Friday, February 12, 2016

Composition and Decomposition

As an educator, I am always trying to develop a schema that is accessible to all, flexible and fluent and effective as a framework. Decomposition and composition are two of the most influential constructs in a primary classroom.  Children spend their days mastering  discreet skills/parts and then applying critical thinking as they compose or decompose parts and wholes. (reading, observational drawing, clay, writing, math, handwriting, sports, dance etc.)

Zoey is completing an experience we refer to as "the counting jar.". The basis of counting is composition. We take one jewel, add another and repeat the process until we have counted all of our jewels. She is exploring the sequence of numbers in the context of a number line framework (each line in the numberline is a multiple of five).

As a class, we consider the strategies that help structure our thinking. Are there more jewels than five but less than ten? How many more jewels than ten are in the counting jar?

This work is a prelude to addition and subtraction. We are beginning to add parts together and subtract parts from the whole. We start with games and then begin to formalize the process with the addition, subtraction and equals symbols. 

Cal explained his strategy for this domino. 
He knows that five plus five equals ten and then he added the remaining one. 

Cal decomposed the six into two numbers facilitating his process. 

When writing the number eight  how do we utilize different lines, curves and circles together (composition)? We start with the parts and then construct the whole number.

 The children understand that varying movement and combination of shapes composes other shapes.  We often play the game Fill the Hexagons. The children may use any of the pattern blocks in different combinations to create a hexagon. Each hexagon must look different.

Again, the whole is defined as the sum of its parts.

 A pattern is created with parts (units) combined in a predictable sequence. We often refer to the whole as the pattern train and the parts(unit) as the cars. Students create a pattern using a unit but also identify the number of units apparent in a pattern. The children compose a pattern and then consider decomposition.

Symbols and algorithm  do not hold meaning until children have ample time to explore the  mathematical thinking  present in the process of composition and decomposition. 

Tuesday, February 2, 2016

Bow to the Earth

Foolishness? No, it's Not     

         Sometimes I spend all day trying to count the leaves on a single tree. To do this I have to climb branch by branch and write down the numbers in a little book. So I suppose, from their point of view, it's reasonable that my friends say: what foolishness! She's got her head in the clouds again. 

But it's not. Of course I have to give up but by then I'm half crazy with the wonder of it-the abundance  of the leaves, the quietness of the branches, the hopelessness of my effort. And I am in the delicious and important place, roaring with laughter full of earth-praise.

Mary Oliver

The recent blizzard left many of us remembering the snowy days of our childhood. We recalled leaving the house early in the morning with siblings or friends and heading to a hill to sleigh or a frozen pond to skate. Parents were at work or at home with the expectation that we would take care of each other and return for dinner. We noticed the quiet of a snow fall, felt invigorated by the cold, adjusted to the glare of the snow and enjoyed the sweetness of returning to warm houses with exhausted bodies and memories of laughter.

We are often asked by visitors to Sabot to outline our goals or expectations for Forest Friday.

 My intention as a teacher is to be a quiet observer...almost invisible. My hope is for the children to feel free and empowered to pretend, sing, chase, study, explore, observe and be filled with joy. We would like our students to glean during the small window of time on Fridays what we spent hours experiencing in our own childhood----the restorative force of nature and play.

We know that play begins when a child feels familiar and comfortable in a setting.  This is why we return each Friday to our "Winter Forest" or the stream during the warmer months.

An impromptu game of Limbo using a large stick

We never take for granted the enormity of the trees, the contrast of the open sky, the shadows of the forest on the snow and the endless possibilities of a stick.

Challenges are everywhere. The children sculpted stone shaped pieces of frozen snow and carefully balanced them. Perhaps a frozen version of Jenga. 

Several children are practicing body balance as they walk a fallen tree trunk. The children rely on each other  for physical and moral support. Several of the children faithfully return each week to the log with the hope of mastering this challenge.

The snow has affordances that the forest floor cannot offer the children. It is a giant slip and slide.

"Children building  enlarge and change their schemas of relative space ("how do I get this "stick" to bridge these other two?"), numerosity (each "stick" is some multiple of the basic unit), symmetry and proportion, balance, stability and gravity. One child, attempting to construct a roof to bridge four walls, soon discovered the walls were too far apart and tried out a number of hypothesis before mastering the relationships involve. Fortunately no one interrupted her or stole her challenge to learn by "showing her how"! 

Your Child's Growing Mind 
Jane Healy

"Fantasy play with others gets children to enlarge their metal frameworks, get outside their own mind, practice using language,  and gain information about other values and point of view. Play, in a sense , is a the gateway to metaphor, to scientific insight, and to invention."

 Your Child's Growing Mind
Jane Healy

Moments shared with family and friends  will nourish for years to come. Sometimes the moments are silly as when mittens become feet and a little girl transforms into a gorilla. Other moments bring a chance for reflection or just a quiet interlude to observe.

The Moth, the Mountains, The Rivers

Who can guess the luna's sadness who lives so briefly? Who can guess the impatience of stone longing to be ground down, to be part again of something livelier? Who can imagine in what heaviness the rivers remember their original clarity?

Strange questions, yet I have spent worth while time with them. And I suggest them to you also, that your spirit grow in curiosity, that your life be richer than it is, that you bow to the earth as you feel how it actually is, that we--so clever, and ambitious, and selfish, and unrestrained-are only one design of the moving, the vivacious many.

Mary Oliver

If you are looking for more inspiration or resources for you and your child to explore together I am listing a few below.

Finnish schools

Learning through Play

Nature Anatomy

Nature Journals

The Girl Who Gets Gifts from the Birds

Outside your Window