Algorithms are Recipes

At 6:30 this morning, I grabbed paper and pencils, and Eric and I figured out why the algorithm for extracting square roots in Katie's math book works. Why did we choose to do math during our early morning time together? Well, finding square roots was yesterday's math lesson in A Beka Pre Algebra. I followed the directions, walked her through a couple of problems, and was ready to set her working on her own when she said, "But I don't understand it. I can't do it if I don't understand it."

Just the day before my mother told me she skipped the section on extracting square roots with my niece. I never did it myself until yesterday. Eric also never learned how in school but taught himself some time along the way using Newton's Method. A calculator makes fast, efficient business of finding square roots. Why should we bother?

An algorithm is basically a recipe for solving a math problem. If you follow the procedure correctly, the right answer will be the result. In traditional math education, like A Beka PreAlgebra, the recipe or algorithm is what matters and helping the student understand why rarely merits mention. A recipe for pancakes may warn against overbeating because it makes them tough but usually lacks an explanation. Knowing that they become tough because the gluten develops and creates more structure in the batter doesn't change the recipe. Following directions and practice make good food and good math, not an understanding of the process.

Do I believe that? Absolutely not. My favorite biblical proverb has always been "Wisdom is the principal thing; therefore get wisdom: and with all thy getting get understanding." I do think knowing how gluten functions in doughs and batters and how I can make changes to vary the results makes me a better cook, even if it is in an intangible way. In cooking I manipulate ingredients to vary the results; in math I vary the results through manipulating numbers. Michael Ruhlman's Ratio: The Simple Codes Behind the Craft of Everyday Cooking explains the value of knowing the mathematical ratios for doughs and batters, imparting the craft of cooking with an elegant simplicity that made the cookbook a pageturner for me. Deriving square roots without a calculator will make Katie and me magicians performing a number trick, but understanding the algorithm will raise it above that.

First we turned to our supplemental math curriculum, Math-U-See. Steve Demme on the DVD usually explains everything comprehensively, but he lacked an explanation for finding square roots, so we decided to figure it out ourselves in the early morning light. I extracted a square root, then squared it to examine the process. Eric compared it to the squares of binomials and trinomials. Somewhere along the way, I found a way that made it clear for me, he found one that did the same for him, and we compared notes.

A couple of hours later I explained it to Katie. "Oh! It's like multiplying backwards!" she said and then completed the lesson. I wish understanding everything about life could be as simple as math and cooking.

A Poetry Assignment

Poetry combines my love of language, music, truth and beauty. The best poetry fuses these elements together in such a way that I think, "That is true. I wish I could phrase it so well." My current nightstand read, The Three Marriages: Reimagining Work, Self and Relationship by David Whyte, while not a book of poetry, is written by a poet. He explains early on that as a public speaker he mostly relies on hundreds of memorized poems that he strings together into speeches. I immediately began my list of "Poems to Memorize." Perhaps we all might be a bit more of a poet if we spent our time reading, writing, memorizing and reciting poetry.

I studied poetry in high school and college but claim no expertise in teaching it. Since grandmother, mother, daughters, and nieces recently began a three-week study of 19th-century British and American poets (not meant to be exhaustive), I have been attempting to feel my way through teaching it. For each poet we study, I have assigned us to write a poem based on one we have read. Speaking for myself, I know it has not made me write great poetry, but I have a greater appreciation for the poets we have studied, and I do feel I can consider myself an amateur poet.

At the request of one of my daughters and one of my nieces, we included Edgar Allan Poe in our study. I gave the following assignment:

Using Edgar Allan Poe’s “Alone” as your inspiration, write a poem on the topic of your choice using the following guidelines:

• Describe a feeling.
• Use dashes as your only punctuation.
• Make each couplet (set of two lines) rhyme.
• Each couplet should have the same number of syllables on each lines, either 7, 8 or 9 syllables.

