Monday, February 28, 2011

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!

Friday, February 25, 2011

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!

Wednesday, February 23, 2011

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.

Tuesday, February 22, 2011

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

Monday, February 14, 2011

Copper and Other Things in Context

Science lessons have been quite sweet lately, even though some demonstrations (trying to create static electricity sparks on a door knob) fail. One of my Charlotte Mason friends helped me to see that scientific explorations should flow out of the books we are reading. I am finding them especially powerful in building a context for material in the books, especially when I focus on doing guided participation where I give Pamela opportunities to observe, think, and share.

Pamela is reading about making a better cable as Field and his compatriots plan to lay the first telegraph cable across the Atlantic Ocean. Since I wasn't sure about what she knew about metals, I stripped the coating off ear bud wires so she could see copper wires for herself. At first, Pamela freaked out when I gently cut into the coating. Because she feeds off emotions around her, I stayed calm and neutral and paused until she got a grip. Then, I quietly told her they were already broken. She quickly settled down and watched what I was doing very intently.

The video illustrates what sharing joint attention looks like. She shifts attention to what I'm doing without any prompting because she is naturally interested in what we are doing. When I move the trash can, she coordinates her actions with mine very smoothly. When I am getting close to pulling off the coating, Pamela smiles in anticipation. She expects to see wires and chips in her own comments like "Wire" and "Got it!" She managed to tie in her favorite topic (ancient history) into our task. She tells me what she observes when we finally peek at the wires. I was quite surprised to find color-coded wires in addition to the copper wire.

The teachable moment is looking at something very familiar (coins including those from other nations for variety) and searching for the coin made out of copper. I hope she can tie in a known (pennies) to an unknown (copper metal). At first she didn't understand the task and, once she understands she is supposed to match the metal, she takes an active part in searching for the right coin. I scaffold the ability to see the color by placing the copper wire against a blank index card.
After we explored copper wire, Pamela asked to read A Child's History of the World. One would think that ancient history has nothing to do with copper wires and coins. Wrong! We were in the middle of the chapter on the Bronze Age and the very first idea covered was Stone Age man's discovery of copper, "Now, it happened that this particular rock was not ordinary rock but what we now call 'ore,' for it had copper in it. The heat of the fire melted some of the copper out of the rock, and it ran out on the ground." I would love to tell you that I am so well organized that I planned this. I did not. The beauty of a living books curriculum is unintentional connections that seem to flow out of nowhere.

We are also reading a biography about Alexander Graham Bell, so we explored the propagation of sound. First, I stretched a rubber band around a plastic cup. She plucked it and I plucked it. We talked about how the rubber band moves after it is plucked and, when it stops, you hear no more "music" as Pamela called it. Then, I plucked it and put my finger on it to stop the sound abruptly. After that, I stretched the rubber band tightly and Pamela plucked away. Suddenly, she said, "It's fast!" I replied, "Yes, high sounds go with fast waves." Then I said, "Let's see what happens when you stretch it loosely." She watched and said, "Slow." I confirmed the connection between low sounds and slow waves. That was a VERY COOL science moment for she made that discovery on her own and thought it important enough to tell me--a true sign of experience sharing.

Then, we built a string telephone. Since I found it hard to pierce the disposable cups, I did that for her. I cut a very long piece of string. I took one cup and waited for her to take the other. I grabbed one end of the string and she grabbed the other. As soon as I started poking the string in my cup's hold, she did the same. She copied me for the rest of the set-up: we pulled the string out of the cup and tied it to a paper clip.

We stood up and walked in opposite directions. To create a contrast, we first tried it with the string on the floor. We tested the string telephone phone (I talked and Pamela listened) with the string touching the ground. She told me, "It's broke!" Then we tried it with the string hanging loosely and she again said, "It's broke!" By now, Pamela looked at me like I was crazy. She was probably thinking, "Not another experimental dud." When we pulled the string tightly and I talked, Pamela didn't even have to report the results. A huge smile broke out on her face and I knew the phone was up and running! We talked some more and I had her observe what the string was doing while we talked, tying into the rubber band explorations. Then, I talked to her some more and pinched the string. Pamela said, "It stopped!"

