Friday, December 27, 2013

Reflections of an Odd Year

Like my friend, Amy in Peru, I prefer doing reflections at the end of the year instead of resolutions at the beginning. I spend more time blogging the resolution of my camera, which captured the lovely reflection of sunshine on Lake Warnock to the right, than I do blogging New Year's resolutions. In fact, not one post talks about them!

I have noticed a distinct pattern in the past decade of my life. The oddest things happen in odd years: major changes of job for Steve (necessitating a move), amazing projects landing in my lap or dwindling away, switching churches (not often I am glad to say). Some of the most surprising shifts that I could not have predicted in a million years (and, yet, God knew all along) happen in odd years.

The year 2013 was no exception. Some things, I have already shared. At the beginning of the year, I had no idea that two friends and I would found a school based upon a Charlotte Mason style of education. God clearly had been carefully laying plans for years, but He did not bother to tell us until June. Watching Pamela integrate into a class (more on that in another post), helping other families with autism, and seeing children get excited about the world makes the hard work worth it. It also keeps me busy when Steve is working in Kansas (and started working there in 2011—another odd year).

While it stinks that eleven hundred miles separate us from Steve, we are enjoying being able to see so many wonderful things on the long trips back and forth as regular readers of this blog know. This time, we are doing something different and, as my friend Di points out, change gives our older children with autism a chance to think and become resilient. Steve scored uber cheap tickets, so Pamela and I are flying back to South Carolina. What luxury!

About a week before we were due to drive to Kansas, Pamela realized that the babies could not come. She has flown enough to see the disadvantages of hauling five babies through TSA. She asked her brother David, who planned to stay home and rack up some overtime, to babysit for her. She also told me she could only carry one backpack, instead of two or three or four. Since we are without typical schooling materials, Pamela texted the following to Steve, a week after our arrival: "I am getting journel, pencil, chip, hamburger, pickles and coke cola."

Two things I loved about Pamela's mindfulness: (1) she spotted the problem and solved it and (2) she shared her plan with me. If your child in the spectrum struggles with being mindful, Di came up with two important questions and changes you might want to try: What am I doing? Why am I doing it? The poster she created summarizes what has helped Pamela learn to think for herself.

Some exciting changes have been brewing all year, but I cannot share them until January 2014. Years are like road trips. You never know what is going to happen along the way. Steve and I took turns driving through two weather fronts on the long trek from Carolina to Kansas. We left pleasant, sunny weather in Carolina. While going through Kentucky, we discovered that the weather app on his phone makes a loud noise when severe weather alerts are issued. A tornado watch and flash flood accompanied the heavy rainfall. The next day, we saw vehicles, askew in odd positions with parts flung every which way, on the icy leg from St. Louis to mid Missouri. [Notice how I subtly worked in another photograph of a reflection.]

Since the ice storm had already blown through, the road conditions were better than we had expected. When we stopped for coffee on the icy section of the trip, we spotted thick layers of ice, coating the branches of the tree. As we headed to Kansas City, the precipitation shifted to six inches of snow. The ginormous Angus cow statue sported an icicle goatee and a white blanket. The temperature on Planet Hoth was a brutal ten degrees and simply getting out of the car sucked the breath out of me.

At sunset, about a half hour from Steve's place, the Missouri river bridge leading to Kansas offered a neat view. Wave upon wave of black birds flew over us. The procrastinating geese that had gotten caught in the frigid weather traveled in their V-formation.

What surprised us most was how uneventful the drive was in spite of all the wide and varied road and weather conditions. The smooth journey ended at Steve's place. The landlord had failed to have the neighborhood and public parking areas plowed. In eleven hundred miles of traveling across half of our country, we nearly got stuck in the driveway when we backed out to make a supply run.

God sure has a sense of humor!
Have you entered the storehouses of the snow or seen the storehouses of the hail, which I reserve for times of trouble, for days of war and battle? What is the way to the place where the lightning is dispersed, or the place where the east winds are scattered over the earth? Who cuts a channel for the torrents of rain, and a path for the thunderstorm, to water a land where no man lives, a desert with no one in it, to satisfy a desolate wasteland and make it sprout with grass?
Job 38:22-27

Friday, December 13, 2013

Peacefully Guided

In God's wisdom, our Sunday school class read Isaiah 55 last week. Reading from this Old Testament book of the Bible in the weeks leading up to Christmas is quite appropriate because so many passages foreshadow the coming of Christ.
Come, everyone who is thirsty, come to the waters; and you without money, come, buy, and eat! Come, buy wine and milk without money and without cost! Why do you spend money on what is not food, and your wages on what does not satisfy? Listen carefully to Me, and eat what is good, and you will enjoy the choicest of foods. Isaiah 55:1-3
Many think the goal of education is employment, or working for food that spoils. Jesus knew that life is more important for he said, "Do not work for food that spoils, but for food that endures to eternal life, which the Son of Man will give you" (John 6:26-27). What kind of work endures? As we head into a new year, we might want to take a breath from busyness and consider what work brings light and life into the lives of others.