Example poem:

Alone

Edgar Allan Poe

From childhood's hour I have not been

As others were — I have not seen

As others saw — I could not bring

My passions from a common spring —

From the same source I have not taken

My sorrow — I could not awaken

My heart to joy at the same tone —

And all I lov'd — I lov'd alone —

Then — in my childhood — in the dawn

Of a most stormy life — was drawn

From ev'ry depth of good and ill

The mystery which binds me still —

From the torrent, or the fountain —

From the red cliff of the mountain —

From the sun that 'round me roll'd

In its autumn tint of gold —

From the lightning in the sky

As it pass'd me flying by —

From the thunder, and the storm —

And the cloud that took the form

(When the rest of Heaven was blue)

Of a demon in my view —

My niece just completed her final course of chemotherapy for leukemia last week. The poem she wrote, "Jealousy," touched me with the true feelings of a 14-year-old girl. Here it is:

Jealousy

Whenever I look around and see—

Pretty girls with hair—unlike me—

Curly—straightened—or wavy hair—

Sometimes it’s really hard to bear—

My thoughts are filled with jealousy—

Why not that hair belong to me—

A wig I wear upon my head—

Taken off when it’s time for bed—

I’m not saying—I’m jealous all the time—

Just sometimes it hits me in my mind—

When I have thoughts of jealousy—

I think—one day—that will be me—

My assignment idea, good or bad, is not the intellectual property of anyone other than myself. You are welcome to use it in your own home or class, but I do politely request feedback on whether you enjoyed the assignment if you do indeed complete it.

Everyone has Parents

"Thomas Jefferson, Patrick Henry, John Adams and your children all have something in common – Parents. You can make the difference."

When I saw this advertisement for a seminar, I thought to myself:

"Adolf Hitler, Benito Mussolini, Hirohito and your children all have something in common: parents."

Right now I find my responsibility and influence for good or bad in my children's lives overwhelming. Suzuki said, "A child improves depending on his parents." The bible reads, "Train up a child in the way he should go, and when he is old, he will not depart from it" (Proverbs 22:6). When a person goes bad, the parents usually get the blame. Last week I read an article about Tiger Woods that placed the blame for Tiger's lack of moral character squarely on Earl Wood's shoulders. The author, Jason Whitlock, wrote:

After his press conference in February, I wrote a column comparing Woods to Michael Jackson. No one blamed Elvis Presley or Quincy Jones for Jackson's fall from grace.

We blamed Joe Jackson, Michael's father.

Is there a difference between Joe Jackson and Earl Woods?

Both focused on raising entertainers more than human beings.

When I read the article, I was ready to blame Earl Woods. I even thought of blogging about it. Of course I am trying to raise caring human beings with character. Shame on him!

This week I'm not so sure. I'm in a Christian, forgiving mood. As a homeschooler, not only do I get the blame if my children are poorly behaved or delinquent, but I also get the blame if they lack knowledge of history, times tables, reading, writing, penmanship, nutrition, science, spelling, grammar, and algebra. Have I missed anything? My husband Eric kindly and quickly pointed out to me mid-rant that I also get the credit, but at that moment I didn't care. It's just not fair!

My Christian mood might not be strong enough. The person I can't forgive is me. Sometimes I get tired or sick and I realize that I am not consistently working with my children on the skills I want to help them develop. In my view, consistency is the hardest thing to be consistent about. Today when I walked in my children's rooms, disgusted with the mess on their floors, I felt angry. When I walked in my own room, disgusted with the week's worth of laundry baskets full of clean clothes on the floor, I felt shame.

Shinichi Suzuki said, "Practice only on the days you eat." How impossible that seems to me! Some days we miss math, on others instrument practice gets skipped, we don't do a little Spanish homework every day no matter how many times I set that goal. When I'm in a dark mood, I conclude that THE thing wrong with my life is me. I lack pretty much everything.