We have also been reading a book about weather and, last week, we covered lightning. Since I didn't expect God to hit us with a thunderstorm in the middle of winter, we watched some videos of lightning on you-tube: a tree getting struck by lightning, tower being hit multiple times, and tree catching fire. When we read the passages on what to do during a thunderstorm, those vivid images gave Pamela context for the readings and her narrations were solid. We used this video to count the seconds between lightning and thunder before we read a passage on estimating distances. Our work earlier in the year on setting up circuits with batteries introduced Pamela to the idea that electricity involves positive and negative charges, so, when she copied this diagram from one of her books, it made sense to her.

Saturday, February 12, 2011

Context Clueless

Last week, I helped a child in primary school with homework. One task was reading four pages on South Carolina history and answering eight comprehension questions. The student, who is bright, read aloud two paragraphs quite fluently and tackled the first question, "What were two money crops early in South Carolina's history?" Here is a semi-faithful transcript:

My little friend: Export?

Me: Do you know what an export is?

MLF: No.

Me: Why did you pick it as an answer?

MLF: Because it is highlighted.

Me: Do you know what a money crop is?

MLF: No.

Me: Do you know what a crop is?

MLF: No.

I felt sorry for my friend! The paragraph included the sentence, "Two money crops important in early South Carolina history were rice and indigo." Anyone adept at thoughtless busywork could have figured out the answer without knowing what a money crop was, much less indigo. I wasn't frustrated because MLF couldn't apply a trick of logic at such a tender age. I was frustrated that such meaning-deprived work exists.

Rather than give MLF the answer, I built context. I asked what farmers in our county grow and got no answer. So, I asked what people buy at the store that a farmer might grow: "Carrots, lettuce, tomatoes." I told the student that a crop is a plant farmers grow for food or to make money. Then, I asked what a money crop might be. Eyes wide, MLF asked, "Do they grow money?" I loved how the wheels turned as the child was trying to make sense of it. I said, "Not exactly. It's a crop the farmer grows to sell and make a lot of money."

Then, I guided MLF's attention back to the paragraph. MLF blurted, "Rice!" Even though, indigo was by rice's side, the child had no idea what it was. No other information about indigo was anywhere on the page. I so wished I had my indigo purse handy and my pictures from our tour of a Colonial Era indigo processing site in El Salvador (in fact, I might just bring pictures and my souvenirs to provide a hands-on, visual experience next time). We discussed how to make natural dyes (strawberries could be red and blueberries could be purple). I told him that the only plant that makes a strong blue like the color of jeans was indigo. People paid a lot of money for this dye.

We whipped through the page about cotton. Before hitting the questions, we studied the pictures and I asked if MLF had ever seen cotton. The child smiled, "It grows in the field near my house." I asked if MLF had ever touched it, and the answer was no. So, I asked if MLF knew what cotton was for and the answer was, "Shirts!" We looked at the picture and talked about how it feels: soft and fluffy. I explained that cotton is hard to harvest because the plant had bristles that would cut your hands and wrists. Then, it took even longer to comb out the seeds. That is why farmers wanted slaves. It was hard work! After our short conversation, MLF zipped through the comprehension questions.

We hit a roadblock on the next page. The main idea of the paragraph was that cotton robbed the soil of nutrients and wore it out. When asked what cotton did to the land, MLF answered, "It made it fertile" because fertile was highlighted. Of course, I asked what fertile meant. No clue. Then, I asked about the color of dirt at home. The answer was gray. I explained, "Fertile soil is dark and black. It grows lots of crops. Cotton takes out the nutrients and the soil turns gray." MLF seemed puzzled, so I gave an analogy about how eating carrots, lettuce, and tomatoes makes our bodies strong. That would be like fertile soil. But, what would eating Cheetos all day do? MLF replied, "Make you weak." That is what cotton does to the soil. MLF answered the questions, and then we moved on.

The last two questions were about opposing views of slavery. The first letter was by the daughter of a plantation owner who didn't think slavery was wrong. That blew the mind of MLF, who read it twice to make sure MLF understood it correctly. Reading the letter by the slave girl, MLF said, "I'd be so scared," when the girl described being separated from her family. Both stories had such an emotional tug on MLF's heart, the answers were crystal clear.

Daniel Willingham's article on reading comprehension dovetails very nicely with this experience. The goal of reading is to find meaning and monitor your own comprehension. He points out that good readers monitor comprehension and seek to correct it when incomplete. When reading the pro-slavery letter, MLF assumed the girl was against slavery and reread the paragraph after realizing the mistake. Willingham discussed how you can apply logic to answer questions, even if you didn't fully understand the meaning, which is what the writer of MLF's questions wanted done.

