Friday, October 16, 2009

Perspective

Monday began like any other day. Steve left at seven-thirty to drive to Tennessee for a short business trip. Pamela and I decided to catch up a little bit of reading postponed last Friday because of the holiday. When I dropped David off at band, I noticed the iffy weather and threw up a quick prayer request for Steve on Facebook at 10:23. Three friends--all prayer warriors and parents of children with autism--responded: Steve's sorority sister gave a thumbs-up plus a local friend and a homeschooler in Tennessee said they would pray.

Pamela read and narrated her books while I worked on Beth Moore Bible study. The orthodontist interrupted us for a few minutes, but we doggedly got back on track. My parents called from their RV in Florida, so I talked long enough to be polite. As soon as I hung up, we tackled our work again: Pamela was reading a chapter from The World of Columbus and Sons while I read Beth Moore's suggestion that, as adopted children of God's royal family, we represent His land just as the Queen of England represents her land when visiting our country.

The phone rang again, and I fussed, "Not another phone call!" I never get three phone calls in succession, and I came close to ignoring it! I got up one more time and heard the words that you never want to hear, "Tammy, don't worry but . . ."

Steve was calling from a concrete barrier in the median of I-40 watching traffic zoom around his wrecked car blocking two lanes of traffic. He didn't even know the nearest exit much less the state. "I'm okay! I'm walking, but the beemer is gone. I just totaled it. I think I'm in Tennessee . . ." It turned out he was in North Carolina!

I could hear the passing cars through the phone and, at one point, a woman asked if he needed help! He asked me to pray for him because he was afraid someone would plow into him before the police arrived. Fortunately, the ensuing traffic jam took care of that problem.

Fearing that Pamela might become unglued if she figured out the truth, I returned to what we were doing and acted like nothing happened. She asked who called and, in a phony calm voice, I told her that her dad called to tell me how he was doing (close enough to the truth to avoid lying). Because of RDI, Pamela can read moods better and, if she had detected my fear, she would have flipped out. Navy training kicked in, so we went back to work.

As soon as I got her going on her reading, I typed a Facebook note at 11:49, thanking everyone for praying, "PRAISING GOD FOR ALL WHO PRAYED FOR SAFETY!!!!!!!!!!!!!! STEVE JUST TOTALLED THE CAR AND HE IS OKAY. THAT IS ALL I KNOW. KEEP HIM IN YOUR PRAYERS FACEBOOK FRIENDS." For the next hour, people from all over the world--his friends, my friends, mutual friends--chimed in with their gratitude and prayers!

Since I was behind in my Bible study, I got back to page 97, which--I am not kidding you--stated:

Not only are you royalty but you also have been placed in your sphere of influence, regardless of the size you perceive it to be, 'for such a time as this.' Ecclesiastes 3:2 tells us there is 'a time to be born and a time to die.' God cut out those exact perimeters for you and me on the kingdom calendar so that we would be positioned on earth right now. Likewise, Acts 17:26 tells us unflinchingly that God 'determined the times set for [us] and the exact places that [we] should live.' You see, even your current location is part of the set-up for your kingdom destiny. As we learned in one of our earliest verses on providence in this series, in Christ 'we were also chose, having been predestined according to the plan of Him who works everything in conformity with the purpose of His will' (Ephesians 1:11). These realizations should be stunning and marvelous to us, exploding our lives with significance.

Yeah, the timing was stunning all right . . . ten minutes after I learn about Steve's brush with death!!!!!!

For the past two weeks, our town of 4,000 people has seen one person after another die: a fifth grader from swine flu, a teacher from an aneurysm, a 10th grader from accidental drowning, a reporter (who wrote stories about my brother's reenlistment and my mom's quilt group before he moved last year) from a car accident Saturday night. Steve could have been the next! At the last minute, he decided to drive the beemer instead of Red (the Kia). Five minutes before the accident, he started to feel nervous about the road conditions: he grabbed the wheel firmly with both hands and kept his eyes peeled. The car slid on what he thinks was a patch of oil, side-swiped a truck hauling a bunch of cars, rotated ninety-degrees before plowing into the concrete barrier in the median, head-on. As it spun and bashed into the barrier several times, two things spun in his head: "Dear God, don't let it be today and don't let anyone else get hurt."

Miraculously, no other car was involved in the accident, and the truck driver could not find a single dent on his rig. Steve was shaky, stiff, and sore with a minor burn on one hand from the airbag. The state troopers and emergency teams were efficient in cleaning up the mess!