Excessive guilt and discouragement are unproductive feelings. I realize that perfect parents don't exist. I do, however, give some priceless things to my children that no one else can:

• I love and want each individual child.
• I spend lots of time, both quantity and quality, with them. Benjamin Franklin wrote, "Dost thou love life? Then do not squander time, for that is the stuff life is made of." I believe that by giving them what "life is made of," it shows that I value my family.
• I know them better than any other teacher could.
• I never give up (for more than the length of a pity party).
• I seek improvement.  

My religion also gives me comfort. A speaker in my church referred to the effort to be like Christ as "attempting the impossible." As a mother, I'm sure that all my attempts are exactly that. However, if we lay our efforts on the altar, Christ accepts our sacrifice, our heart and our spirit, and we can be given beauty for ashes. That is a grace, a strength, a promise I can rely on, because everyone has parents, and we can all also be the children of Christ.

Remember Your Manners

Remember your manners: last year I decided this was something I couldn't ask my kids to do because I wasn't sure if I had ever taught them enough about manners for them to know them to begin with, much less remember them later. Because I happened to remember this fact while Christmas shopping, the result was a gift to the Leonard family of the book 365 Manners Kids Should Know: Games, Activities, and Other Fun Ways to Help Children Learn Etiquette by Sheryl Eberly. It has been a simple and straightforward way to incorporate manners lessons into our daily family life. For each calendar day of the year, the book discusses one aspect of manners in approximately two to three paragraphs. So far we have completed units entitled "A Great Beginning," "Family Time," "Getting Along with Other Kids," "Introductions," "Telephone Talk," and are partway through "You Are What You Say." I read selectively from each day's portion at the breakfast table, and then we discuss it.

The book is not without flaws. Some topics seem misplaced on the calendar, like February 16, which discusses rules for using friends' or neighbors' swimming pools. It must have been a challenge to decide on 365 mini-topics that fit into larger units, but some of them seem trivial, like "Frightening Others" (January 24),while others I don't even consider part of manners, like "Allowance" (January 30), which we don't pay in our family. At times we disagree somewhat with Eberly's advice, but the lessons have generated meaningful conversation.

Occasionally the lessons include activities. My children are looking forward to May with the beginning of table manners and an activity almost every day. I have promised them that we will eat all of the different foods specifically discussed after we learn how to handle them properly. So far my favorite morning has been February 28, "Remembering names." The activity was to come up with a rhyming word for everyone in our family's name so we could practice inventing mnemonics for people's names. Karina suggested we come up with alliterative phrases instead, so soon we were all "Terrific Tommy from Tacoma" or "Little Luke from Louisiana."

Ultimately, my favorite outcome from our breakfast manners class has not been my newfound ability to say "remember your manners" and indicate something specific we've read. Instead it has been the days that Tommy and Jack have opened the door for me on the way into church after the "Opening doors" lesson or last week when Tommy introduced his friend Taylor to his piano teacher exactly like the book describes. My children's manners aren't perfect, and the book keeps showing me that mine need quite a bit of improvement as well. Of course! That's why we need it.

Teaching Letters to Young Children

My children as toddlers, in their first burst of language acquisition, have loved to learn the names of animals and the sounds they make. When Karina, my oldest, turned two, my mother suggested I teach her the letters as well. She said that in her experience it was easier to teach children letters as toddlers when they are enthusiastically labeling everything in their environment than it is to wait until they are four or five years old. When we were children she taught my brothers, my sisters and me our letter sounds at two years old; we learned the letter names later. I decided to teach my children both the names and sounds at the same time, reasoning that if they knew that a cow says moo, they could learn that "m" says mmmm.

I agree with Shinichi Suzuki that education begins at birth and that we tend to underestimate what young children are capable of learning. My daughter Helena, 18 months, has reminded me of the enormous potential in every human being this week. Yesterday after eating a banana, she carried the peel to the garbage can by herself. At dinner when I asked someone to pass the milk, she pushed the milk carton towards me. These are simultaneously ordinary and miraculous accomplishments to me, ordinary because every normal child seems to blossom at this age, suddenly understanding and doing things they have been absorbing since birth, miraculous because of the explosion of latent ability that I always underestimate until it emerges. I consider throwing trash away a miracle, in part because I frequently wish my older children did it more consistently. I also sometimes sit patiently at the table pleasantly repeating, "please pass the milk" for a few minutes, then becoming less patient and pleasant when everyone ignores me.

