Friday, September 25, 2009

More Outdoor Hour Challenges

Lichen Follow-Up
Last Friday, Pamela became interested in lichen, but she did not know what it was. During the week, she googled "green bark tree trunk" for images and found out its name. We looked up information on lichen, and she typed the following narration for her science notebook:
I saw green stuff on the brown bark. It was lichens. It was a fungus with blue-green bacteria. It grew outside on bark, tree trunks, wooden fences, and even rocks. It will not hurt the tree.

Challenge #2
On Tuesday, we combined Lesson 5, Day 1 of Writing Strands Level 2 with Outdoor Hour Challenge #2, which focused on using words. This series guides parents in guiding their children in nature study. Challenge 2 asked us to read The Field Excursion and How to Use This Book from Handbook of Nature Study. I loved the idea of taking a well-planned, efficient field trip of only fifteen minutes, which my busy schedule demands. The suggestion to preview the outing by talking about what you expect to study dovetails nicely with how we homeschool anyway. I learned to "make the lesson an investigation and make the pupils feel that they are the investigators." How? Keep the information shared in the book's studies to myself just like I avoid giving away spoilers in a novel. Likewise, imperative language (direct questions) kills a nature study in the same way it douses conversation. "If the questions do not inspire the child to investigate, they are useless"--perfect advice for an RDI parent.

For this challenge, Pamela and I sat on the steps of our back porch with lined notebook paper. I explained that we were going to practice sequencing in a story with nature study. She would find words to describe what she saw, heard, and felt and use sequencing words like first, second, third, etc. Since we have been making nature journal entries regularly, I skipped that part of the challenge. Unlike me, Pamela remembered that Tuesday was the first day of fall and I loved what she wrote:
Summer is over. First, I saw the green-and-brown tree with green-and-brown leaves. Second, I heard the wind, and it was blowing. Third, the yellow leaves were falling, and I felt cool. Fourth, the birds were whistling. The season is fall.

Autumn Challenge #1: Cattail
Before heading out, I reviewed the challenge and skimmed (busy schedule, remember?) the part about spring, summer, and flowers in the study on cattails and focused on what to expect in the fall. I even printed out the notebook page and packed some markers.

I called my friend Brenda because I figured she would know where to find cattails. She went above and beyond the call of duty (it fits--she's a veteran of the Coast Guard and I'm a Navy veteran). Brenda gave us a ride on her golf cart up and down several hills until we reached a beautiful fishing pond with plenty of cattails.

Pamela and I orally observed the setting first: weather, date, season, location, etc. We noticed how cattails grow along the edge of the pond. She touched the cattail and said it was soft. I added that it felt like a sponge. She drew a detail of one cattail and then drew a bunch of them, very neatly and abstractly. During the week, she will write her observations for science class. The book asked if the cattail would float and Pamela guessed that it would. I snapped off a cattail and handed to her to throw. Impulsively, she ripped off some of the seeds and said, "Dandelion seeds." They are so soft, white, and downy. We talked about the wind blowing the seeds away.

Pamela went to the edge of the pond and threw the cattail. She was right! Before we left I snapped some pictures for our follow-up study next week.

The sweetest moment was when a mother showed up with her little girl, probably no more than two years old. Pamela asked for her name and repeated it when she heard it. Pamela looked at me and said, "New friend?"

"She who opens her eyes and her heart nature-ward even once a week finds nature-study in the schoolroom a delight and an abiding joy." Anna Comstock

Wednesday, September 23, 2009

Vermeer and the Latest Twist on Picture Study

Swine flu has hit our town, shutting down one of the private schools until next week. One family is mourning the loss of their 5th grader who woke up sick on Monday and died today. I do not know them but I am praying for them. I cannot imagine their grief, and it gives me a new perspective on autism. It makes me savor little moments like folding clothes and sitting on the couch next to Pamela while she draws on her dry erase board . . .

Last week, we wrapped up our Monet picture study by looking at his water lilies. Since one goal is for Pamela to know an artist's personality through the paintings, I chose Vermeer based on the startling contrast between neoclassicism and impressionism. Before moving on, we talked about our favorite paintings. Pamela understands that Monet's lilies stand out as uniquely his and observed that the painting with the bridge looks like the one at Swan Lake.

You can see in the video that Pamela and I enjoy picture study, which puts us "in touch with the great artist minds of all ages. We try to unlock for [our] delectation the wonderful garden of Art, in which grow most lovely flowers, most wholesome fruits. We want to open [our] eyes and minds to appreciate the masterpieces of pictorial art, to lead [us] from mere fondness for a pretty picture which pleases the senses up to honest love and discriminating admiration for what is truly beautiful - a love and admiration which are the response of heart and intellect to the appeal addressed to [us] through the senses by all great works of art" (Miss Hammond).