I called my closest friend, who totaled her car last year. She said that she was so worthless after her wreck that she could not have driven a half hour to get home, much less five hours. Her description convinced me to take no lip from Steve, who has been known to drive three hours with a high fever caused by the measles, telling me that it was nothing. I told Pamela that Dad missed us and we were going to visit him in North Carolina (which was another half-baked truth). Luckily, she was so delighted by the impromptu trip that she bought my excuse without question. I picked up David, asked for more prayers from my friends on Facebook, email lists, and Twitter, and drove off.

The roads were nasty most of the way: slick with plenty of rain and later fog. Every stalled car, every tow truck, every cross on the side of the road came alive as I thought about what happened to Steve. Knowing about all those people praying for us calmed me.

On the five-hour trip, I reflected upon Oswald Chamber's book If You Will Ask, which busy days caused me to put down after the first chapter. Oswald wrote, "Only when a man flounders beyond any grip of himself and cannot understand things does he really pray." Steve and I sure experienced that kind of helplessness!
Prayer to Him is not a way to get things from God, but so that we may get to know God. Prayer is not to be used as the privilege of a spoiled child seeking ideal conditions to indulge his spiritual propensities; the purpose of prayer is to reveal the presence of God, equally present at all times and in every condition. . . It is not so true that 'Prayer changes things' as that prayer changes us.

Because of Pamela, I had to stay calm: I had two choices: a very bad situation or a worse situation compounded by autistic meltdown! As Oswald pointed out, "The secret of Christian quietness is not indifference, but the knowledge that God is my Father, He loves me, I shall never think of anything He will forget, and worry becomes an impossibility." The only way I could stay calm was through the eternal perspective. As my pastor pointed out in his sermon last Sunday, we can live life in the light of the Gospel, regardless of chaotic chapters in our lives, because we know the end of the story (Isaiah 65:17). He also observed at our Wednesday night Bible study that prayer is the inverse of anxiety:

It means the more you pray, the less anxious you feel. Likewise, the less you pray, the more anxious you feel. Do I hear an amen?

That is what I experienced on Monday through prayer: hearing the whisper from God to pray for Steve's safety and ask others to pray before he crashed . . . to answer the phone, however inconvenient it was . . . to continue the Bible study and receive consolation while he was still in danger . . . to share the circumstances with those who pray so that they too could spend time with God . . . to feel at peace because God wants what is best for my family . . . to rejoice with our friends when I shared news of his safety. The first chapter of Oswald's book came alive before our eyes last Monday.
"As long as we are self-sufficient and complacent, we don't need to ask God for anything; we don't want Him. It is only when we know we are powerless that we are prepared to listen to Jesus Christ." Oswald Chambers

P.S. Once we hooked up with Steve later that day, Pamela's curiosity ignited when she saw him without the car. She asked, "Where is the gray car?" Because he very quietly explained that it crashed and because she could see with her own eyes that her Daddy was safe, Pamela took the news with great calmness. That surprised me. Two days later, she cried when she realized he had left some beloved CDs in the car along with the keys. The tears were short lived because he promised to call the towing company to see if they could mail them to us, which means she will start nagging us in about a week . . .

Thursday, October 08, 2009

Cube City

There is a difference between mindlessly checking things off a to-do list and doing things worth doing. Pamela frequently confirms the meaning of what we are doing. Recently, she started watching DVDs without closed captioning and sets the audio to either French or Spanish! She pulled out an old twaddly companion book to a kid's tape for learning Spanish words, and she reviews it for fun. Second, Pamela has started building things, mainly houses, with the Math-U-See blocks. Unlike her brother, who will never admit to how recently he put away his Legos, she has succumbed to the Lego bug. I may just drag David's collection downstairs for her! She still plans to trick or treat this year, dressed as a mom, taking her babies (Baby Alive and Baby David) out because they are toddlers now. When she flips through old photographs and asks me a question, she turns it so that I can see without hinting, "I can't see it." When we do money transactions, Pamela asks what we are doing so she can figure out if it is negative or positive. Making mathematical connections to the real world because she can easily memorize without understanding.