"Human ability will not exist if it is ignored when in the seedling stage," Suzuki wrote in Ability Development from Age Zero. Children will only observe and learn those things that have been a part of their environment, and the most crucial part of this environment is the people in it. Parents and siblings need to spend time interacting with infants, toddlers, and preschoolers, consciously trying to model good character. In this way, "inspiration and interest are acquired involuntarily by an infant from everything he sees and hears, like a seed that is planted. This is what molds--forms--the character . . . . It is a frightening fact. By no means only words or music, but everything, good or bad, is absorbed" (Shinichi Suzuki, Nurtured by Love).

In a few minutes a day, children can learn their letters. None of my children have considered this to be work or pressure because I have approached it like a game, and they have frequently asked to do their letters. One fun and methodical way to teach letters I discovered when my second child was two. A friend of mine told me about the way her daughter's kindergarten taught letters with sounds and actions. I loved the idea, copied it, and over the years my mother, sisters and I have adapted and changed it. You can find the method and the flash cards explained more fully on my mother's blog. My favorite is the letter O, singing opera. We always sing the short o sound to a passage from Mozart's The Magic Flute where the Queen of the Night is singing.

Because I believe in exposing my children to "whatsoever things are lovely, whatsoever things are of good report" (Philippians 4:8), I have some favorite alphabet books that incorporate beautiful art. The first is Museum ABC, which also comes as a board book, My First ABC, published by the Metropolitan Museum of Art (I own both versions). I appreciate the fact that all the examples for vowels utilize the short sounds. I try not to confuse my children with vowels when they are very young, so I teach them the name and as the sound I teach only the short sound. I find it easier to pretend that it only has one sound. When they are older, I explain that it sometimes says its name. Another book I like that is illustrated with fine art is Tigers and Sails and ABC Tales, but the vowel sounds are not as consistent. Sometimes with alphabet books I skip the pages with vowels if they use the long sound.


Flash cards, actions, sounds, books: what else is there? I also like letters that children can manipulate, especially the magnetic ones from Melissa and Doug. They come in both uppercase and lowercase. We use these to play games like "help the mommy M find the baby m" or "which one says sssss?" The more contexts children discover letters in and the more they use them, the more automatic that knowledge will be when time to learn to read arrives.

 "Inspiration and interest," acquired by a positive environment, are the foundation for all education, especially in the seedling stage. Whole-language enthusiasts are right when they say children reared in a print-rich home acquire literacy readily. Early childhood education, when approached in a positive, patient way, lays the foundation for a lifetime of enthusiasm for learning. I believe this is best done in the home, which by nature should be less stressful and competitive than a school. As a mother, I can appreciate three-year-old Luke handing me a piece of paper last week on which he wrote "L l."

"Oh, it says "LLLLL," I said.

"No, it says Luke loves Mommy."

Somehow, I don't think a teacher would retain that forever in her heart as I will.

A Cake on a Pedestal

I inhaled a sweet lemon-coconut-butter scent as I opened the oven door. Golden brown, risen to the top of the bundt pan, the cake seemed perfect to me as I poked a skewer in the middle to see if it was done. Only a couple of crumbs clung to the skewer--done but not overbaked to the point of dryness. As I placed it on a cooling rack, I thought with anticipation of the gorgeous and delicious cake I would be taking to the reception after my children's piano recital later in the afternoon.

After mixing together powdered sugar and lemon juice for a glaze, I prepared to flip the cake onto a cooling rack. It's easy: simply put the rack on top of the pan, then flip in one motion while holding everything together. I've done it hundreds of times. But this time partway through the turn, the pan slid and the cake slipped, disintegrating into a pile of crumbs on the counter. I desperately tried to retrieve at least a portion of the cake until I noticed that the biggest chunk was only as big as about two pieces of cake. The cake definitely had a delicate, tender crumb.