Last Friday, we read Tennyson's "The Dying Swan," so today, we discussed our poem for recitation ("The Owl") before finishing the last chapter of our science book. One student wondered why Tennyson chose the word hay instead of grass. We ended up talking about the last word in each line and then came the "aha" moment for her. Then, we noted what Tennyson was trying to portray (the owl's view from the belfry). Another student added, "Owls can turn their heads all the way around"—implying how much of the world the bird could see while sitting still. I had not intended this for happen, but the section of the science book that we read included this quote,
Other aircraft are a danger as well. Turbulence from a helicopter can slam an ultralight to the ground. When an army helicopter cut in front of Mark south of Numidia, he had a few anxious moments before he knew he was safe. As for swans—they can hit the plane. Mark says, "You have to know where the birds are all the time and be ready to dodge every second. I need an owl’s head so I can turn to see directly behind me."
Everyone's eyes lit up. We were all amazed that an accidental pairing between poem and science book had happened twice in a row! Accident, or whisper from God?

Education is life. A mind awakened to beauty and truth in the world God created. A soul seeking His presence. A person who cares enough to ask, who longs to know.
Pay attention and come to Me; listen, so that you will live. Seek the Lord while He may be found; call to Him while He is near. Isaiah 55:6

In this busy season, we find it hard to pay attention and come to the Lord. Yet, the only way to live is to seek Him and pay attention. This habit is hard to come by in this screen-infested world. Getting outdoors and seeing what God created with His own voice is one way to practice the habit of attention, especially when we are quiet and still. Nearly everyone in our walking group passed this katydid without noticing it. The student who found it explained, "I just saw this tiny bit of green. Everything is so brown right now that green just pops!" She has been walking this trail for almost a year and a half, which helped her develop the habit of attention.

"For My thoughts are not your thoughts, and your ways are not My ways." [This is] the Lord's declaration. "For as heaven is higher than earth, so My ways are higher than your ways, and My thoughts than your thoughts." For just as rain and snow fall from heaven, and do not return there without saturating the earth, and making it germinate and sprout, and providing seed to sow and food to eat, so My word that comes from My mouth will not return to Me empty, but it will accomplish what I please, and will prosper in what I send it [to do]. Isaiah 55:8-11
Some friends are facing a season of rain and snow because of heartbreaking challenges in life, due to no fault of their own, beyond their ability to change or control. The extreme and exhausting behaviors of puberty on top of autism. Sitting at the bedside of dear ones in the hospital. Waiting in the emergency room watching your child in pain. In the long winter nights of cold, hope is hard to see. God's ways and thoughts are hard to understand when things appear bleak. Somehow, even after tears saturate the earth, God provides and His will is done. Narnia will thaw; it always does. Spring is always around the bend, whether the bend is in this lifetime or the eternal one.

You will indeed go out with joy and be peacefully guided; the mountains and the hills will break into singing before you, and all the trees of the field will clap [their] hands. Instead of the thornbush, a cypress will come up, and instead of the brier, a myrtle will come up; it will make a name for the Lord as an everlasting sign that will not be destroyed. Isaiah 55:12-13

Sunday, December 08, 2013

Poetry for Its Own Sake

A few weeks ago, I copied the following entry from The Living Page in my commonplace book.
When my aunt gave me a poster for the back of my bedroom door so that I regularly fell asleep to Emily Dickinson's avowal, "or help one fainting robin into his nest again" no moral imperative needed to accompany it. I knew that Love notices. I knew already what the "poor robin" looked like.
Because the elementary class at Harvest studied Dickinson last term, I shared the quote with them. A deep magic began.

Two students recited "or help one fainting robin into his nest again" as I read it. Then, they begged to recite the whole poem "If I Can Stop One Heart from Breaking." Half the class joined in the group recitation. One student stood up, announced with dramatic flair, "Let me say it alone," and recited it from memory in a crisp, joyful voice.

One student confessed, "When we did exams last week, Mrs. Tammy let me say only one poem. I wanted to do them all."

Another chimed in, "Me, too!" A third said, "Let's do it now."

The class recited three more Dickinson poems en masse: "Hope," "I'm Nobody," and "Autumn." I saw smiles beaming from the large table around which the students gathered.

