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
Turkey
Cornbread Stuffing
Cranberry Conserve
Mashed Potatoes
Roasted Asparagus
Biscuits
Maple Bacon Pecans
Pumpkin Pie
Coconut Cream Topping
Little Sides for the Non-Dieters
Toasted Bread with Butter
Whipped Cream for the pie
AUT-2B-HOME IN CAROLINA ~ Teaching our twenty-five-year-old daughter with autism and aphasia, who is still learning about God, the world, and its people with a little help from Charlotte Mason
Friday, November 29, 2013
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."
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:
On the first day of our foray into fractions, he explored fraction overlays. To pique his interest, I asked, "Guess what I made!"
"What!"
"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?
"Sure."
"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?"
"Two"
"So, if we had those pieces, what kind of fraction would we have?"
"Sixths."
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."
"Really?"
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)
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!"
"What!"
"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?
"Sure."
"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?"
"Two"
"So, if we had those pieces, what kind of fraction would we have?"
"Sixths."
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."
"Really?"
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)
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