Crackers and cheese were now the only food I had to take to the recital. My children didn't mind. Within two minutes all six of them were shouting with glee as they descended on the cake like vultures, tearing off bits, pouring glaze over the crumbs, and devouring all of it.

I went outside to help Eric with the yard work. He had no sympathy either. "Good," he said. "You don't need everything to be perfect."

My life in my mind is fully organized, never running late, as perfect as a centerpiece cake, beautifully building expectation until the moment when it is cut with ceremony and delicately eaten with forks and china. My real life consists mainly of cakes so delicate they become a pile of crumbs on contact, then get shoved greedily but joyfully into six mouths followed by twelve feet smashing crumbs and tracking sticky glaze across my kitchen floor that I have to mop up one hour later, two hours later, and the next morning. Today I can't help thinking, though, that the unveiled enthusiasm of that moment is a life I should cherish in my mind because a cake on a pedestal will never match it.

Harmony Between Sisters

Six hands at a single keyboard played Debussy's Clair de Lune, the pianists three sisters seated side by side. The gossamer melody wove tranquil threads and their hands crossed and uncrossed with perfect coordination; I couldn't always tell whose hand played which notes. While watching them I felt suspended in a web of music, cooperation, harmony, and peace within my reach, glistening like beads of dew on the silken strands. With sudden clarity I knew that this piece now represented for me the benefits of a strong family.

We went as a family to see the 5 Browns in Tacoma Saturday night. These five Mormon siblings, who all attended Juilliard simultaneously and now perform and record together, play orchestral pieces arranged for five pianos as well as duets, trios and solos. They engage audience members of all ages both by the way they play and by their quirky introductions for each piece that are personal and educational. While I loved the music, what I gained most was a sense of the worth of family, siblings especially. They performed together in a united way that I feel only siblings could, people who shared a childhood, parents, toys and everything else in the years identity and individuality emerge and begin to cement.

I have never played a piece at one piano with my two sisters. I do not play the piano as well as the 5 Browns and never will. I have, however, felt cooperation, harmony, and peace while working in the kitchen with my sisters. Tatiana and I spent one Thanksgiving morning baking an apple pie that had a top crust consisting of overlapping, individually cut out and etched pastry leaves. Another year at Christmas time we made chicken tamales. For her daughter's first birthday, Johanna and I wrapped individual chunks of cake in fondant, decorating them to look like alphabet blocks.

A couple of years later for her next daughter's birthday, we wreathed a cake with flower petals to look like a sunflower.

My sisters and I also share a dedication to home education. They (and my mother) are my greatest homeschooling resource because I still prefer a live person I can engage in conversation to any online support. We each have our individual approach. I am amazed by Tatiana's commitment to speaking only Spanish in her house a few days a week, resulting in a bilingual family. Johanna has a balanced, moderate approach I learn from as I struggle with my tendency to either try for the ultimate or do nothing. Even though our homes dot the west coast--Southern California, Northern California, Washington state--I feel that even now we share our lives in a way no one else can. We do not always get along perfectly (although it's been at least two decades since I can remember any friction with Johanna, who I know deserves all the credit for this feat). However, my memories of our time together are like an inviting porch welcoming me home, a place where I'm capable, understood, and loved.

I decided to have six children in part because I felt my daughters deserved to have two sisters. My own two sisters are irreplaceable, as we are three women with a shared childhood culture who are now mothers contributing to the culture of a new generation of children. As a group I might work with all my brothers and sisters as the 5 Browns did on five separate pianos, each playing their part and contributing to an orchestra of one instrument. It is a greater unity I visualize with my sisters and I as a trio harmonizing on one piano, our hands crossing each other, reaching towards the same goal. For our next family reunion I plan to suggest that we play a trio.

To see video clips from a 5 Browns concert, including Debussy's "Clair de Lune," visit their home page, http://www.the5browns.com/.