We turned to the term's poet Alfred Lord Tennyson. One boy asked why we were not reading Dickinson. He seemed a bit sad! We sailed into new territory, and I recited a new poem, "The Eagle." They quickly spotted alliteration in "He clasps the crag with crook hands, close to the sun in lonely lands."

The first time they studied alliteration required attentiveness and thinking. I wrote several examples from Dickinson's poem "Forbidden Fruit" and asked them to spot the pattern. To prevent one person from robbing another of the opportunity to discover, each student had to come to me and whisper what they noticed. The class was delighted to work out the definition for themselves:
  • forbidden fruit
  • hopeless hang
  • color on the cruising cloud,
  • the hill, the house
Poetry is rich towards words. We cannot help mining new gems from poems. The students wondered what Tennyson meant by the phrase azure world, so I pointed them toward their knowledge of Spanish. "Azul!" declared one student. "He's talking about the blue sea," exclaimed another. Another opportunity to wonder and think and discover.

On Friday, on a whim that turned out to be a whisper from God, I read "The Dying Swan" to the class. At the end, several students remarked about how sad the poem was. Then, another smiled and concluded, "At least, we know it's in swan heaven." I picked the poem to go with the science book we have been reading all term. Unbeknownst to me in advance, the passages we read included the death of a swan! We all marveled at the unexpected connection, and again, they reiterated, "As least we know it's in swan heaven."

We also assigned the next poem, "The Owl." Pamela and I spent the weekend memorizing the first three lines (yes, I memorize them, too, for my own sake). Pamela struggles with the first line because it lacks articles. The second line comes more easily because the grammar follows the rules. Learning to be flexible with language for the sake of beauty gives her the chance to think dynamically. Since this poem has such a striking rhythm, I have spotlighted rhythm for her to feel why Tennyson leaves out the article the.
When cats run home and light is come,
And dew is cold upon the ground.
Adding proper grammar crumbles the meter.
When the cats run home and the light is come,
And the dew is cold upon the ground.
As Law writes in a Parents' Review article about Tennyson,
The first poets were invariably minstrels, and it is still expected of a poet that he should be able to "sing a good song." Nor is this a bad test of poetic faculty. In a song a lack of melody (if I may borrow an illustration from music) cannot be disguised by cunning harmonies or learned orchestration. It is also a test of sincerity: a song makes a direct appeal: we can tell at once if it rings false. Again, we know as soon as we hear it whether our poet is quite spontaneous, or straining himself, forcing the note. As a song writer, Tennyson ranks with the highest.
As we are studying John James Audubon for our artist and birds for nature study to prepare for the Great Backyard Bird Count in February, we will ask them to classify the owl based on the clues in the poem. Several phrases ought to give away habitat: "merry milkmaids," "new-mown hay," "thatch," and the cock singing "his roundelay." "The white owl in the belfry sits" gives it away completely if you ask me.

Students in some schools churn out slipshod didactic cinquains as a scheme to practice their parts of speech—a recent experience for me during a tutoring session last month. The children at Harvest are far more blessed. They get to build memories of sitting with a friend and reciting together for practice... acting out a poem to forge a link to the next line... sharing a poem with a student in another class at lunch... getting to recite a poem as part of their exams...

For more on the teaching of poetry for its own sake, check out this Parents' Review article.

Friday, November 29, 2013

Thanksgiving Menu

Food choices have come a long way since Pamela started a gluten-free, casein-free diet. In fact, they have come a long way since I blogged my first Thanksgiving menu post which always gets hits this time of year. I am very thankful that we can put on a traditional spread with traditional ingredients missing.

This year, we had a turkey and stuffed it with the cornbread stuffing mentioned in that first post. We have never missed making a favorite in our house, cranberry conserve—delicious on top of the turkey and very yummy mixed with yogurt in the race to gobble leftovers before they go bad.

I continue to experiment with old favorites as new products have come on the market. I have found coconut oil a delicious substitute for butter and shortening, which we used in mashed potatoes and biscuits made from the recipe on the back of a box of Bisquik, which debuted on our menu three years ago. The other wonderful product is Pillsbury's refrigerated dough for pie crusts. What's not to like: convenient and edible for Pamela. [Pillsbury now offers tubs of gluten-free pizza dough and chocolate cookie dough, too!] I still make the pumpkin pie recipe from the back of a can of Libby's pumpkin, double the spice.

We added two new items to the menu this year. Both were a hit. Neither required any substitution. I made maple-bacon roasted pecans for snacking, and they are so addictive! I am heavy-handed with spice, and I will probably increase the spice next time. Our vegetable was roasted asparagus: quick, easy, scrumptious.

