Clear Thinking about Math Part 1

Sometimes, the best plans fall apart. Pamela seemed to track the review of fraction addition I did early last month. When we went back to area and perimeter problems, something got lost in translation. Fortunately, a friend posted about how she made tiles with numbers and symbols to use on a magnetic board with her grandson. Having to write added enough challenge to chip away at his working memory and make it difficult to a new concept to gel. Pamela writes and draws very well, but I thought it worthwhile to remove any potential memory drain while she was trying to visualize adding fractions. I suspect Pamela lost her thread of thought every time she had to stop and draw her thinking.

I also heeded Mary Boole's advice in an old Parents' Review article,

"Beware of writing, in play-lessons, anything which does not represent some process actually going on in the child's mind."

I created a set of pie charts in a spreadsheet, some representing wholes, some representing wholes split into fractions, and fractions. I stayed simple by limiting it to halves, thirds, fourths, and sixths. I cut out all the shapes, covered them with clear contact paper, and cut them again to make them more durable. Before we worked on a problem, we sorted between wholes and fractions to help Pamela familiarize herself with these homemade manipulatives. You can see the first step in our first lesson in the video below. Since Pamela understands fractions, I am using very declarative language as we collaborate.

Then, we started working on her problem, adding 4 3/4 and 4 1/2. Before writing, she set up a model for each addend so that she could represent her mental process visually and spotlight what adding fractions and simplifying meant. You can watch how we worked through the problem together: first, she made both denominators alike. Because I didn't build any models for eighths, she had to think through another option: fourths.


Then, she added them and ended up with an improper fraction 5/4.


Using the models helped her see what she was doing when converting to a mixed fraction and adding the wholes again.



The video below shows how we collaborated step by step. We wanted to show what we were doing physically and write it on paper.

Working together like this cleared up other glitches. Pamela had a habit of forgetting to write the wholes until she needed them again. While she usually remembered to pick the wholes back up when she needed it, that mathematically incorrect habit could lead to disaster in algebra. When finding a common denominator, she tended to multiply the denominators (2 x 4 = 8) rather than going for the least common multiple (4). The lack of eighths forced her to think of a smaller denominator, which turned out to be the LCM. We worked on similar problems together for about a week. I made a set of twelfths for more challenging ones. Then, I faded myself out of the picture and she did well flying solo without anymore issues.

"Let his arithmetic lesson be to the child a daily exercise in clear thinking and rapid, careful execution, and his mental growth will be as obvious as the sprouting of seedlings in the spring." ~ Charlotte Mason (page 261)

Semi-Wordless Wednesday: Nature Notebook Pages

An update to what we have been doing with our nature notebooks and I have enjoyed keeping my own as well!

JC RIP Deathday Party

Here at Aut-2B-Home in Carolina, we go where angels fear to tread.

We try to learn Spanish while English is being still learned as a first language.

We read poetry and teach vocabulary with nary a worksheet in sight.

We are NOT afraid of Plutarch or the bard.

We are in the middle of Act I, Scene II of Julius Caesar.

Why Caesar? Because Pamela likes him!

We have been reading some Plutarch for more background information and have been previewing the BBC version of this play. Then, we tackle reading a scene or half together. Pamela loves it as you will see in the still-shot and video coverage of our first annual JC RIP Deathday Party. I baked a semi-red velvet cake that is red-dye free, gluten-free, and casein-free in honor of the occasion. Yum! (Seriously, it was delicious.)

David's Home Next Year

For the past two days, we have driven back and forth to Charleston, SC, where David stayed overnight at his number one pick for college: The Citadel, a military college with a long tradition, longer than my alma mater (United States Naval Academy). Steve and I figured that one of two things would happen: David would come home (1) fired up to put on the uniform of a cadet or (2) wondering what on earth he had been thinking. He ended up being the former and even shaved his head last night! We snagged these photos from The Citadel Admissions Facebook page.




The pre-knob visit not only held David captive with programs, classes, and experiences for 23 hours but it also provided the parents with presentations on what parents need to know to get students prepared to become cadets. David has his head and heart set on Marine ROTC and, in the next few months, he will continue to drive up the number of pullups and crunches he can do and drive down his three-mile run time. Actually, he can already pass the PFT's minimum standards but he wants to be competitive for the three-and-a-half year Marine ROTC scholarship and must work hard to be one of the few and the proud. He is excited, and we are excited for him. Ultimately, it is his choice. Nobody wants to be stuck in a place like that unless they really want to be there. I know from personal experience of having seen the most miserable human beings on earth: kids attending USNA to please their father and grandfather who were both graduates.


