way of the will" to myself.

God has prepared me for this situation through two Sunday school books read in the past year. Counterfeit Gods by Tim Keller has helped me identify idols in my life while Facing Your Giants by Max Lucado helped me realize the importance of focusing on God instead of my giants. He is also sustaining me through it for He keeps pointing me back to Beth Moore's James, Mercy Triumphs, a Bible study we just finished.

Until Friday, I did not apply head knowledge to real life.

God is encouraging me. Two Sundays ago, our pastor, unaware of the issue, addressed the situation perfectly in his preaching. I found myself texting Steve during the sermon. A few days later, John Piper posted a conference message on the very same verses! As I listened to that message, God orchestrated the sun to peek out of the clouds and fill me with delight just as He did five years ago when I was sitting on my back porch reading the book Desiring God. Friends on Facebook have posted my favorite Bible verses. In one case, I had been meditating on a passage falling asleep the night before and the next morning it was in my message feed. God is there when we seek Him instead of trying to fix a problem.

Even on the way to Kansas, when traffic bogged down due to road construction, He let my eyes rest on these words and on this brilliant sunset.





My local friends have built me up instead of tearing me down: one stopped by bearing the gift of a fragrant basil plant and a card that quoted Plutarch! A friend who can find the perfect card is truly constant! I dislike contradicting the wisdom of Plutarch but constant friends really are not all that rare when you have friends in Christ. God is reminding me of His love through my spiritual family at church, homeschool friends, and long-term friends.

On Friday, I chose "I will" (keep my eyes on God) instead of "I want" (having my way in a situation beyond my control). Each time my thoughts drifted off, I studied a Bible verse I hope to memorize. I turned to the book of James. Since then, I have slept better than I have in weeks. I feel more peace.

God is encouraging me to choose instead. He put that word on Pamela's heart—imagine Him giving such a word to a person who has struggled with words most of her life. Yesterday, whenever she did not like a choice we were offering, she deliberately used it in a sentence. "I want to go to the park instead." "I'm doing instead: Wednesday, not Sunday." Whenever she says, "Instead," I am reminded to be more mindful about my choices. By choosing to dwell on God instead, I am dwelling with Him. When I let Him handle my burdens instead of me, He gives me rest.

Jesus, I am resting, resting, in the joy of what Thou art; I am finding out the greatness of Thy loving heart. Thou hast bid me gaze upon Thee, and Thy beauty fills my soul, for by Thy transforming power, Thou hast made me whole.

O, how great Thy loving kindness, vaster, broader than the sea! O, how marvelous Thy goodness, lavished all on me! Yes, I rest in Thee, Beloved, know what wealth of grace is Thine, know Thy certainty of promise, and have made it mine.

Simply trusting Thee, Lord Jesus, I behold Thee as Thou art, and Thy love, so pure, so changeless, satisfies my heart; satisfies its deepest longings, meets, supplies its every need, compasseth me round with blessings: Thine is love indeed!

Ever lift Thy face upon me as I work and wait for Thee; resting ’neath Thy smile, Lord Jesus, Earth’s dark shadows flee. Brightness of my Father’s glory, sunshine of my Father’s face, keep me ever trusting, resting, fill me with Thy grace. ~ Jean Pigott

Science—Absolutely FASCINATING, or creepy—or BOTH!

Another chapter in The Raptor in My Prius series.

Every other week, bloggers write for the Charlotte Mason Blog Carnival. This round we discussed how education ought to be about a life well-lived. I like how the hostess of this week's carnival added a nugget to the principle "Education is a life"—"Homeschooling for life and not a lifestyle." Another shared, "Being the living, breathing example we wish our kids to follow is one powerful way to educate them. Allowing them to see us being self-disciplined, kind, interested in the world, curious, loving, humble, happy, thankful, careful—just letting them see good things in us—is one-third of a Charlotte Mason style education."

That got me to thinking about our weekly walks...

Amy Tuttle, organizer of the carnival and homeschooler in the mission fields of Peru, also got me thinking about those walks: "What about the bits that LOTS of people, including myself in my youth, have had a mind to think are unbearably boring and void of living matter, like Math? And Science? There's so much memorization of Latin names and body parts and tables and elements and formulae and hypotheses and lab book entries... We might admit, if it weren't for such an immense body of facts, it would be absolutely FASCINATING."

Is your study of science absolutely FASCINATING?

Ours is. The Friday feast at Santee National Wildlife Refuge is one reason why. Every week, something new captures our attention and thoughts and ideas begin to sprout in our minds. Last Friday, we came across an oak gall. We noticed caterpillary things crawling out of it, which didn't make sense for wasps pupate in galls (we know that from reading these wonderful nature readers). At first we were absolutely fascinated and wondered what these "caterpillars" could be. We saw some here.



We saw some there, clinging to moist spots on tree trunks. We even found a "tree of life"—a term coined by one of our young naturalists—a spider, slug, and caterpillars all in one crook.



As we walked, we began to notice more of these things, writhing on tree trunks. Hundreds of them. The hair began to creep up on the back of my neck. Or was that one of those, um, THINGS?