Since we did not have time to make a health food store run, I invented with a whipped cream topping for Pamela's pie. I skimmed the layer of fat at top off of a can of coconut milk and put it in the refrigerator to harden. I whipped an egg white into a meringue, adding in a little sugar once the soft peak formed. Then, I folded the egg white into the coconut fat. Pamela loved it!

Our GF/CF Menu
Cornbread Stuffing
Cranberry Conserve
Mashed Potatoes
Roasted Asparagus
Maple Bacon Pecans
Pumpkin Pie
Coconut Cream Topping

Little Sides for the Non-Dieters
Toasted Bread with Butter
Whipped Cream for the pie

Monday, November 25, 2013

Making *GOOD* Time on the Road

Nancy Kelly's wonderful advice for rich holiday reading has inspired me to share tidbits for rich holiday travel as well. Pamela and I are making two trips to and from Kansas this season. As the drive is twenty plus hours one way, we include an overnight stop. We also take advantage of inspiring rest stops like Carl Sandburg's home, the house that Manly built, a replica of Little House on the Prairie, the National World War I Museum, Gettysburg, just to name a few. While some stops cost a little and last an hour or two, we never regret making the effort. As one of my friends says, "I like to make good time on the road—emphasis on good!"

Taking time to stretch our legs, our eyes feasted on beauty at the St. Louis Art Museum for nothing more than a voluntary donation. I chose to keep ten dollars for parking underground in my pocket and walk in the bitter cold because of the plentiful free parking. The added bonus was this gorgeous view of the reflecting pool in front of the museum.

While we had planned to visit a couple of dear friends (van Gogh, Monet, Millet, and Winslow Homer), the first painting that captured our attention was this ginormous painting of King Charles I by Dutch artist Daniel Martensz Mytens the Elder. This trip revealed that art is a shared experience, not just with your companion but also with friends from afar. When we spied this commemoration of his coronation, I recalled a conversation with the elementary class at Harvest Community School last week. The students are very much aware that Charles I lost his head, so they were intrigued that Carolina and Charleston are named for his son, Charles II, who managed to keep both head and throne.

Pursuing van Gogh, we came across this version of the madonna and child by Davide Ghirlandaio. The Roman numerals, MCCCLXXXIV, painted on the stairs caught Pamela's eye, and she quickly read the date as 1486. Again, I thought of the elementary students at Harvest because they want to learn Roman numerals since some books number chapters in this manner.

Monet's Water Lilies were gorgeous, and seeing someone notebooking increased my delight as I revel in The Living Page by Laurie Bestvater! We finally found three van Gogh's in a row. Pamela said her favorite is the one to her right, Factories at Clichy. Van Gogh included two tiny figures in front of the factory, hard to spot, but logical when considering how small we are beside the mechanical wonders made by our hands.

While the dancing grapevines in Vineyards at Auvers (shown clearly in this detail) tugged at my heart, my favorite is Stairway at Auvers, a painting which quivers with delight. Again, I am reminded of our school for the primary class adored this painting by the artist they call "Rainbow Man." When I texted a picture of Pamela standing beside the stairway to a friend whose children attend Harvest, her kids were amazed that we saw the masterpiece with our own eyes.

On the way to Millet, we spied greyhounds painted by another realist Gustave Courbet. We had to take a picture for our friend Eman, the ultimate dog lover. We even texted a picture of Pamela and the greyhounds to his mom. The other day, when we were walking with him to pick up lunch, we saw this cute little white dog named Lily. He could not contain his delight and said, "It's a Maltese! I love her!" As she was wearing a brown sweater, I let it flow into an impromptu Spanish lesson with the teen who had joined us. We figured out how to describe the encounter in a second language, "Veo una perrita blanca con un sueter pardo. Su nombre es Lily."

Right next to Knitting Lesson by Jean Francois Millet, we saw Girl with Mandolin by Jean-Baptiste-Camille Corot. Seeing the mother teach her daughter to knit brought to mind the finger-knitting lessons on the porch swing at school. One student taught another, and, before long, the entire elementary class knew how to make scarves and belts. I had to take a picture of the Corot for my friend Leslie adores this artist. I tagged her once I posted the shot on Facebook.

Before reaching our final destination, we met George Washington by Gilbert Stuart, pictured on Pamela's left. Apparently, Stuart cranked out so many of these portraits that he called them hundred dollar bills! Pamela and her class has been reading a short version of his biography in Four Great Americans. How serendipitous to find his portrait on the way to Winslow Homer's The Country School, which brings to mind Understood Betsy, a book that our entire school just finished reading.