My biggest challenge is not to call cadets David will bring home on weekends "bus drivers" . . . gotta love the military college rivalries!

P. S. The folks at The Citadel told us this was their largest pre-knob visit ever, which makes sense since last summer saw its highest number of applicants ever.

Revolutionary War Encampment and the Science of Relations

Last Saturday, we explored the annual Revolutionary War Encampment held in our county. Opportunities like that can quickly turn into information overload and fragmented thinking because the number of activities is overwhelming. Trying to do everything, even spread out over a day, makes for a pounding headache, so I heeded Charlotte Mason's advice on the science of relations,

Our business is not to teach him all about anything, but to help him to make valid as many as may be of–-
"Those first-born affinities
That fit our new existence to existing things" (Page xxx).

At first we walked aimlessly until something caught Pamela's attention. She chose the display of rifles and muskets. She saw the musket balls and didn't mistake them for marbles because of a dramatic clip from America: The Story of Us in which a musket ball spins out of the rifle, heading directly toward the camera with the footage slowed down enough to make you sweat. Steve (in the green shirt) was surprised at how heavy the British rifle was while the three-sided bayonet, which the Geneva Convention banned because of the hideous wounds it inflicted, caught my eye. The reenactor also showed us a blunderbuss, which brought to my mind The Matchlock Gun, and his powder horn, which reminded me of Little House in the Big Woods.


Then, she decided to sit for a spell in front of the fire.


Pamela is testing the weight of a cannon ball and checking out a cannon.



Activities like this encampment fit really well into the science of relations because the environment is built for everyone to enjoy. Last Thursday and Friday, local third-graders took field trips to the encampment. Friday night, reenactors led groups of fourteen people into the woods for a lantern walk in which we were being accosted by Hessian soldiers in the middle of the swamp, saw a Tory prisoner escape and get shot, and watched the barber put leeches on some poor schmuck with a musket wound, etc. We heard sporadic gunfire as we tripped over tree roots on the path. I scouted the walk out for Pamela and, next year, I think she will be able to hand the sensory stress because she enjoys pretending. A situation in which people from all walks of life and of all ages share what they love is a perfect atmosphere for the science of relations.

We all relate to things in different ways. When Pamela saw the blacksmith, she connected the hot coals to the burned hand of Johnny Tremain while I thought about The Village Blacksmith. The air bellows and other engineering details fascinated Steve. I pointed out to Pamela that, while Johnny Tremain worked with silver, the blacksmith worked with iron. She added, "Iron age. Child's History of the World." She studied the blacksmith's wares and turned to the triangle to give it a few whacks!

One exciting moment was recalling a new vocabulary word Pamela has learned, not by writing a definition and using it in three sentences, but by focusing on context in wide and varied settings. I gave her the kettle and asked Pamela if she remembered the name of the metal. Her knee-jerk response was silver. I asked her to think about the color and Pamela smiled and slowly said, "Copper!" The copper kettle contained soapy water that we used to felt real sheep wool! The lady showed us the simple steps. Pamela wasn't exactly thrilled about the texture of the soap when we squeezed it out of the felted wool. I loved this connection to the handwork we have been doing, and it reminded me of what Mason said was the point of handwork that "he may know the feel of wood, clay, leather, and the joy of handling tools, that is, that he may establish a due relation with materials" (Page 31).



Francis Marion, who was a sickly child, encouraged all his patriots to drink vinegar water to stay healthy and ward off mosquitos. The smell of vinegar didn't thrill Pamela, and the glories of leeches creeped out Steve and I. Fortunately, no bloodsuckers were on display. Pamela loved the rope bed with its hay-stuffed mattress. She thought of Ricitos de Oro y los tres osos while I recalled Heidi and the bed at her grandfather's house in the Alps.


Pamela's favorite stop reminded me of a trading post with a table of delights that Pamela explored thoroughly. She stayed here the longest and enjoyed all of its delights. It had a bone, obsidian arrowhead, bag of musket balls, lens, turtle-shell rattles, a kalimba, beadwork, knives, cups, elk rawhide, almost anything a patriot could imagine. That table alone was a wide and varied curriculum that provided scope for the imagination!

We Came, We Saw, We Counted . . .

Last weekend, Pamela and I counted birds for the Great Backyard Bird Count and entered our data online and in our nature notebooks. We even made the obligatory watercolor. Until we painted, I had never noticed the light turquoise rim around the eye of a mourning dove.