Bringing Charlotte Mason into the digital age, I set up the screensaver on the computer to rotate through the Monet paintings that we studied, a trick I learned from other moms. Miss Hammond suggested inserting the picture in a book to enjoy on a rainy day. I printed out all the pictures we studied and placed them in a folder.

1. To start a study of Vermeer's pictures.
2. To develop interest in Vermeer's works.
3. To help Pamela learn to give enough information accurately about a painting to allow me to single it out from other choices.
4. To let her see the natural consequences of leaving out important ideas from a painting.
5. To teach her to picture something in her mind and share what she sees in her mind.
6. To reflect about the painting and how it relates to our lives.

Modifications from Charlotte Mason (Volume 1, pages 309-311):
1. Since the focus is accurately describing what she sees in her mind without the other person seeing it, we will not discuss the picture before putting it away.
2. Since we are helping her with theory of mind, I will ask questions about details to help me get a clear picture in my mind.
3. I cannot give a preview of the picture because I do not know which picture she will pick. So, I will begin the next lesson by asking her to recall the previous picture. Then, I will tell her the story behind the previous picture to link the known (the last picture talk) with the unknown (the current picture talk).

1. Select and cut out twelve pictures by Jan Vermeer. Let Pamela pick one without me knowing what it is.
2. Tell her that the new artist we will study is Vermeer.
3. Encourage her to study the picture attentively so that she can remember it after we put it away.
4. Ask her to describe the picture with the most important features that will help me select the right one.
5. Ask questions for more clarity.
6. When finished, mix up the pictures and slowly review them, letting her know why I reject the pictures that sound wrong and why I accept the picture I think she described.
7. If my guess was wrong, brainstorm together what would have helped me.
8. Look at the pictures and talk about anything we missed.
9. Talk about what the picture reminds us of or any special meaning we get from it.

My favorite part of the video was how Pamela personalized the painting. The maid in the painting was sleeping and Pamela thought she was tired from walking. Whenever we return home from our daily walks, Pamela sits on the couch and rests, recovering from her exhaustion!

Monday, September 21, 2009

Weeks Three and Four Recap

Life got in the way of blogging, so I'm combining weeks three and four, both made of four days due to Labor Day and the local school district teacher's administration day (Pamela likes having her school year line up with everyone else's). We are now full steam ahead, working five hours or less a day (including exercise and practical skills).

My favorite moment in Week Three was when Pamela called Ctrl-Z (the undo feature of Excel) "rewinding". In Week Four, I loved her use of dynamic thinking. On Thursday, Pamela reflected that we had Friday off and said to me, "Tomorrow is to be continued." I suspected she hoped to split up the work between two days, so I asked if she wanted half days. She told me, "Twenty-two more, eleven today." After studying her schedule, she adjusted her plan to twelve on Thursday and ten on Friday. That is what I call dynamic thinking, which is the point of RDI!

Pamela and I continued to practice sharing our feelings in Spanish plus we reviewed colors and learned pets. To mix things up, one day we colored a picture, saying the names of the colors in Spanish and we played "I Spy" in Spanish, Yo veo . . . morado. Pamela's favorite Spanish word is for orange. She may have struggled with aphasia most of her life, but the word anaranjado glides off her tongue like silk. We added Los pollitos dicen, which Steve learned as a child, to our sing-a-long time. Pamela loved figuring out many of the words by watching the video on youtube.

We continued splitting time between geometry, number theory, and algebra/arithmetic. In geometry, not only did we cover the idea of 0-D (point), 1-D (line), 2-D (plane), 3-D (solid), and square units for problems without measurements, we hit surface area from many perspectives, doing problems from Lesson 15 in Math-U-See's Pre-Algebra:
  • Cutting up 3-D boxes, cubes, prisms, and pyramids (check out this awesome link), measuring and calculating the area of the faces, and summing to get the total.

  • Unfolding and flattening paper models, outlining their shape on paper, and calculating the areas in the diagram to get surface area.

  • Looking at a drawing of a 3-D shape, drawing the flattened version, and calculating surface area.

  • Viewing the surfaces of a room and house as solids to determine the material is needed for painting, siding, and roofing.

Because Pamela has not completely mastered these ideas after four weeks of work, one thing is clear: she could not have come this far in only one week which the book suggests is possible! I still plan to introduce volume next week while continuing to hone Pamela's ability to calculate surface area.