Then, we began to see thousands of them. It seemed like millions of them: wriggling and writhing. We started to feel a bit horrified, as in Alfred Hitchcock movies. While I felt like fleeing from the woods screaming, never to return again, the Mrs. Frizzle in me calmed down and took pictures. "I can't wait to post these on Facebook!" However creepy they are, they are part of nature. God created these things for some reason.



Then, we came to the gauntlet—branch hanging over the path. And, I know you can guess what was crawling all over that too-low-for-comfort branch. THOSE THINGS!!!!!!!!!!!!!!! Somehow, we kept our composure and managed to stifle our discomfort into small shudders. I admit to ruffling my hair and shirt just to make sure no unwanted visitors had hitched a ride. And, what was the reaction on Facebook from friends whom I know to be avid enthusiasts of nature? "EWWWWWWWWW!" "Oh, and what is this?" "nononononono" "Oh! I was about to say how beautiful the design on that tree was. Didn't realize they were alive! lol!" "Bleh!" "That is weird." Nobody seem to know what they were, so I posted a spotting at Project Noah (hat tip: Jennifer Gagnon). As much as I adore BAMONA, my intuition said that these things were not going to transform into lovely moths and butterflies.

The folks over at Project Noah identified them as MILLIPEDES! Their reaction was a bit warmer. "These are definitely millipedes—I can see two sets of legs per segment. I've never seen so many together before! Neat Find Tammy." "Interesting! This is awesome Tammy." "It is probably also a group of young millipedes that are about to leave the home site." "Here's another millipede aggregation of a different species. It looks like it happens every once in a while! Lucky you! :)"

LUCKY US!

I've always wanted to see MILLIONS of MILLIPEDES! I can take that off my bucket list now. Did we go back the following week? Of course! We had to know if they were still haunting the trails of Santee.

An idea struck me. All of our students are still in elementary school and preschool. They are a few years, or more, away from all that memorization often required in high school biology. When they reach the study of myriapods, they will remember when they saw millions of them leaving their home site.

These children will not have to memorize the difference between toads, frogs, and tree frogs. Just yesterday, they caught a southern toad eating a worm. They are raising southern leopard frogs from egg to frog. They know where green tree frogs hang out on sunny mornings (in the swamp grass).





They have seen parents grow curious about a spider. This arachnid is a wolf spider, but not our state spider (the Carolina wolf spider). This sad little fellow, Schizocosa crassipes does not even have a common name! How tragical is that?

When the time comes to learn about the order Odonata, they will remember the day they had to sit still in the grass and wait for dragonflies to rest on some grass or a leaf. The meadow where eastern pondhawks buzzed overhead like a horde of helicopters, and their littlest sister kept trying to catch them. They will know why dragonflies earned such a name because they saw one carrying around some bug for breakfast. High school biology will be more about memories, rather than memorization, for them.



They will remember how odd we must have looked, sitting on the grass, quietly waiting for the perfect moment to shoot these pictures of predator pondhawks.





They will remember how different seeing a fleeting picture of a horde of pondhawks is from experiencing the real deal. They will appreciate how fewer mosquito bites occur with dragonflies on patrol.

They will know that nature is to be respected. When you kick at an ant hill, you might get bit!

Consider, too, what an unequalled mental training the child-naturalist is getting for any study or calling under the sun––the powers of attention, of discrimination, of patient pursuit, growing with his growth, what will they not fit him for? Besides, life is so interesting to him, that he has no time for the faults of temper which generally have their source in ennui; there is no reason why he should be peevish or sulky or obstinate when he is always kept well amused. ~ Charlotte Mason

Turtle Release Day

What is an idea? we ask, and find ourselves plunged beyond our depth. A live thing of the mind, seems to be the conclusion of our greatest thinkers from Plato to Bacon, from Bacon to Coleridge. We all know how an idea 'strikes,' 'seizes,' 'catches hold of,' 'impresses' us and at last, if it be big enough, 'possesses' us; in a word, behaves like an entity.

If we enquire into any person's habits of life, mental preoccupation, devotion to a cause or pursuit, he will usually tell us that such and such an idea struck him. This potency of an idea is matter of common recognition. No phrase is more common and more promising than, 'I have an idea'; we rise to such an opening as trout to a well-chosen fly. ~ Charlotte Mason

An idea is a slippery thing. It is not something to capture in a snapshot because an idea is alive. It is hard to recognize until seen in action. Once an idea takes hold, it grows into something beyond the initial inkling. When I first saw a friend post pictures of slider turtle eggs on Facebook in the summer of 2011, I thought it would be neat to study them. She ended up bringing her babies to Pamela's watercolor class. Seeing the turtles swimming made me long to study them more in-depth and attend their release.

Last summer, when my friend posted pictures of the nest, I begged her to let us come over and study them. She graciously obliged us, so Pamela and I saw their nest, peeked at their eggs, and visited them for a well baby check up. Bubbling over with excitement about the turtles, I shared the news with the children in our church afterschool program about nine yellow-bellied slider turtles a friend of mine was raising over the winter. The idea of seeing these little reptiles seized hold of those children. Unfortunately, my friend, a very busy volunteer who gives her time to others in so many ways, could not line up time for the turtles to visit us at church. Nearly every week, the kids would ask, "Mrs. Tammy, when is your friend going to bring the turtles?" Once the idea caught hold of them, they did not let up on begging to see them.