Somehow, nature notebooks and watercolors have merged into one and the same. Guilt over having done only one watercolor this year has bugged me--and we didn't even put it in the notebook. We have made regular entries whenever we studied a topic (like painted butterflies, ladybugs, and camellias), all in markers. When I didn't have a study planned, the notebook collected dust. When I posted the pictures on Facebook, one wise friend opined that "we all have our favorite medium for drawing and do our best work with it." I think we will try other media and see what Pamela likes best. I have a feeling markers will win the day because she likes vivid colors and fluidity.

Charlotte Mason saw these notebooks as "travelling companions and life records wherein the 'finds' of every season, bird or flower, fungus or moss, is sketched, and described somewhat in the manner of Gilbert White" (Page 223). While I gloss over peers mentioned in her books, another brilliant friend emphasized the need to know who exactly Gilbert White was! White, an eighteenth-century naturalist, gardener, and priest in Hampshire, England, "observed things closely in their natural state" rather than "dissect and examine in detail the animal or plant before them; dead, cut off, out of it’s natural environment, there, on their table or desk" (Tony Grant). White kept regular, dated records of his locale so that he understood the life cycles in his habitat. If you peek into his book, you see occasional pictures and a great deal of description based upon years of careful observations like the ones Pamela has been making (and her wisterbuds are from watercolor pencils).


Since White and children differ in developmental levels, Mason scaffolded the study of nature. The source of these notebooks was the nature walk, an artful blend of atmosphere, discipline, and life, "Every day's walk gives him something to enter: three squirrels in a larch tree, a jay flying across such a field, a caterpillar climbing up a nettle, a snail eating a cabbage leaf, a spider dropping suddenly to the ground, where he found ground ivy, how it was growing and what plants were growing with it, how bindweed or ivy manages to climb" (Page 55). As soon as children could draw, they kept a nature diary illustrated with dry brush drawings. Over time, they form relationships with things in nature and "know a plant by its gesture and habitat, its time and its way of flowering and fruiting; a bird by its flight and song and its times of coming and going; to know when, year after year, you may come upon the redstart and the pied fly-catcher, means a good deal of interested observation" (Page 236). As the writing skills develop, children "keep records and drawings in a nature notebook and make special studies of their own for the particular season with drawings and notes" (Page 219). In later grades, they focus on knowing what to expect in a particular habitat, know the parts of different things, keep lists of birds and plants, and supplement their personal knowledge with carefully chosen books. In upper levels, their work begins to fit into branches of learning typically seen in schools gleaned through field work and scholarly books, instead of textbooks.

Because of Pamela's aphasia, I'm not sure how incidentally I can teach scientific vocabulary. Mason avoided dousing the joy of nature walks with a flood of scientific blather with beginner nature notebookers. Teachers threw in a word here or there, but too much jargon would make it harder for children to store up common knowledge needed to understand formal instruction in later years. The ultimate aim is for them to "know and delight in natural objects as in the familiar faces of friends" (Page 237). Books and occasional object lessons and microscope work supplement outdoor study. To give Pamela a framework, we are going to document signs of spring and note the life cycle of the neighbor's wisteria right now.

One thing you may notice about Pamela's nature notebook is the imperfect writing mechanics, especially in this world of beautiful lapbooks. Now, I am not knocking lapbooks at all, just illustrating a distinction. From a Mason point of view, we aim for notebooks to represent where our students are in their understanding and we hope for it to be a product of their hands, minds, and hearts, grammar glitches and all. If I mined notebook entries for writing lessons, Pamela would figure that out, robbing her of the joy of writing. Mason wrote, "Certainly these notebooks 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).

A nature notebook records where she is today. If we peek into where she was two years ago--when we were wrapping up speech therapy a la the Association Method, we can see the progress from stilted, repetitive language to something more free and original. Mason pointed out, "The children keep a dated record of what they see in their nature notebooks, which are left to their own management and are not corrected. These notebooks are a source of pride and joy, and are freely illustrated by drawings (brushwork) of twig, flower, insect, etc." (Page 236).

I also wavered back and forth between wanting to keep my own notebook and feeling guilty because Eve Anderson, a thirty-year veteran of teaching PNEU schools, discouraged teachers from making their own entries during a nature study lesson. I began to think of my class of one student who loves to draw and writes with ease, albeit with a few errors here and there. Pamela really doesn't need me to supervise each and every step of making entries. Why not keep my own notebook? I shared that decision with friends on Facebook and a homeschooling friend wrote that she does the same. It helps her to be in the role of a fellow learner, easing the way to share pencils and paints and discuss color choices and observations. So, I am going to try keeping my own notebook, side-by-side with Pamela.