In number theory, Pamela played more games involving the concept of negative and, for the first time, we used that words negative and positive as we transitioned to working on a number line, doing word problems, and providing answers for problems in numbers and symbols. Because of Pamela's aphasia, I developed a long list of situations that go with negative (buy, owe, lost, pay, spend, etc.) and positive (earn, found, have, received, sell, etc.). She even worked some problems from Lesson 1 of Math-U-See's Pre-Algebra. In algebra, we reviewed fractions (falling back on blocks and drawings as necessary): comparing, adding, subtracting, reducing, and proper/improper/equivalent fractions.

We worked out of six books for our history threads, and Pamela added pages to the book of centuries. For the most ancient of history, Pamela read and wrote a narration of Seth and his extended family, including Enoch's startling story (Adam and His Kin and an illustrated version of Genesis). For the era leading to the birth of Jesus, she read passages about the births of John the Baptist and Jesus (an illustrated version of The New Testament) and the family of Octavius, Cicero, the five conspirators (Brutus and kin), and Mark Antony (Augustus Caesar's World). We read the myths behind the founding of Britain in Our Island Story and read about the early childhood of Christopher Columbus and Isabela of Castile in a time when Mohammed II was eying Europe (The World of Columbus and Sons).

Language Arts
Pamela did studied dictation of two myths, Egyptian Creation and Gilgamesh's Flood, requiring no special lessons. She wrapped up her recitation of The Horseman. She practiced articulation through reciting, reading aloud poems, and singing songs. She typed narrations of Watership Down, myths, and her history readings and wrote notes for geography and literature. Pamela copied the story "A Rainbow for Sarah" into her copy journal for penmanship. She took several pictures and typed stories about her beanie babies. Pamela orally narrated her readings and paintings by Monet.

Pamela completed Lessons 3 and 4 of Writing Strands Level 2 (emphasizing reporting what you see, replacing nouns with pronouns, and combining sentences). Pamela wrote the following stories:
The Cat and Mouse
My white mouse with a long, tail ate the small, pink fish on the white-and-blue table. My brown-and-white cat with a long tail was walking on the brown deck. My brown-and-white cat with a long tail saw a white mouse with a long tail and a small, pink fish on the white-and-blue table. It screamed and fell on the white mouse with a long, tail and a small, pink fish on the white-and-blue table. The white mouse with a long, tail was under the brown couch.

My mom with a wand had a pumpkin. She was waving a wand and made magic. The elephant and giraffe were on the brown deck. They were six: the elephant, hippo, giraffe, monkey, lion and ostrich. They were two: rhino and zebra. The pink shoe was small. It sat on the lion.

Pamela read eight poems by Walter de la Mare, two chapters of Watership Down, two chapters of Little Women, and three chapters of Harry Potter and the Sorceror's Stone.

Charlotte Mason covered geography through interesting travel books. Pamela followed the Fisher family on their WorldTrek through England, Ireland, and Norway. To help her better visualize their journey, I created pages in a folder with pictures and maps. To supplement our other readings, we studied maps of ancient Rome plus Europe, Northern Africa, and the Middle Ages in the fifteenth century.

Life Skills
Pamela finished her first introductory course in Excel and started a new one about typing formulas (I learned a new trick about the Auto-Sum feature). She decided where to go during our daily walks and delighted herself by exploring a street we have never walked or driven. Pamela is learning to crochet chains, which requires such effort that we can only work at it five minutes at a time. She has mastered phase I (hooking with her left hand), and I started her on phase II (controlling the yarn and chain with her right hand).

We exercised by walking the dog. Pamela painted in her nature journal. Pamela classified her first tree (the flowering dogwood on the left), noticed lichen, and joined me for Green Hour Challenge #1. Pamela sings Blessed Assurance, Land of the Silver Birch, and Los Pollitos Dicen well and even adjusts her pace to mine when I deliberately spend up or slow down to assess her co-regulation skills. We listened to Mozart in the car and did four picture studies of Monet's water lilies.

Thursday, September 17, 2009

Green Hour Challenge #1

We have exercised every school day this year, logging in 18 30-minute walks so far! One of the benefits of walking is getting to know the neighborhood better. This week was full of interesting nature finds: a bird nest on the ground, a lizard in a tree just at our eye-level, a dead baby snake (and, YES, I squealed when I saw it), and a chicken trying to cross the road. We think it fell off a chicken truck bound for the poultry plant thirty minutes away. I nearly always carry the camera to give Pamela a chance to practice her photography skills. The interesting things we see offer many opportunities to reinforce declarative communication, thinking and wondering, writing, Spanish (yo veo la gallina blanca), and nature study.