Volume
To teach volume, I cut out a bunch of flattened cubes (a spreadsheet I made in Excel), built them, and taped them together. We recycled some of the boxes used for calculating surface area and filled them with cubes. Not only did it give her a feel for what volume is (how much space an object takes up), building with cubes spotlights the idea of cubic units being very different from square units. We carefully took the cubes out of the box and compared it to it, side by side. We separated each layer of the volume to enable Pamela to be certain of her count.
Pamela did free lance explorations in which I gave her 20 cubes and let her figure out how many ways to create a volume of 20 cubic inches. Another variation was to take a pile of blocks, create a rectangular prism, and count the dimensions and volume. Activities like this appealed to her orderly, patterned mind. She recorded everything she did in charts to allow her to discover the formula for volume.



By the fourth example of volume, Pamela spotted the formula for volume: length times width times depth. She quickly transition from doing hands-on work to picture (even trying her hand at drawing a 3-D box) to words and symbols. Once she solidified her ability to do volume problems, I introduced one variation: being given a problem with mixed units (1 foot by 10 inches by 14 inches). She is learning to be vigilant about checking the units before labeling her drawings.

Covering a Surface
Pamela struggled with coverage problems like,
Susan needs to buy paint to cover 2100 square feet. One gallon of paint covers 400 square feet. How many gallons of paint does she need?

I realized she did not quite understand what the problem was asking so we backed up and did some concrete activities like covering a 9" x 12" notebook with 3" x 3" sticky notes (pictured left) or covering books with index cards (or cut-up index cards of a standard size to make the numbers work). When we made the leap to word problems, I knew Pamela understood when she illustrated her problem with paint cans.


The next variation I plan to address are house problems including painting or covering sides with siding (you only hit the sides, unless you have triangular shaped attics) and shingling roofs. More variations will involve subtracting out the area of doors and windows or applying two coats of paint.

Wednesday, October 07, 2009

Dynamic Solutions, Not Bandages

FREEBIE ALERT:
"I Love the '80s" download from Amazon. By '80s, they mean the following compositions by the following composers:
  • Brahms' Symphony No. 3 in F major, Op. 90
  • Mahler's Symphony No. 1 in D major, "Titan"
  • Tchaikovsky's Symphony No. 5 in E minor, Op. 64
  • Dvorak's Symphony No. 6 in D major, Op. 60, B. 112
  • Borodin's Symphony No. 3 in A minor
  • Saint-Saens' Symphony No. 3 in C minor, Op. 78, "Organ"
  • Bruckner's Symphony No. 9 in D minor, WAB 109 (1894 version)

Now back to your regular programming . . .
Adjusting to school has left me little time to blog our RDI journey, which we still do, of course! In fact, I am trying to incorporate dynamic intelligence into our school lessons.

A few Sundays back, a minor problem at church bothered nobody but David. I usually sit in front with the choir for half of the service, while the family stays in the pew. Steve ran eight miles that morning, instead of five, and was too drained to get off the couch! During the service, Pamela usually draws on the bulletin, sermon notes and quotes, and guest registries. While the pastor was speaking, she stood up, looking for a sharpened pencil.

Our very understanding congregation are Pamela's biggest fans. They are delighted when she speaks to them, even if, before the service, she abruptly points to someone with an eye patch and says, "You broke it!" While David (face turning beet red) guided his sister to sit down, Pamela remained oblivious to his discomfort. The lady behind him was chuckling the whole time, and I found out later that her grandson is autistic and sits behind us for that reason!

After church, David begged me to work on this problem. Two quick-fixes that get the job done in a static way are:

Plan A (Nothing more than a band-aid): Put enough paper, pencils, and lead in her purse to keep Pamela happy. This static solution (single response) will get David through church.

Plan B (A more sophisticated band-aid): Come up with a set of rules on how to behave in church and make her learn them. I will not try this plan because it is a static solution that does not promote dynamic thinking.

While we implemented Plan A, we also addressed the real problem through RDI. The underlying issue is that Pamela is not doing a good job of monitoring her actions and those of people around her and then reflecting on her behavior in comparison to theirs.

Lesson 1 - We spent two weeks people watching at every opportunity we could. Whenever we walked into a new setting, we observed what other people were doing and made declarative comments about them. We also talked about our actions.
video

Lesson 2 - Now, we are working on the second lesson. In addition to people watching, we figure out the kind of group we are watching. Pamela then assesses whether or not she belongs to the group. Then, she decides what her behavior ought to be. The goal is not to force conformity but to think about each situation dynamically. For example, in church last Sunday, my men were down hard and Pamela came to church with me and sat in the choir. She decided the choir was not her group, so she sat whenever we stood and sang. Later, in the pews, she decided to stand up with me for the last song (instead of sitting) but chose not to sing.