My friend Jeannette Tulis faced a similar dilemma. She taught a co-op class with 17 first graders and never had success with dry brush watercolor for the fine motor skills of her crew were not developmentally ready. They spent most of their time indoors but did head out on particularly beautiful days. Even though she didn't perfectly line up with a Mason nature study program, she met the number one objective of a Mason science program, to inspire awe and wonder: "Where science does not teach a child to wonder and admire it has perhaps no educative value" (Page 224). Tulis wrote, "I was delighted by the spark I saw in many of my students’ eyes as we learned together of the intricacy, wisdom and wonder of God’s creation. And that, in the words of several of my students, was truly cool!"

P.S. If you want to understand why nature notebooks are so valuable in teaching children many things, including science, check out Carroll Smith's keynote presentation on nature study. Be prepared to be inspired and have fingers itching to head straight outdoors and observe and record!

Grand Conversations

Today Pamela and I delivered meals on wheels, and I became very mindful of how much she has changed in her ability to experience share. If I only assessed quantity (length of sentences and number of words), I might be disappointed because of her aphasia. The quality of her conversations are terrific. Persons with autism tend to speak in verbal stims or focus only on certain favorite topics. Pamela still does that to some extent and I see it most when she is feeling incompetent or upset. It is her way of calming down and reassuring herself.

This morning the third stop on our list caused Pamela to scream. We walked to the apartment, and the gentlemen was sitting outside in a chair. So far so good. There was another man inside his place cleaning, and it was absolutely empty, not one stick of furniture. On the ground near the sidewalk was a large sheet of broken glass. After her squeal, I reassured her that everything was fine. I gave the meal to the man, and he explained that he was moving to another apartment in the complex. Pamela pointed to him and said, "No! You're not moving." He told her that he was, and we said good-bye. As we walked to the car, I told Pamela, "The man is moving over there." She looked and added, "Not leaving Manning." I replied, "Yep. He wants to be near his family."

We were getting near the end of our route and I decided to sign the sheet. I handed it to Pamela for her signature. She looked up at me surprised, "Are we done?" I answered, "No, we have two more stops." I did something out of the norm, so she commented on it, which is part of experience sharing. She could have waited to see what would happen but her curiosity drove her to ask.

As we were driving home Pamela pointed out the saucer magnolias blooming and asked, "What's that?" I answered her question and loved that she wanted to continue a conversation from yesterday. When we drove home from lunch, we noticed the signs of spring. I pointed out the flocks of robins and pink crepe myrtles blooming. She noticed the bright green grass in one of the fields. We are going to add our observations to nature notebooks.

We were almost home and here was another little gem:

Pamela: What about April?

Me: What about it?

Pamela: April 24

Me: Oh, Easter!

Pamela: It's late.

Me: You're right! It is late.

Pamela: What am I going to wear?

Me: I don't know!

Pamela: Short sleeves!

All of these questions were fresh like Spring. Pamela shared new thoughts that were emerging in her mind. They were important enough to her that she wanted to tell me. She reflected on the context of what we have been doing: delivering meals and looking for signs of Spring. She pondered what everything meant. She stayed in the moment. Isn't that grand?

P.S. It goes to show that one doesn't need to question, prompt, and correct to chat with a person with autism.

Sweet Moments Treasured in My Heart

Saturday afternoon, Steve and I drove the Chevy to the levee (okay, it was the uncatchy VW) and walked about three miles along the lake. The sun glimmered on the waters, and a gentle breeze cooled us as we headed back to the car. When we returned home, Pamela and I counted birds for the Great Backyard Bird Count. We stood for a half hour at the kitchen window and, although the count was low due to a pesky hog-faced squirrel at the feeder and an evil cat who adopted a neighbor last summer, we enjoyed our quiet time together. Yesterday was our final day for the count. At seeing our last two customers, I broke out into song, "Two mourning doves!" Without missing a beat, Pamela improvised, completely impromptu, "And the cardinals on a bird day!"

Then, the Saturday miracle happened. You might not think of it as miraculous but any family dealing with autism knows one when they see it. Pamela and I headed to the store to pick up some things. She picked out a small bag of chips to go with her burger for dinner. I know I bought the chips. I saw the clerk put them in the bag. I put all the bags in the car. Somehow between the car and the house, the bag of chips disappeared. I don't know where it went. I don't know how it happened but the chips vanished.