I will conclude with this collection of arms and armor from the Middle East and Far East, which remind me of the boys who spend recess imagining themselves as heroes and villains in battles, real, fictional, literary, historical, and invented. Making GOOD time is not about how fast you finish a journey. It is about making good memories, reflecting on past experiences, and sharing your discovery with friends.

We study art for its own sake! However, if you must find a utilitarian reason to visit art museums in this standardized-test-obsessed world, this article might convict you. "Students who, by lottery, were selected to visit the museum on a field trip demonstrated stronger critical thinking skills, displayed higher levels of social tolerance, exhibited greater historical empathy and developed a taste for art museums and cultural institutions."

Friday, November 15, 2013

Where I Host the Charlotte Mason Blog Carnival

I am thrilled that our gracious hostess Amy Tuttle has invited me to write the Charlotte Mason blog carnival on my very favorite topic: mathematics. Of all people, our missionary friend, who lives in a valley between mountain ranges in Peru, understands why Mason called mathematics "a mountainous land which pays the climber, makes its appeal to mind." I encourage you to read Mason's actual words because what she wrote about this invigorating topic may not be what you expect: pages 230 to 232 in her sixth volume (the modern paraphrase of this section is here).

Once you have Mason's words firmly in mind, check out Nebby's consideration of Mason's warning about proportion and mathematics, which rings true in our STEM-obsessed society: Why Study Math? Barb McCoy, a veteran homeschooler who has graduated her children, describes in great detail what I mean by STEM-obsessed society in her post, Our Children Have Not Changed, Math Standards Have. The culture, wrapped in its Enlightenment thinking, has forgotten the point of education: "We homeschool to create a better person in our children. We all are not brilliant in math or science or art or whatever subject you can fill in the blank with. We can let our children be the best that they can be without looking at a standardized test score."

Children are born persons, not percentiles!

You may be scratching your head and wondering how math could offer joy and beauty. Read what Amy Marigold, who is starting to see math with her Maker's eyes, shared about her journey with math: "The natural world is filled with numerical and spatial relationships, that man has been discovering for generations. And God put it all there—to create it, to order it, to keep it running."

How does it look teach math in a way that invites children to appreciate its beauty and truth? Mason stated that "Mathematics depend upon the teacher rather than upon the textbook and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination." As Sarah points out in Math Lesson, good teachers like her husband use the textbook as a springboard and supplement with manipulatives when necessary. In Third Grade Math, Laura also offers real-life activities with concrete objects to go with a computer program and a free arithmetic textbook from Mason's time.

Good teachers present living ideas that inspire and engage and consult textbooks for problems.

Some of us in the Charlotte Mason community are exploring what Richele Baburina calls living teaching in her book on mathematics. I encourage you to read it since she had access to a short, but insightful publication that Mason quoted extensively: The Teaching of Mathematics to Young Children by Irene Stephens. Because the pamphlet is copyrighted by none other than His Royal Majesty, King of England, you cannot simply find it on a search engine nor can you find it on eBay. Thus, one cannot digitize it and post it as a free PDF. Richele drove to Harvard Library in researching Stephens' writing for her book. Richele filled in many gaps for me.

I met Richele at the Living Education Retreat where her talks on math inspired some of us to apply and blog inspiring ways to reveal the truth and beauty of math. In her blog carnival post, she explains how to teach children about multiplication. Bobbie-Jo also attended the retreat and posted her reflections on how to teach mathematics in a living way. I have also written about applying living teaching methods to a child in the autism spectrum who likes math as much as Sam liked green eggs and ham. Two blasts from the past at the Common Room offer ideas for teaching math through play and laundry. At LER, Bobbie-Jo introduced us all to paper sloyd, a wonderful way to blend mind, hands, and heart with math (a student made the envelope in a paper sloyd class) and Nancy Kelly, one of LER's founders, shares what loving eyes and patient hands in her home have done. And, if you still have not had your fill of math, check out another blast from the past: math week at Afterthoughts.

Because "education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child's mind should deal with," I am happy to share posts on other topics dear to this mathematician's heart. Why? As much as I love math, I love other beautiful things in God's creation. No life should be shut out of the living page, poetry, nature, and art!

Notebooking - Notebooking is integral to how Pamela lives and learns. Every time we visit a museum she draws at least one picture of her favorite item. Today, we joined our school away from homeschool, Harvest Community School, on a field trip to the South Carolina State Museum for the Tutankamun: Return of the King exhibit. Because our school follows Mason's principles, the students brought notebooks and sketched their favorite item (or two or three). If you want to learn more about notebooking from a Charlotte Mason perspective, The Living Page by Laurie Bestvater, is a must-have, even if it is the only book you buy for the rest of the year! She is the person who inspired my excitement about notebooking and now we have a whole school of children filling up living pages. For a lengthier review, check out what Dewey's Treehouse has to say about this new and worthy contribution to CM literature.

