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 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.

Mud Pies and Other Messes

"Can I make a Mississippi Mud Pie?" asked Tommy (10), inspired by the recipe in his Christmas gift, The Boys' Book of Greatness. Already in the kitchen chopping celery, carrots, and onion for a Bolognese sauce, I readily granted permission. So he began to cook alongside me, asking for my assistance in finding springform pans, getting chocolate from the garage, and melting the chocolate in the microwave. I multitasked in the absentminded manner I have when I'm both cooking dinner and calculating mentally exactly how much time I have left in my afternoon and which half of the things I originally planned on doing will actually fit in the next two hours.

With the sauce simmering, I started accompanying Karina on the piano as she practiced singing. Her voice inched higher in her warm up exercises and I congratulated myself that I had left enough time to practice with her before we left for ballroom dance. Then I heard a yell.

"Mom! The pan's leaking!"

I ran into the kitchen. Runny chocolate batter seeped from the pan onto the counter, dotted the oven floor, rack, and door, and trailed around the kitchen island in a nearly complete oval. I sighed as I stared at the mess. The destruction of my afternoon plans, my kitchen, and my equanimity must have shown on my face because Tommy asked, "Mom? Are you mad?'

"No. I'm just trying to decide what to do."

I have heard that all springform pans leak. This may be true, but mine has been bent out of shape enough that instead of a drip, it flowed freely.

"I'll move it to a new pan," I said, pouring the batter into a bowl and scraping the remnants of the graham cracker crust, now mixed with chocolate, into a tart pan, "you clean up the floor."

Life is messy. This has been on my mind recently, ever since I read The 10 Commitments: Parenting with Purpose by Chick Moorman. He outlines ten aspects of parenting, suggesting that parents congratulate themselves where they are already successful and improve in the areas where they are less than stellar. I knew I had found one of my weaknesses with the very first one: "I commit to remembering that experience can be messy."

He continues, "I accept that sand, mud, food, paint, cooking, eating, relationships, emotions, and social interactions can be messy. I allow my children to learn from making messes and the cleanup that follows. I recognize that experience can be messy."

"The cleanup that follows"--four words I cannot get out of my head. In my household, the making messes half of the commitment reigns. Crafts, books, food, clothes, papers, and toys get spread everywhere. I have failed to assist my children in developing the good habit of cleaning up after themselves, taking responsibility for the messes they make. They constantly walk away from messes, completely oblivious to the chaos trailing behind.

Establishing good habits, especially neatness and everyone cleaning up after themselves, is my main focus right now. Comparing habit to a train track that enables our life to run smoothly, the educator Charlotte Mason wrote, "it rests with parents and teachers to lay down lines of habit on which the life of the child may run henceforth with little jolting or miscarriage, and may advance in the right direction with the minimum of effort" (Mason, Home Education, 119).

How I would love to have a household where the trains of all our lives can progress steadily along the track of good habits! I suspect that the problem is my inconsistency in demanding cleanup after every mess. Charlotte Mason explained how the failure to be perfectly consistent is the major pitfall mothers have in helping their children develop good habits. She wrote that sometimes a mother thinks a child should be rewarded after forming a habit, so she gives him "a little relaxation" without continuing to enforce it, "and then go on again. But it is not going on; it is beginning again, and beginning in the face of obstacles. The 'little relaxation' she allowed her child meant the forming of another contrary habit, which must be overcome before the child gets back to where he was before" (Mason 121).

My greatest failing may be that I not only grant my children a little relaxation, but myself as well. I need to set the example of cleanliness I want my children to follow, and it will only happen if I make a continual effort. Suzuki said, "You don't have to practice every day--only on the days you eat." Cleaning up needs to be practiced every day until it is as habitual as eating.

In the Suzuki Method, students develop a repertoire as they continue to review old pieces even as new ones are learned. Through repetition, learning continues. I think this relates to everything we learn, so this year, I hope to teach my family and myself at least one new habit each month, and then maintain it the next month as we begin a new one. Even though I'm not sure how far we can take this or how many habits we can develop and keep up, I'll continue trying.

It's embarassing to admit my faults. I almost feel like I should title this entry, "Confessions of a Messy Housewife" because I do struggle with such basic, mundane things. My habits for January have been to wash every dirty dish in the house before going to bed at night and to do all the laundry on Monday and Thursday. My children are learning, too, as Tommy did when he mopped up the chocolate under my supervision while the Mississippi Mud Pie baked in a new, one-piece pan. Now on day 24, I have plugged away at the dishes every night, even when I didn't want to, because of my conviction that even one lapse could make the track of habit I am laying get derailed. However, I will keep in mind if I do miss a day that repairs are always possible, that laying new track may be a step back, but it works.