Another way to enrich understanding is to relate the passage to what you already know, which is what I was helping MLF to do. The more background knowledge you have, the more you are able to understand. Willingham illustrated this with a paragraph on logistic regression. A good reader could infer a great deal from the text, but someone like me (a person with a background in statistics) would have a greater grasp of the text. Because my background knowledge of car mechanics is poor, I would fare poorly with a paragraph on that topic.

Willingham listed a bunch of reading strategies and then pointed out, "Knowledge of strategies is only a small part of what makes an effective reader. A good reader also decodes fluently, has a broad vocabulary, and has wide-ranging background knowledge." A writer cannot include every possible detail because nobody would want to read the text. Writers assumes what the reader knows and doesn't cover that information. If background knowledge is less than anticipated, the reader will struggle. Willingham reasoned, "An individual with background knowledge on a wide variety of subjects will less often be confused when reading than an individual with limited background knowledge." He concluded that systematic instruction and constant exposure to high quality books, films, conversations, etc. is what will broaden vocabulary and knowledge.

Anyone familiar with Charlotte Mason's principles will see the connection:
But we, believing that the normal child has powers of mind which fit him to deal with all knowledge proper to him, give him a full and generous curriculum; taking care only that all knowledge offered him is vital, that is, that facts are not presented without their informing ideas. Out of this conception comes our principle that,--

"Education is the Science of Relations"; that is, that a child has natural relations with a vast number of things and thoughts: so we train him upon physical exercises, nature lore, handicrafts, science and art, and upon many living books, for we know that 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."

In devising a SYLLABUS for a normal child, of whatever social class, three points must be considered:

(a) He requires much knowledge, for the mind needs sufficient food as much as does the body.

(b) The knowledge should be various, for sameness in mental diet does not create appetite (i.e., curiosity)

(c) Knowledge should be communicated in well-chosen language, because his attention responds naturally to what is conveyed in literary form.

Monday, February 07, 2011

Work of Our Hands

To give you a breather before another math post, I thought you might enjoy the work of our hands.

Pamela's Watercolor of a Wolf

Her Latest Drawings

My Scarves

My Potholders and Hot Pad

Friday, February 04, 2011

Adding Fractions with a Graphic Model

I have slowed down the pace of completing Intermediate Math because Pamela is coming across concepts completely new to her that RightStart built into earlier levels. It isn't her fault. What she needs to learn isn't all that hard. It's mainly vocabulary words for concepts that she picks up easily with her pattern-driven mind: classifying triangles as acute/right/obtuse or equilateral/isosceles/scalene, being able to identify parallel versus perpendicular or horizontal versus vertical, knowing what a line of symmetry is and what bisect means, etc.

A person with aphasia struggles with learning new words, so we are spending a month or two going through these ideas at a reasonable pace. That means we will spread out RightStart Intermediate over two whole years. That is okay because I am focused on Pamela and her individual development. Children are born persons, and my goal is to teach Pamela, not to force her into a curriculum. She has already knocked out 45 lessons and all she needs is another 23 to be at the halfway point of its 135 lessons.

A problem with fractions cropped up while working on area and perimeter problems. She started crunching numbers so mindlessly that she confused adding fractions with multiplying fractions. Do you add the denominator, numerator, or both? Do you multiply the denominator, numerator, or both? Many people still confuse these two operations with fractions and turn to their calculators for help. I could have done the same. Or, I could have simply shown her the two different procedures and showered her with worksheets. That is why children in the United States do so poorly in math. We focus too much on memorizing and not enough on understanding. Then, we give up and hand them calculators.

A friend of mine whose son with Asperger's Syndrome is at Cal Tech told me that he had a hard time memorizing procedure. He was fine as long as he understood the concepts. If he forgot the procedure, he could think of a simpler form of the problem and figure out what to do. Pamela had lost touch of the concepts, so we have spent the past three weeks building understanding. First, I focused on addition. Why do we add the numerators only (assuming the denominator is the same)? Did some sicko make up that rule to ruin the lives of elementary school children?

Uh, the answer to that last question is, "No!"

Given the problem 99/8783 + 3401/8783 without a calculator, one might choke. Or, you could turn to an easier problem like 2/5 + 2/5. If you think about it logically, you are adding two numbers, each just under a half. Your answer should be a bit under a whole.

Suppose you are unsure of whether to add denominators, numerators, or both. Try each one and see which makes the makes the most sense:

Scenario 1 - Adding denominators only (the number on bottom) would be 2/10, or 1/5. If you add two positive numbers, you will never get something smaller. That makes no sense!