Last night, even though her dad was home and she could have stayed with him, Pamela wanted to attend my women's Bible study. When she was in the mood to explore and be apart from the group, she identified herself as not being in the group. However, at the end, when they prayed, she decided to be in the group and sat quietly during the prayer. She even said, "Amen," at the end. The beautiful expression on Pamela's face when she heard the music from the DVD cue-in will surely cheer you up if you have had a horrible, no-good, awfully rotten day.
video

Saturday, October 03, 2009

Corndog, or Cattail?

To complete Outdoor Hour Challenge #3, I read pages 16 and 17 of Handbook of Nature Study. The first section covered language arts and nature study. As a Charlotte Mason homeschooler and RDI mom, I heartily agree that "the purpose of a language is, after all, merely to convey ideas" for I wish to know what Pamela discovers. In the cattail study, Pamela connected cattails to cotton and dandelion seeds all on her own! While nature study supplies excellent subject matter to narrate, the quickest way to kill the benefits is to turn it into a language arts exercise. I try to look at journal entries and written narrations as a record of her understanding of the English language.

The other natural form of expressing ideas found in nature study is art. We usually try our hand at water colors, but the handbook encourages allowing students "to choose their own medium, pencil, crayon, or water color." For the tree study (this week's challenge), I brought all sorts of choices: markers, watercolors, pastels, and oil pastels. The most freeing statement in the book concerned my own issues with art because my family has many talented artists, and I am not one of them:
Too much have we emphasized drawing as an art; it may be an art, if the one who draws is an artist; but if he is not an artist, he still has a right to draw if it pleases him to do so. We might as well declare that a child should not speak unless he put his words into poetry, as to declare that he should not draw because his drawings are not artistic.
The irony of it all is that usually children who draw what they see in nature study develop their own style and learn to draw very well!

We followed up the cattail study by painting water colors based on one of the pictures I took: mine, which is entitled "Cattail, or Corndog?" is on the left and Pamela's is at the top. Pamela wrote some notes about the cattails: "It felt like cotton. The seeds were like a dandelion seeds. It floated on the pond." Notice that Pamela made a tiny grammatical error, but I did not correct it.

Yesterday, Pamela selected a tree, well a sapling, from our backyard to do a year long study. Every season, she will record her observations to help her understand how trees grow and change throughout the year, so I printed out the tree study page for autumn.

Before we headed out, I read pages 622-624 of the handbook, focusing on autumn work. Pamela drew an incredibly geometric picture of her tree, while I snapped pictures that will help us study and classify the tree next week, focusing on the leaves, seeds, roots, trunk, bark, and crown.

How has my attitude about nature study changed since starting the challenges? I have longed to be more consistent but thought a weekly field excursion was too time-consuming and the handbook, too intimidating. Thanks to Barb's bite-sized plan to ease families into short but effective studies and her scaffolding of the handbook, I feel much more confident. I have kept my own nature journal, sporadically in fits and starts over the past three years, and seeing Pamela's art is inspiring me to do my own. The benefits of nature study are plentiful--exercise, fresh air, attention, science, language arts, topics for conversation, art, etc.

P.S. Pamela's tree is weeping mulberry (female cultivar), a variety of the white mulberry, so we will be doing a mulberry study for science next week. Since the handbook does not cover it, Barb's article on subjects not specifically covered will come in handy!

Friday, October 02, 2009

The First Pre-Algebra Test

Number Theory
Last week, Pamela worked through the odd problems in Math-U-See's Lesson 1 according to plan. We transitioned from concrete work through the games I blogged in the plan to number lines (click the picture on the right to enlarge it), which was where I first introduced negative and positive signs. When we started working on word problems, I made a list of actions that usually go with negative and positive, grouped in +/- opposite pairs (sell/buy, have/owe, earn/spend, find/lose, etc.). Whenever we do one of these transactions in real life, I spotlight it for Pamela. Finally, last week, I introduced her to abstract symbols for problems like (+7) + (-10) = _____. She shifted very smoothly from concrete to pictures to words to symbols in the process of understanding the concept of negative.