Walking outdoors dovetails very nicely with nature study. Every year, I have had good intentions but only managed to hit it sporadically. Our schooling must be going well this year because we have managed to do a nature walk, complete with watercolor painting four weeks in a row--how many weeks does it take to build a habit? Pamela does not paint complicated, detailed pictures. She probably spends less than five minutes on her subject.

Before I head out, I pack the following supplies in a hip-pack:
  • a well-sealed container of water, bagged in a ziploc,
  • a few paper towels
  • different sized paintbrushes
  • watercolor paints
  • the camera
  • crayons (if we do a bark rubbing of last week's tree)

You can do nature study almost anywhere, even the backyard. Since I am trying to combine exercise with nature study every Friday, we walk to a little park next to City Hall and walk around until Pamela finds something interesting. The first two weeks she painted leaves from trees. Actually, I am not sure they were true trees because they have multiple trunks and that usually means glorified shrubbery. Instead of getting wrapped around the axle because I could not figure out what they were, I used the opportunity to work on classification skills. I took pictures of key features of the tree and brought a leaf home. During the week, we spent about five minutes a day analyzing and recording characteristics like the kind of bark; leaf margin, shape, and veins; fall leaf color; leaf arrangement (simple versus composite or alternate versus simple); buds; etc.

Thankfully, last week I recognized the tree trunk full of holes that caught Pamela's attention! The clusters of bright, red berries, leaf color and shape, and alligator-skin bark told me it was a flowering dogwood tree. I resisted the temptation to steal an opportunity for Pamela to discover the identity of the tree. Pamela painted a small detail of the holey trunk in her nature journal, and we spent all week studying the characteristics of the mystery tree. Today, we entered data in an interactive tree identification program for Piedmont Carolina and only required three characteristics to zero-in on the dogwood.

During today's walk, Pamela painted some lichen from another dogwood tree and I plan to let her investigate lichen next week. Last year, I wrote two lengthy posts about the value of nature study and how-to-do nature study. For more details than you can ever imagine, try Harmony Art Mom's awesome blog and her Green Hour Challenge series on how to apply Anna Comstock's Handbook of Nature Study is simply inspiring. I gleaned the following ideas from the first eight pages, which Harmony Art Mom assigned for the first challenge:

The Benefits of Nature Study
  • Cultivates the habits of accurate observation, discernment, curiosity, and declarative communication.
  • Provides understanding of things close to home, opportunities for exploration of the land of the undiscovered, practical and helpful knowledge, wise respect for what happens when some break natural law, and new interests.
  • Develops an appreciation for nature, beauty, color, form, music, and how creatures live.
  • Nourishes the soul, mind, and body.
  • Releases children from too much instruction and repetitive lessons that dull the mind.
  • Permits the teacher to feel young again by not knowing, to let students pursue their interests, and to take a break when nerves are raw.
Caution: "If nature-study as taught does not make the child love nature and the out-of-doors, then it should cease."

Prescription for Teachers:
Spend Saturday morning either outdoors or napping in bed . . . z z z z . . . you can guess where I will be . . .

Wednesday, September 16, 2009

Variations on Picture Study

Pamela and I are doing a twist on picture studies like the ones described in the lesson plans last June. Not only do picture studies allow opportunities to explore fine art, but they give us scope to have conversation and make connections.

Now, we are working on theory of mind. I printed out six different Monet paintings of water lilies. In a typical lesson, Pamela picks one picture, and I put the rest away. She describes the picture and I ask questions to help me visualize better. When we come to a shared understanding, I pull out all of the pictures and mix them up. Then, I go through them, one by one, try to guess which picture she chose. I tell her my reasoning as we go along so she has the chance to see how important her details are.

Saturday, September 12, 2009

A Righty Scaffolding a Lefty into Learning to Crochet Chains

The picture above is the result for four five-minute beginner crochet lessons with Pamela this week.

Trying to teach Pamela to crochet takes us both to the edge of our collective competency. I don't know about her, but I feel like a pig on roller skates. Short lessons are a MUST because only five minutes of effort is exhausting. The longest we have every lasted in our first week of lessons was six minutes and forty-five seconds. Here are some tips that have worked for me this week:
  • Crochet as a lefty just long enough to be able to demonstrate it to her.
  • Scaffold the task by assigning roles: she manipulates the hook while I control the yarn and tension.
  • Keep the lesson as short as our mutual patience can tolerate.
  • Use declarative language to describe my mental process and preview what she will be doing in the future. "The yarn is too loose. I need to fix my tension."
  • When something goes wrong, describe what happened, "Oops, I am holding the yarn too tight."