Poetry - One of the delights of this week was being able to hear every student in the elementary class recite. One young lady blew me away with nearly perfect recall of Joshua 1:6-9, which she memorized during the first two weeks of school! Several children chose "Autumn" by Emily Dickinson, the poem from last week, while one picked "Hope" and another, "If I Can Stop One Heart from Breaking". For an example of students reciting poetry, read Bonnie Buckingham's thousand thoughts blog post. Ann at Harvest Moon by Hand also offers how her daughters react to the intriguing words of Walter de la Mare. You cannot help but long for beautiful words after reading these posts!

Nature Study - What would a Charlotte Mason blog carnival be without nature study? You are never too young or too old to become enchanted by God's marvelous handwork. Here, one of the scribes (recorders of oral exams) meets our classroom pets: Ben, the worm snake, and his friends, a frog and a slimy salamander. Our school has weekly nature outings to a nearby wildlife refuge as does Celeste, who documents her family's experience with pictures of their visit, collections, and notebooking (glorious living pages for you to see). If you are up for an Outdoor Hour Challenge, Barb McCoy offers some ideas for studying woodpeckers. I know it's cold out there, but get out and enjoy creation! And, if you decide to blog time spent watching nature, feel free to post a link at Fisher Academy International.

Picture Study - Our school just wrapped up a study of an artist whom they affectionately call "Rainbow Man" because of the colorful way he paints his hair and beard in self-portraits. During the term finale, I marveled at the wide and varied things our students remember about van Gogh. Of course, the salacious story about why his ear was bandaged is at the top of the list. One student thought his art was very messy, but another was fascinated how awful it looks when you are close to the painting and how it transforms into something beautiful as you back up. One child observed how sad he must have been when he painted the peasants because they were so dark. The three most talked about paintings were Starry Night, Sunflowers, and Self-Portrait in Front of an Easel. We concluded our study with a two-sided puzzle and an alternative way to recall the painting of van Gogh's bedroom. For more impressions of what children have to say about art, read a post by Ann at Harvest Moon by Hand about a study of the work of Carl Larsson.

A hearty thanks to all contributors which made this carnival blog possible!

Monday, November 11, 2013

Help for Those Who Hate Math

Last July, I had the pleasure of meeting Richele Baburina, author of Mathematics, An Instrument for Living Teaching, at the Living Education Retreat. Her insights have helped me enormously with a student in the autism spectrum who has declared loudly to us at the school: "I HATE MATH!" "IT'S TOO HARD!" "IT'S BORING!" "YOU JUST WANT TO ME WRITE PAGES AND PAGES OF STUFF!"

I empathize with his views of typical math curricula. As Richele points out in her first blogpost on mathematics, "Though its use in daily life was important, it was the beauty and truth of mathematics, that awakening of a sense of awe in God’s fixed laws of the universe, that afforded its study a rightful place in Charlotte’s curriculum."

Does typical math curricula inspire awe over God's fixed laws of the universe? Does it point to the beauty of mathematics?

When he sees a worksheet full of equations, my young friend shuts down or melts down! As Richele states in her second post on mathematics, such worksheets are not CM-friendly. They are convenient for moms and teachers because they give us a break from individualized instruction.

Rather than haul out workbooks, I assessed his addition facts orally with different manipulatives: dominoes, dice, etc. He seemed to know them, so the headmaster of our school and I assessed him in two-digit addition. Rather than pass out a worksheet, Angie pulled out her 5" x 8" notepad to emphasize the shortness of the lesson! She asked him how many problems he could do. He told her six. So, she gave him a couple of problems that did not require carrying. He made no errors.

When she wrote down one that required carrying, he struggled. Rather than disrupt the flow by pulling out manipulatives, she appealed to his sense of reason. She wrote above the two columns of the problem, tens and ones, and explained that this number is like a house. It has two rooms, the tens room and the ones room. Only numbers that are 9 or less can fit in the room. She asked him where he thought then ten part of 13 should go. He answered, "The tens room. Is that why they do that?" (carry the ten). From that day, he always knew when to carry and when not to carry. That week, he gave correct answers for tricky two-digit addition problems: some with a three-digit answer or with 0 in the ones place of the solution. He sailed through three-digit problems!

His math book offered addition problems with decimals next, so I asked his mother what he understood. Not much. I asked her about his understanding of fractions because they lead to decimals. She stated that he knows the basics, so, this week, I shifted to assessing him in fractions.