Scenario 2 - Adding numerators only (the number on top) would yield 4/5, which is just under a whole. That has potential.

Scenario 3 - Adding both would be 4/10, or 2/5. Adding 2/5 to itself would be like doubling it. It makes no sense to double a number and get itself (unless you're talking about 0).

Applying my friend's theory, the one scenario that makes sense would be to add the numerators only. Using reason, we were able to determine that, given the same denominator, adding the numerators is the only logical step. Another logic check would be to think of a real world problem. I cut a pie into 8 pieces. Steve ate 3 pieces, 3/8 of the pie, and David ate 4 pieces, 4/8 of it. That means only one piece is left (1/8), and the menfolk ate almost the whole thing (7/8). The total eaten was 7/8, or 3/8 + 4/8. You could create a visual model, too. The bottom line is that we add the numerators (if the denominators are the same) because it makes sense, not because of some pie-in-the-sky procedure.

"Heeding the call of the indispensable mathematical principle to always break down a complicated problem into simple components" (Wu pg. 6), we focused on adding small fractions with like denominators. Wu also wrote, "It is good to start with simple fractions that children can visualize, and they should do many such problems, until they have a firm grasp of what they are doing." I gave her picture problems like the one above and had her draw the answer and write the symbols for the solution as illustrated below.

Because of her strong eye for patterns, Pamela figure out to add the numerators only after the first day. We spent another day solidifying that "rule" and then I assigned a combination of problems written in symbols (i.e., numbers, plus signs, and equal signs). Knowing the rule is just as important as understanding the concept because we cannot draw complicated problems. "We should not make students feel that the only problems they can do are those they can visualize. We should explain to them that of course they cannot draw a picture . . . But this does not mean they cannot do the problem! Or that more complex problems like this one are not essential" (Wu pg. 2). Once rules makes sense, they are easier to know, or as Wu puts it, "Children always respond to reason when it is carefully explained to them."

We scaffolded the learning of adding fractions in this way:
  • Pictures of fractions with like denominators that add to less than one (5/16 + 7/16).
  • Symbols of fractions with like denominators that add to less than one (5/16 + 7/16).
  • Pictures of fractions with like denominators that add to more than one (15/16 + 7/16).
  • Symbols of fractions with like denominators that add to more than one (15/16 + 7/16).
  • Pictures of fractions with different denominators in which one is a multiple of the other (3/4 + 7/8).
  • Symbols of fractions with different denominators in which one is a multiple of the other (3/4 + 7/8).
  • Pictures of fractions with different denominators (1/2 + 2/3).
  • Symbols of fractions with different denominators (1/2 + 2/3).

In case you struggle with finding a common denominator for 3/4 + 7/8, here it is in pictures:

Here is 1/2 + 2/3 in pictures:

Pamela hasn't mastered the art of finding the least common multiple (or least common denominator or lowest common multiple or lowest common denominator--is there any wonder why kids get confused?). If I introduced it now, she might see it as a pointless exercise. I plan to let her chew on more complicated problems like 11/144 + 17/40 first. Why? I want her to appreciate how wonderful finding the LCM after having experienced the school of hard knocks.
It should be plain to the children (even if they may not be able to articulate it) that this is an efficient compression of a valuable piece of mathematical reasoning into a compact shorthand. They would appreciate this efficiency, let it be noted, only if they have meticulously gone through the laborious process . . . Because young minds are flexible and discerning, the children will learn the algorithm logically . . . they will learn how to reason effectively, and the whole experience will stand them in good stead in their later work. Wu
Now, here's the really cool part for me. Charlotte Mason said these sorts of things a century or so ago:

~ "How is this insight, this exercise of the reasoning powers, to be secured? Engage the child upon little problems within his comprehension from the first."

~ "Arithmetic becomes an elementary mathematical training only in so far as the reason why of every process is clear to the child."

~ "Carefully graduated teaching and daily mental effort on the child's part at this early stage may be the means of developing real mathematical power."

~ "Nothing can be more delightful than the careful analysis of numbers and the beautiful graduation of the work, 'only one difficulty at a time being presented to the mind.'"

~ "The child, who has been allowed to think and not compelled to cram, hails the new study with delight when the due time for it arrives."

~ "Mathematics are delightful to the mind of man which revels in the perception of law, which may even go forth guessing at a new law until it discover that law."