Thursday, September 10, 2009

Our Second Week in Review

Our daily walk provides enough exercise to flush Pamela's face!

Like I said in last week's review, Pamela is clearly in a search for meaning. Sunday morning, Pamela and I had the following conversation that she brought up in reference to our number theory games. Note: She brought up this topic outside of official school hours because her mind is working through these living ideas and she wanted to share her thoughts with me:

Pamela: "What does even dice mean?"

Tammy: "It means up. Two, four, and six are even numbers. Do you know any others?"

Pamela: "Eight, ten, twelve. . . . Even means up and odd means down."

Tammy: "Even means it will be spring soon."

Pamela: "Even dice just like the black cards."

Tammy: "Yes! An odd dice is just like the red cards."

Pamela: "Yes!"

Tammy: "That was a very clever thing to figure out. There is a special word for that. I will tell you about it Tuesday in number theory."

What this conversation tells me is that Pamela saw the link between what I am using for negative and positive numbers in the Time Travelers and the Minnesota Winter games. She understands the idea of having opposite numbers on either side of zero. These concrete games have created a known (odd dice and red cards) to an unknown (negative numbers).

Once again, Pamela adored poetry and told me it was her favorite subject. She connected to Walter de la Mare's "The Cupboard" because it reminded her of where Harry Potter slept in the first two chapters of the book, while "Hide and Seek" reminded her of the Pevensie children. She predicted this poem would be about children and was surprised to imagine the moon, wind, waves, and clouds playing the game. While I read aloud to her "The Window"--her favorite, Pamela looked through the shutters to watch our neighbors doing yardwork. The following is what we accomplished last week, according to plan. We are not at full schedule yet, but we managed to pull this off in 4 hours a day.

The new kid on the block was Spanish. I did not plan to try Spanish again since Pamela is just making strides in English as a first language. Deep conversations about teaching foreign language with other Charlotte Mason educators have convinced me otherwise. They believe in focusing on oral language and building an ear to avoid getting lost in grammar and syntax.

Steve, a native speaker in both Spanish and English, agreed based on his experience. He learned English from his parents at home and spoke Spanish elsewhere, including the local parochial school. Even though he NEVER took a formal class in English (NEVER), he managed to score well enough on the language section of the ACT to enroll in college in the United States. He earned A's in his remedial English classes.

How did he learn to read and write in English? He taught himself! Learning to read and write Spanish enabled him to do the same in English. His parents never taught him formally and, like his siblings, he figured it out on his own. Steve and his five siblings managed to accomplish the same feat and earn bachelor's degrees in the United States without the special programs available for English as a Second Language.

What was their secret? Being orally fluent in English! Charlotte Mason wrote, "French should be acquired as English is, not as a grammar, but as a living speech. To train the ear to distinguish and the lips to produce the French vocables is a valuable part of the education of the senses, and one which can hardly be undertaken too soon" (Volume 1, page 300). Pamela is twenty, and I am over twice her age, so we are relying on the "better late than never" theory! My plan is to focus on developing vocabulary used in every day life and learning Spanish nursery songs that Steve learned as a child.

With the help of some free online resources (hat tip: Masterpiece Theater), we focused on answering feeling questions for girls--boy feelings here--letting us practice facial expressions and body language. After doing a very short lesson together in a shared experience fashion, I said in a flat voice, "Me siento feliz" or "Estoy enojada," and Pamela showed her understanding by acting the feeling while repeating my words. If she said a feeling in Spanish, then I acted it out and said a complete sentence. Sometimes during the day, I asked, "¿Cómo se siente hoy?" and waited for her to share her feelings or I shared my feeling, "Estoy cansada," after a hard workout. Pamela loves saying, "Hola," and I often followed up with "Hola. ¿Cómo se siente hoy?"

We continued splitting time between geometry, number theory, and algebra/arithmetic. In geometry, Pamela continued to work on measuring in both inches and centimeters, calculating the area of triangle and rectangles (not with formulas, but through understanding the process, doing things like drawing a rectangle around the triangle, finding the area of the rectangle, and taking half of it). On Friday, we started doing the surface area of real things like a plastic cube that holds paper clips and an empty taco shells. In number theory, Pamela played various games that preview the concept of negative and handled every combination of adding positive and negative numbers. In algebra/arithmetic, we reviewed fractions and covered comparing fractions with the same denominator or the same numerator, comparing whole versus fractions, and comparing half versus fractions.