My homeschooling friends were also intrigued at the thought of studying the turtles. I suggested the idea of having a release celebration to the turtle lady, and she thought it would be marvelous to have a send-off for her babies. We timed the party for after our homeschooling gathering, and I invited the children from church, too. It turned out to be a wonderful day. After the initial surge of excitement died down, all my little friends had a chance to study the turtles up close.







Then, my friend dabbed non-toxic paint on the shells. It ended up being a bit messy because the turtles began climbing all over each other, smearing the painted. She placed the turtles in the center of a ring we formed around the turtles. We had a race to see which critter would reach a person first.





After my friend washed the paint off the turtles, we lined them up at the beach and watched them swim away, one by one. Some boldly headed off into the water. Others needed a little more guidance and encouragement from us, as you can see in the video below.

The traveler’s eye picked up a turtle trail,
Between the dotted feet a streak of tail,
And followed it to where he made out vague
But certain signs of buried turtle’s egg;
And probing with one finger not too rough,
He found suspicious sand, and sure enough,
The pocket of a little turtle mine.
If there was one egg in it there were nine,
Torpedo-like, with shell of gritty leather,
All packed in sand to wait the trump together.
~ Robert Frost

Pondering Art on a Good Friday

What makes art worth stealing? As my friend Megan shared this week, Nazis robbed paintings from Jews whom they massacred in the Holocaust. Many items are in museums and private homes. Survivors have struggled to recover treasures of their perished beloved. By the way, this Portrait Study of a Child by Lilla Cabot Perry reminds me of Megan's daughter Hannah, a brilliant violinist with a fabulous voice and author of Brightleaf.

Why is art so important?

Edith Schaeffer—mother of Susan Schaeffer Macaulay who wrote For the Children's Sake, dear to ones applying Charlotte Mason's ideas—left a legacy of art to her children. She died yesterday. Her son Frankie wrote in his tribute to her,

Mom’s great-grandchildren were growing up loving what she’d loved: words, art, music, gardening, cooking and playacting. Mom was unable to speak any longer but she was nevertheless communicating with her children, grandchildren and great-grandchildren every time they were read to, listened to music or when we painted together.

Frankie lists the world's finest artists his mother introduced to him as a child. Now her great-grandchildren love them as well.

I really can't explain why art is so important.

We visited the Nelson-Atkins Museum, which may be an odd way to spend Good Friday. Then, again, maybe not.

Our aim was to meet a Winslow Homer in person. First, we bathed in the art of Europe. Steve spotted St. Francis of Assisi Adoring the Crucifix by Guido Reni. He snapped and posted this picture on Facebook. A new pope with a new pope name has put St. Francis in the headlines. Steve grew up Catholic in Latin America as did Pope Francis.

Speaking of which, Edith Schaeffer was both mother and wife to men named Francis. Frank, the son, wrote of his mother, "Mom was a wonderful paradox: an evangelical conservative fundamentalist who treated people as if she was an all-forgiving progressive liberal of the most tolerant variety." Francis I, also a paradox in thinking conservatively and acting liberally, showed his love for the marginalized by washing, drying, and kissing the feet of twelve juvenile delinquents at a nearby prison, including two girls and two Muslims.

Opposite to St. Francis was Christ on the Cross by Philippe de Champaigne. Christ. The ultimate paradox. And between them, Nicolas Poussin's The Triumph of Bacchus—the very opposite of that paradox, foreshadowing of the excess in our culture.

Studying Peace on Earth by Jacques Lipchitz on Good Friday brought Easter home. Love come down from heaven on the wings of the Holy Spirit. The dove's body, shaped into a cross. Love, the foundation to the gruesome reality of the ultimate sacrifice. What a lovely touch to see clouds hovering overhead, a symbol of the tears shed by our Lord on that dark Friday and of the tears of joy to come three days later. "He will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away."

On our way to finding Winslow Homer, we came across a spectacular view of Jerusalem from the Mount of Olives by Frederic Edwin Church. Even this high resolution image fails to do justice to seeing the painting in person.



We met our Winslow Homer: Gloucester Harbor shared a room with Jerusalem. I admired the gorgeous pink and cerulean blue and wondered if the lads would fish some day like those fishers of men.

In our first meeting with American art, we saw a Georgie O'Keeffe (Apple Blossoms) loved two paintings by Frederic Remington (Teaching a Mustang Pony to Pack Dead Game and Hostiles Watching the Column) and a End of the Trail sculpture by James Earle Fraser.



This silvery illustration for Drums brought to mind the picture of the fluttermill from The Yearling for N. C. Wyeth illustrated both novels.

We explored Kansas City Sculpture Park, the grounds of the museum, for the first time. The weather warmed us as we watched robins seeking worms and daffodils sporting cheerful bonnets. How could one not smile with ginormous shuttlecocks dancing on the lawn? The last sculpture we will share offers one clue to the value of art: Auguste Rodin's The Thinker, which Pamela imitates in her pose.