My friend bores easily, so variety is the name of the game. Because I am mindful of shared experiences (the joy that comes from collaboration—a challenge for those in the autism spectrum), I seek situations that invite him to work with me. Richele calls this living teaching:
  • Teach math concepts in a hands-on, life-related way that assures understanding.
  • Encourage daily mental effort from your students with oral work.
  • Cultivate and reinforce good habits in your math lessons.
  • Awaken a sense of awe in God’s fixed laws of the universe.
On the first day of our foray into fractions, he explored fraction overlays. To pique his interest, I asked, "Guess what I made!"


"I made this basket."

"You did? What's in it?"

"Some fraction overlays.

"What are those?"

"Take them out and see!"

Eman pulled out all of the overlays and made circles with the fraction slices. As he put them away in the way he found them, we talked about the names of the denominators for halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths. He knew them all, so I took notes on what he did and what he knew. This task covered more than fractions: taking out and storing the pieces exactly as he found them required fine motor skills and practiced the habits of attentiveness and order. He spent at least twenty minutes doing math and enjoyed it!

Knowing that Eman loathes repetition, I found another hands-on task the next day. I asked, "Guess what the kids in your class are making!"

"I don't know. What?"

"Leonardo da Vinci's parachute."

"Really? Can I try?


"But I want to work outside!"

"We can do that."

We headed outdoors with pencil, ruler, and four pieces of paper. Together we folded each paper in half, drew diagonals, and cut along the diagonals until we had four triangles. We talked about the shapes we noticed (rectangles and triangles). Then, we put them together as shown in the picture and I said, "It reminds me of the fraction overlays from yesterday." He agreed, so I probed.

"It looks like there are pieces missing. How many do you think are missing?"


"So, if we had those pieces, what kind of fraction would we have?"


After that exchange, I began to wonder if boredom might be the culprit. This hands-on, meaningful task revealed a keen understanding of fractions that rows and rows of problems might not have uncovered. Then, we taped the triangles together and I showed him how he could make a tent. I asked, "Do you know what this shape is called?" "A pyramid." Yes, he really is bright.

Eman's mother loved the parachute project and told me that his visual-spatial awareness is keen. The next day, I printed out a model of a dodecahedron. Before we started, we had a little chat about the pentagons. Then, he wanted to know what a ten-sided shape was called and then a twelve-sided shape. I made a grid with twelve squares for him to color to represent each side: 3 red, 3 green, 3 yellow, and 3 blue. My printer was running out of cyan, so only one pentagon was true blue. Eman insisted that the other two were purple, which made for a more interesting problem. While coloring the grid, he said, "I remember doing these in school. I liked it." Then, he wrote fractions for all five colors.

He seemed worried that cutting would be too hard. When asked what he could not do, he said, "The black lines."

"I can cut the white tabs. What can you do?"

"The colored ones."

We took turns cutting, and then he folded all the sides without any help. Then, we took turns taping it all together. When finished, he just had to roll the dodecahedron like a dice!

To avoid boring him, I chose six red and six blue buttons the next day. Eman had to sort them by color, size, and number of button holes and make fraction grids. After doing the color count, he told me he wanted to try his own problem. He insisted.

I asked for a topic. He chose cats and dogs, and I selected a much more challenging problem: conduct a survey about liking cats or dogs. When Eman had a hard time choosing cats or dogs, he created a new category: both. He polled students, teachers, parents, and even the ladies painting the new elementary classroom. He interviewed 27 people and checked their preferences. He asked how to spell their names and wrote them down! This math problem encouraged writing, communication, social interaction, attentiveness, and patience (we had to wait for kids in the primary class to come out for bathroom breaks and lunch). Moreover, this problem inspired Eman beyond the length of a typical math lesson.

I made a printout to show his data and apply equivalent fractions. Tasks were picking a color scheme, coloring a grid that had bars the same size as labels for him to convert thirtieths to fifths, and making a bar graph as well as a pie chart in both denominations of fractions.

Because of the trust we have built, his first reaction was not complaining about it being too hard. He studied it for few seconds and asked, "Did you make this?"

"Yes. I did. I learned how to make these in college."


He enjoyed picking out the color scheme, counting up the responses, and coloring in the grid. At one point, he told me, "I like this!" He figured out the fraction in thirtieths and had no problem seeing that 6/30 was the same as one bar and that he needed three brown bars to make 18/30. He has not fussed about math in over a week.

Tomorrow, we will make the connection to fifths, color the bar graph, and make the pie charts. In time, I hope he will learn to love math for its sake because he has encountered enough inspiring ideas to endure the repetition required to learn those facts that must be learned.