We worked out of five books for our two threads of ancient history, and Pamela added pages to the book of centuries we started last year. For the most ancient of history, Pamela read and wrote a narration of Cain and his extended family (Chapter 5 of Adam and His Kin and Genesis 4:16-26 from an illustrated version of Genesis). For the era leading to the birth of Jesus, she read passages about Joseph's dream (Matthew 1:18-25 from an illustrated version of The New Testament) and the Ides of March and Cleopatra and her son (Augustus Caesar's World).

Language Arts
Pamela did studied dictation of a one page story about Heracles and three golden apples. She kept practicing her recitation of The Horseman for recitation. She practiced articulation through reciting, reading aloud poems, and singing songs. She typed narrations of Watership Down, Pandora, and her history readings. Pamela copied the story Who Took the Farmer's Hat? into her copy journal for penmanship. She took a picture and typed a story about her beanie babies. Pamela orally narrated her readings and two paintings by Monet.

Pamela completed Lesson 2 of Writing Strands Level 2 (emphasizing making lists and using commas). Pamela wrote the following story called "Africa" about her favorite toys:
My mother put the peach-brown-and-white ostrich with the long peach beak, the black-and-white zebra with the black stripes and the yellow-and-brown giraffe with the brown spots on the green-blue-and-white cup.

Pamela read five poems by Walter de la Mare, one chapter of Watership Down, one chapter of Little Women, and two chapters of Harry Potter and the Sorceror's Stone (her request for this year).

Whenever we start a fiction book set in a particular location, we always pull out the atlas: this week, we found England and Massachusetts. We studied a map of Egypt and another depicting the conquests of Julius Caesar. I plan to start a travel book next week to fill out geography.

Life Skills
Pamela learned to enter various types of data in Excel: date, time, fraction. She practiced tricks like autofill, autocomplete, and current date [Ctrl ;] and time [Ctrl Shift ;] and navigated through the workbook with the enter, tab, and arrow keys. She decided which way to turn during our daily walks, taking a different path every day. While sometimes we took the dog with us (even the principal once), we headed to the Post Office to mail eBay packages twice.

We exercised by walking the dog or walking to the post office. Pamela painted a tree in her nature journal. We noticed these interesting buds and plan to investigate them further next week. Pamela nearly has the melody for Blessed Assurance and Land of the Silver Birch. We listened to Mozart in the car and did two picture studies on Monet: The Walk, a Woman with a Parasol and The Red Kerchief.

Sunday, September 06, 2009

How One CM Homeschooler Stays Organized

I am not one of those "school in a box" homeschoolers nor do we use workboxes. In the Barbie-pink crate are the books we are reading and the myriad of folders for each subject that hold graphic organizers, narrations, notes, math materials, printed out stories and poems, etc. I prefer pronged folders over three-ringed notebooks because paper doesn't tear out as easily. Since Pamela loves going through her old materials many years later, pocket-only folders do not work for us either.

Over the weekend, I type up the weekly plan in Excel and print it out. I also prepare graphic organizers, math manipulatives, etc. if time permits. Pamela, like her dear daddy, gets jazzed about marking off items as she goes and picks the order in which she does her work. She is quite the doodler, too.

Charlotte Mason considered a schedule one of the sound principles of a well-managed homeschool. Students need to know what they need to do and how long each lesson should last. On page 142 of Volume 1, she explained, "This idea of definite work to be finished in a given time is valuable to the child, not only as training him in habits of order, but in diligence; he learns that one time is not 'as good as another'; that there is no right time left for what is not done in its own time." To emphasize that point, I have a stopwatch to keep us from taking too long on a lesson.

Since things do not always go according to plan, on the weekend, I revise the list from the previous week to document what we actually accomplished. Then, I print out a clean copy and file it in a folder, pronged, of course.

You may look at our schedule and think we must spend every waking hour homeschooling! We do not.

Last week, we worked about four hours every day, doing the majority of the work in the morning. What we do is the antithesis of block schooling, which is all the rage in the schools in my town (four classes per semester, each class earning a year's worth of credit). We have very short lessons on wide and varied subjects, just as Charlotte Mason did at her schools. On page 286 of her third book, she stated that students aged elevenish to fifteenish spent 3 1/2 hours a day, using thirty-five books, to cover Bible lessons, recitations, English grammar, French, German, Latin, Italian (optional), English, French, and Ancient History (a la Plutarch's Lives), Singing (French, English, and German Songs), Writing, Dictation, Drill, Drawing in Brush and Charcoal, Natural History, Botany, Physiology, Geography, Arithmetic, Geometry, and Reading.