While she is mature enough to avoid a full-blown meltdown, we usually cannot avoid tears in such situations. I spent ten minutes looking in all the cabinets, drawers, refrigerator, and car. Pamela remained calm and joined me in the search. I apologized several times while we looked everywhere. When she realized that the chips were gone, she looked over to the gluten-free bread our neighbor picked up for us Friday. She said, "Chips, next time." She quietly opened the bag of bread and fixed her hamburger. Pamela kept herself so well-composed I stopped her after she grabbed two pieces of bread. I hugged her and looked her in the eye. I told her she was so brave and stayed so calm about the chips. I smiled at her, and she smiled back at me and nodded, "Yes!"

Today was another warm, gorgeous day and so many lovely things filled my heart to near bursting. Pamela and I studied in the morning. She flew through math and remembered many details from our readings about the Presidents. Last week, I introduced her to the electoral vote by playing with a spreadsheet about the 2000 presidential election. We looked at the popular vote first which leads you to one conclusion. Then, we went state by state, looking at the results of the popular vote, and assigning electoral candidates. Since Florida was the source of so much controversy, we did that state last. The electoral vote lead to another conclusion, which is the constitutional one.

Today, when Pamela narrated the presidential elections, she told me they were counted by state! Woo hoo! Then, we read the lesson which talked about how Andrew Jackson held the first national convention to pick a candidate for the party. That was something I had forgotten (if I ever learned it in high school). The first one for Jackson's party, the Democrats, occurred in Baltimore, Maryland in 1832.

Before plunging into A Child's History of the World, Pamela told me what she remembered about the Bronze Age. She said, "Caveman had fire. Made copper. No wire. No electricity." I replied, "They didn't make wires. I wonder what they made." She answered, "Hammers. Knives." After reading and narrating, we talked about the map in the book. Pamela made a connection to the Caspian Sea because it reminded her of Prince Caspian.

Our lesson on sculptures was spectacular. Sculptures? Yep!

As always, we recalled what we did last time, which was draw an Assyrian tree of life into a slab of Sculpey clay, which we baked to harden it. To start today's lesson, Pamela made rubbing with crayons. Then, we inked it and tried making stamps. The original drawing was more like a sunken relief sculpture (the one on the right) because she carved into the clay. We made a second slab and made an imprint of it, which turned out to be like a high relief sculpture (the one on the left). But, that was not even the cool part!



I glanced over the first sentence of the book, which talked about a chop. "Today in Japan and China, artists sign their names with a stamp made of carved stone called a chop." Suddenly, I realized that we have a couple of them in our house! Whenever Steve travels overseas on business, he always picks up interesting objects. On one trip, he brought home some chops. I sprung off the couch and grabbed one. We inked it up and stamped the paper. I told Steve about what happened later on and we both had a good laugh. When we were in the Navy, senior officers had to put their chop on paperwork, which meant they had to initial it--the Captain in green and the Executive Officer in red. We had no idea the term's origin was connected to the Chinese stamps in our office! If that wasn't enough, the reading ends with talking about different museums in which you can find Assyrian sculpture--one is located in Baltimore (a connection to our reading on the Presidents)!

The rest of the morning went smoothly. Pamela had another surprise for me. When we sang "El Coqui" in Spanish, Pamela harmonized! Since it is a very short song and we are still learning the lyrics, we repeated it a few times. Every time we sang it, Pamela sang a third above the melody. She has never done that before, and I just loved it!

We ate lunch with some homeschooling friends who are interested in Charlotte Mason's ideas. They asked me to do a "show and tell" to give them a glimpse of how we do things. We sat at umbrella tables in an outdoor patio out back and the children who came enjoyed playing together. As we talked, we soaked up the sunshine and fresh air. Afterwards, as we began to chat about how we all met one by one in unusual ways for a small town, we realized that only the hand of God could make such a meeting possible. So many disconnected threads all woven in such a beautiful way. I have been hoping to become involved with a local study group for the past ten years, and it looks like this one has fallen into my lap. Suddenly, I felt very loved and cherished by my Father in heaven.

‎"The world is perishing for lack of the knowledge of God and the Church is famishing for want of His Presence. The instant cure of most of our religious ills would be to enter the Presence in spiritual experience, to become suddenly aware that we are in God and that God is in us. This would lift us out of our pitiful narrowness and cause our hearts to be enlarged." ~ A. W. Tozer