Education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child's mind should deal with. ~ Charlotte Mason (page 231)

Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the 'Captain' ideas, which should quicken imagination. ~ Charlotte Mason (page 233)

Monday, October 14, 2013

Science for Students in the Autism Spectrum

Temple Grandin worries that schools do not value of hands-on learning. In a recent blog, she wrote, "One of the worst things the schools did was taking out the hands-on classes such as art, music, sewing, woodshop and auto mechanics." Art gave her something to look forward to doing at school every day: "My ability in art was always encouraged, and both my mother and my teachers encouraged me to draw and paint many different things. I loved getting recognition for several of my best elementary school art projects."

We are blessed to have part-time and full-time students in the autism spectrum at our school. I think Grandin might like our approach to science and art by the scenic trail of nature study. The primary and elementary classes are reading Minn of the Mississippi by Holling C. Hollings. To help them feel the "realness" of the story, I shared pictures of my family's visit to the headwaters of the Mississippi at Itasca State Park about ten years ago.

Some autistic students develop the habit of frustration for a variety of reasons. It takes time to help them find joy in learning what is beyond their pet interests. Every person is different, so what works for one autie may not inspire another.

Eman is teaching me so much. He often refuses to try because either "it's too hard" or "he's bored." He does not enjoy keeping a nature notebook until he finds something that delights him, in which case he begs to draw. One day when he was dragging his feet, I let him tape pictures to a page and narrate what I should write. Novelty is a big hook for him, and being able to use double-sided tape for the first time made a few notebooking experiences positive. When that novelty wore off, I tapped into a positive episodic memory of last year when he joined us for the turtle release party. I showed him pictures of those very turtles: the cage my friend constructed to protect them from crows, the nest, the hatchlings, and the dud.

When the classroom after lunch was too much for him, we switched to reading Minn in the morning. We focused on finding joy in his tasks. When he wanted to draw a story about Minn in his silly notebook (comic strip things that make him laugh), I encouraged him to start an unsilly notebook (comic strip things related to what he is learning). When he asked to read outside on a sunny day, I agreed if he promised to do his best on the notebook. And, he did! One day, he drew seven different scenes representing the most emotional moments of Minn's life: her hatching, getting her leg shot off, her canoe ride, meeting the fox, scaring the boys in the pond, laying eggs, and snapping at the dog's tail.

Right now, working on the pond gives him joy. Watching what happens when we turn on the water pump that pushes water through our homemade water filter is exciting. We stand at the little pool and watch it with anticipation until the water reaches the top of the stones and forms a waterfall. One day, the filter overflowed and he watched the headmaster solve the problem. Somehow, cleaning leaves out of the pond gets him to thinking about turtles. Before long, he is ready to read more about Minn's adventures, draw it in his unsilly notebook, and read it to his mother.

On another day, a cockroach caught his eye. He was shocked when I shared my plans to draw it in my nature notebook. "You keep one, too?" He was so interested in seeing mine that I promised he could look through it once he had finished making an entry in his.

At another time, two doves enchanted us with a stroll around the little pool to get a sip of water.

Speaking of problem-solving, Grandin spotlighted another value of hands-on projects: "Practical things do not always work right and people skilled in the real world learn how to improvise. When I made a mistake on a sewing project, I was sometimes able to fix it and other times I could not. Mistakes I made cutting the fabric wrong on a sewing project taught me that I had to slow down. I had to be more careful before I cut the material."

One day, he helped his class with the compost bin. The lesson screeched to a halt when they discovered worms. He watched the students find grubs and toss them into the pond to feed the fish. Two weeks later, his cat showed up at school. He decided to see if she would eat a worm and he knew exactly where to find them. The cat did not!

And, then, there was the day he found the dead fish. Eman studied it in the net for quite some time. He wanted to touch it but was afraid he might get cut. So, I offered to do it first. A bit grossed out, I put my finger on it for only an instant. "No, you need to do it longer!" So, I held my finger on the squishy fish and it must have been long enough. He mustered his courage and touched it himself.

Mason's thoughts in connection to literary books like Minn of the Mississippi: "The approach to science as to other subjects should be more or less literary, that the principles which underlie science are at the same time so simple, so profound and so far-reaching that the due setting forth of these provokes what is almost an emotional response" (Pages 218-219).

Mason's thoughts in connection to outdoor work: "They are expected to do a great deal of out-of-door work... They keep records and drawings in a Nature Note Book and make special studies of their own for the particular season with drawings and notes" (Page 219).

Mason's thoughts on nature notebooks: "The nature note book is very catholic and finds room for the stars in their courses and for, say, the fossil anemone found on the beach at Whitby. Certainly these note books do a good deal to bring science within the range of common thought and experience; we are anxious not to make science a utilitarian subject" (Page 223).