The secret to so many subjects is having short lessons. Notice that reading a poem only takes five minutes on my schedule. Most lessons are twenty minutes or less, even math because I have three twenty minute math lessons (Geometry, Algebra/Arithmetic, and Number Theory). Charlotted Mason recommended short lessons for reasons beyond having a wide and varied curriculum on page 142 of Volume 1,
  • The sense that there is not much time for his sums or his reading, keeps the child's wits on the alert and helps to fix his attention.
  • He has time to learn just so much of any one subject as it is good for him to take in at once.
  • If the lessons be judiciously alternated––sums first, say, while the brain is quite fresh; then writing, or reading––some more or less mechanical exercise, by way of a rest.
  • The program varying a little from day to day, but the same principle throughout––a 'thinking' lesson first, and a 'painstaking' lesson to follow,––the child gets through his morning lessons without any sign of weariness.

They had no homework!

Neither do we! If Pamela finishes everything up by Friday, she has no work on weekends and holidays. Charlotte Mason held classes on Saturday mornings, so our days last a bit longer. I find no need to dole out rewards or stickers because of one lovely, natural consequence: Pamela has more time to do what she enjoys doing, whether that be rocking on the porch rockers, using the computer, playing with her toys, making calendar lists, etc.

Saturday, September 05, 2009

Original Thinking about Number Theory

Last week, I explained my rationale for splitting Pre-Algebra into three tracks (twenty minutes a day) and showed my plan for geometry and blogged our first week of geometry lessons. The second track for this year is number theory, a branch of pure--the opposite of practical and hands-on--mathematics. It includes topics like negative numbers, prime numbers, integers, whole numbers, rational numbers, etc. Number theory includes finding the greatest common factor and least common multiple.

Of the three tracks (geometry, algebra/arithmetic, and number theory), the latter worries me the most because number theory is the most abstract. Last June, after I split it all up into three tracks, I began experimenting with how to introduce negative numbers, which my plan covers in fourteen weeks. The most difficult aspect of using negative numbers is knowing how to add and subtract them. The concept of negative exists everywhere, even though we do not always use negative signs. I developed a series of games that addressed going from a number in one state of being, crossing 0, an going into another state of being. Rather than getting wrapped up in abstract terms like positive and negative, I found concrete situations to which Pamela can relate:
  • Crossing the year 0 to study either the years B.C. or A.D.
  • Crossing 0 degrees Celsius to temperatures above or below zero.
  • Crossing the equator to go either North or South.
  • Crossing 0 cents to have money or go into debt.
  • Crossing 0 points in a card game to have points on the table or in the hole.
What makes the games fun is how we use context and imagination. We used to live in Minnesota and know full well what going above and below freezing temperatures feels like. So, when we play Minnesota Winter, we get upset at dropping temperatures and cheer when the thermometer rises. Pamela's favorite game is Time Travelers because we get to visit certain people (Mozart if we land on 1700 A.D. or Jesus if we arrive in 0). The most exciting moment for us is hitting 1900 A.D. because we talk about electricity, televisions, and computers but know we can't have HDTV until we hit 2000 A.D.

Time Traveler - Pamela and I both play this game, which starts at 0. We pick a card: red means to go backwards in time, while black means to go forward. The number of centuries jumped is the value of the card. If the value takes us out of range of the board (past the lowest year B.C. or highest year A.D.), we reject the card and keep picking until a value works. Pamela keeps track of her years on paper to help her see the pattern. When we first started playing the game, we counted each and every move. Now, she can do all aspects of movement in her head with few mistakes!

Minnesota Winter - This game does not have players because our imagination makes it fun. Pamela rolls the dice and keeps score. We place the red paper clip at 5 below to allow more opportunities to straddle 0. If she rolls an even number, the temperature increases by that amount. If odd, it decreases by that amount. She keeps track of the temperatures on her sheet, while I move the paper clip up or down. Over many rolls, the temperature will rise and once it hits the highest temperature on the paper, the game ends.

Going to Kenya - I already have a link for the map game, and the video shows Pamela and I playing it last week.

Chores - I already have a link for the chore game.

Cards - I do not have video of this game because it is not all that exciting. Pamela picks a card. If it's red, she loses pennies; if it's black, she gains pennies. The number of pennies are the value of the card. "On the table" is for a positive number of pennies left, while "in the hole" represents how many pennies she owes. She keeps track of the pennies on a sheet like the ones above.