Last Friday, Pamela ACED her first test straight from the book with no help from me. I was busy typing something on the computer while Pamela took her test. She must have thought about the time when her brother took his first Math-U-See tests because she grabbed the calculator and used it herself. Pamela proudly commented on using the calculator, probably a sign of growing up to her. You can see how she completed most of the test unassisted because she showed her work up until Problem 15. I am more delighted about Pamela reflecting on how David took tests and altering her behavior than the test score!

Algebra/Arithmetic
If you examined the test closely, you will see some fraction problems. Like Math-U-See suggests, we have been reviewing fractions for the past five weeks, falling back on manipulatives, drawings, real-life activities, etc. for concepts that are murky. We examined concepts like whole versus fractions, equal versus unequal parts, terms (numerator, denominator, proper, improper, equivalent, etc.), adding and subtracting fractions, and reducing fractions. I have assessed her understanding of fractions from concrete to pictures to words to symbols, and Pamela is recovering what she did not retain. One of these days, I might get around to blogging our plan for algebra/arithmetic, the third track, which focuses on the review of fractions, decimals, and percents until the seeds are sown for doing algebra.

Geometry
We are making steady progress in our plan for geometry. After blogging our first week of geometry, I left you hanging!

Area of Triangles
Since Pamela caught onto the relationship between the area of a rectangle and the area of a triangle, we reinforced what she knew, NOT through kill and drill, but through new ways of exploring the same idea. She cut out rectangles on a grid and found the area of a rectangle. Then, she cut the triangles out of the rectangle and matched up the pieces to prove to herself that the triangle has the exact area as the remaining pieces of the rectangle. Since the triangle plus the group of remaining pieces form two equal parts of the rectangle, then you know the area of the triangle is half the area of the rectangle.



Then, we transitioned from the hands-on to pictures and she learned to draw a rectangle around the triangle, find the area of the rectangle, and divide by 2 to get the area of the triangle.


Pamela spent some time learning to measure the base and height of physical triangles or pictures of them to avoid the trap of thinking that half of one side times another side will work. I helped her get far enough to be able to handle finding the surface area of a pyramid which was the ultimate goal. Down the road, we will revisit the area of triangles and delve into why and how to extend the base to find the height.

Surface Area of Rectangular Prisms
We began by counting the number of surfaces of various polyhedrons to introduce the idea of a solid having faces. I found an awesome resource for making my own out of cardstock paper (you must check out the link--some of the models are fantastical). The first item we chose was the paper clip container, which perfectly matched the sticky notes (top and bottom) and only required minor adjustments for the sides. We labeled each side with letters and identified their position (top, bottom, front, back, left and right) to prepare her for transitioning to pictures later. Then, we made up a table of the areas of all the faces and added them up. Her eagle eye spotted a pattern right away (top = bottom, front = back, left = right).



I showed her how to open the box and flatten it out and draw a two-dimensional picture of it. Given the flat picture, Pamela easily found the surface area. Given a box in real life, she had no problem! The tricky part was, when shown a 3-D drawing of a box, drawing the flattened picture and correctly transcribing the height, width, and length. We continued to practice one a day, looking at the picture, and pointing to the parts of a real box. After consistent and slow work, everything fell into place suddenly and she figured out the logic in a pattern that made sense to her:

  • Every number gets copied four times.

  • Figure out the dimensions of the bottom and copy them to the top.

  • Logically, you have to copy the width of the top and bottom to the front and back.

  • The front and back involve the height, so transcribe that.

  • Logically, you have to copy the length of the top and bottom to the left and right sides.

  • The only thing remaining to transcribe is the height, which gets assigned to the left and right sides.




By now, your eyes are probably bugging or your head is spinning. Here is the thing to keep in mind. Unlike reading words on a page or taking notes in a lecture, working through these problems, day by day, develops understanding. Pamela thought of this way of solving the problems by knowing what makes sense and what does not make sense. That kind of knowledge comes from going from concrete to picture to words to abstract numbers and symbols.

Surface Area of Triangular Prisms
We applied the same process to a pyramid with a square based. She had no problems making the connections for this solid, drawing what she calls "the star", and transcribing numbers correctly.

To assess whether or not Pamela truly understood calculating surface area from a flat drawing, I gave her a slightly different problem. The last thing I want her to do is work math problems on automatic pilot. The only way to understand math is to think and make logical connections. I gave her dimensions for a pyramid with a triangular base and the star suited for that solid. Pamela had no problems adjusting her strategy for this problem.