What are the results of playing these games? Pamela understands the following concrete concepts about the idea of using negative numbers:
  • If you go forward and are in positive territory, you add the numbers and stay in positive territory: 500 A.D. + 300 years = 800 A.D.
  • If you go backward and are in negative territory, you add the numbers and stay in negative territory: 300 B.C. - 1000 years = 1300 B.C.
  • If you go backward and are in positive territory, you subtract the numbers and stay in positive territory only if the number going backward is less than the starting number: 800 A.D. - 400 years = 400 A.D.
  • If you go forward and are in negative territory, you subtract the numbers and stay in negative territory only if the number going forward is less than the starting number: 800 B.C. - 400 years = 400 B.C.
  • If you go backward and are in positive territory, you subtract the numbers and end up in negative territory only if the number going backward is greater than the starting number: 500 A.D. - 900 years = 400 B.C.
  • If you go forward and are in negative territory, you subtract the numbers and end up in negative territory only if the number going forward is greater than the starting number: 800 B.C. - 1200 years = 400 A.D.

Number Theory Track
I picked out Math-U-See lessons that fit into the category of number theory and spreaded them out over thirty-six weeks.

Week 1 - Practice crossing back and forth zero in games (money, map, time, temperatures, cards, etc.
Week 2 - Practice crossing back and forth zero in games (money, map, time, temperatures, cards, etc.
Week 3 - Transition to doing number line problems and introduce the concept of negative and positive.
Week 4 - Transition to word problems involving situations encountered in the games plus the number line to focus on the idea of negative versus positive.
Week 5 - Do selected problems for adding negative numbers from Lesson 1 of MUS Pre-Algebra.
Week 6 - Add a twist to the game where you can draw a card that will subtract some or all negative points before you make a move. Transition to doing subtracting negative numbers on a number line.
Week 7 - Transition from subtracting negative numbers on a number line to word problems.
Week 8 - Do selected problems for subtracting negative numbers from Lesson 2 of MUS Pre-Algebra.
Week 9 - Demonstrate multiplying positives and negatives through the concept of adding or subtracting multiple times.
Week 10 - Transition to multiplying negative numbers on a number line to word problems.
Week 11 - Do selected problems for multiplying negative numbers from Lesson 3 of MUS Pre-Algebra.
Week 12 - Demonstrate dividing positives and negatives through splitting up a negative or positive number into groups.
Week 13 - Transition to dividing negative numbers on a number line to word problems.
Week 14 - Do selected problems for dividing negative numbers from Lesson 4 of MUS Pre-Algebra.
Week 15 - Demonstrate additive inverse with concrete objects and a balance and Math-U-See blocks.
Week 16 - Transition to additive inverse in stick diagrams and word problems.
Week 17 - Do selected problems for additive inverse from Lesson 9 of MUS Pre-Algebra.
Week 18 - Demonstrate commutative and associative properties with concrete objects and a balance and Math-U-See blocks.
Week 19 - Transition to commutative and associative properties in stick diagrams and word problems.
Week 20 - Do selected problems for commutative and associative properties from Lesson 11 of MUS Pre-Algebra.
Week 21 - Demonstrate multiplicative inverse with concrete objects and a balance and Math-U-See blocks.
Week 22 - Transition to multiplicative inverse in stick diagrams and word problems.
Week 23 - Do selected problems for multiplicative inverse from Lesson 13 of MUS Pre-Algebra.
Week 24 - Demonstrate distributive properties with concrete objects and Math-U-See blocks.
Week 25 - Transition to distributive properties in stick diagrams and word problems.
Week 26 - Do selected problems for distributive properties from Lesson 12 of MUS Pre-Algebra.
Week 27 - Set up a chart of prime numbers and divisible numbers and see if Pamela can discover the pattern. Work past the chart to determine if other numbers are prime. Explore multiples with Math-U-See blocks.
Week 28 - Transition to factorization and visual ways of doing that. Explore common multiples with Math-U-See blocks.
Week 29 - Explore least common multiples with Math-U-See blocks. Factor the multiples to see if there is a pattern with primes.
Week 30 - Transition to pictures and fractions problems.
Week 31 - Do selected problems for prime numbers and least common multiples from Lesson 21 of MUS Pre-Algebra.
Week 32 - Explore common factors with Math-U-See blocks. Transiton to exploring the greatest common factor with the blocks.
Week 33 - Transition to pictures and fraction problems.
Week 34 - Do selected problems for greatest common factor from Lesson 22 of MUS Pre-Algebra.
Week 35 - Describe kinds of numbers and group them (counting numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers). Develop a Venn diagram and identification ideas.
Week 36 - Do selected problems for irrational and real numbers from Lesson 30 of MUS Pre-Algebra.