Our Ever-Evolving Pedagogy

I finally got my hands on a copy of John Holt's classic, How Children Learn," and I am loving it.  His observations take me right back to when A. was a toddler and my own fascination with her innate ability to learn.  I'm about a quarter of the way through and will try to post some of my thoughts and favorite excerpts as I go.  

If you've followed our blog for very long, you might have noticed our ever-evolving methods.  In preschool, I fell for the "more-faster-better" mindset of early education.  I was so mesmerized by how fast A. learned that I thought the best thing to do was set up a little version of school at home, teach formal lessons, and keep spreadsheets of what was learned.

By Kindergarten I'd seen the error of my ways, began slowing down, and became more conscious of the need to nurture A. as a complete human being and not just a mind to be filled with information.  We began exploring Waldorf and Montessori methods and incorporated both into an eclectic style of home-education.  

For First Grade, we used the complete Oak Meadow curriculum and, while we both enjoyed it, I felt as though my own creativity was being squashed a bit by my conflicting desire to go by the book.  I also noticed that A.'s natural pace is pretty fast and that she, like I imagine all children, becomes board when she's not challenged.  I learned that I needed to balance nurturing with inspiring.  The beauty of home-education, of course, is that we can curtail each day to keep interest high and encourage that innate passion for learning.

For Second Grade, we're flying without a net for now -- although I am considering purchasing the Oak Meadow Second Grade Syllabus and using the lesson plans for inspiration.  I'm also reading the California Content Standards through Third Grade and thinking up ways to reach those goals without worksheets or too much desk time.  I'm not married to the standards, however, and do plan to take great liberties with them.

I'm discovering that, if left to her own devices, A. will draw, paint, read, observe nature with her binoculars, write and illustrate little books, play piano, invent games (she's particularity fond of creating board games with intricate rules and pieces), and, of course, engage in imaginative play.  I'm trying to cultivate a more relaxed attitude and trust that learning takes place naturally; however, I am also admittedly so conditioned by my own education that, for me, it's essential that we stick to a flexible schedule and work towards specific goals.  I guess you could say that we're eclectic, partially child-led homeschoolers still slightly fearful of taking the leap into purely orthodox unschooling.

We're studying Homer's Odyssey right now.  We found a great edition titled, The Adventures of Odysseus by Barefoot Books and we're using this myth to inspire inquiry into all of the other subjects -- including math.  We're working with fractions right now and have had some great discussions about how fractions, like myths, are small parts of a greater whole. 

We made salt clay yesterday and worked with fractions -- slicing the "pie" into half, quarters, eighths, and sixteenths, looking at equivalent fractions (two eighths is the same as one quarter, etc.) and exploring the four functions with fractions.  I gave A. some informal instruction in this last week and made a point to compare fractions to the musical notation with which she's already so familiar.  A. is keeping a Main Lesson Book and has drawn circles and pies and toyed with some simple equations (If 1/4 plus 1/4 equals 1/2, then 1/2 divided by 2 equals 1/4).  

Later, we used our salt clay to make Greek-inspired "pottery" and spent the early evening painting our creations with geometric shapes and black silhouettes (we'd planed to paint scenes from the Odyssey but quickly discovered that painting on clay is much more difficult than we'd imagined).

Every year I ponder the same questions, explore the same fears and worries --- mainly, can we do this without that formal institution called "school?"  Every year I come back to the same answer.  That answer is yes; however, it does require, as Holt explains, faith that children can and will learn on their own.  I'm working to loosen my grip a little each day -- while still encouraging self-discipline.  I think Holt said it best when he called it faith:   

"Call it a faith. This faith is that man is by nature a learning animal. Birds fly, fish swim, man thinks and learns. Therefore, we do not need to "motivate" children into learning, by wheedling, bribing, or bullying. We do not need to keep picking away at their minds to make sure they are learning. What we need to do, and all we need to do is bring as much of the world as we can into the school and the classroom; give children as much help and guidance as they need and ask for; listen respectfully when they feel like talking; and then get out of the way.  We can trust them to do the rest."

Music, Math, Mapping, and More

With the holidays behind us, we're getting back into a steady rhythm at home.  We started the morning with a little music.  Like her dad, A. loves composing her own...

Figuring out the notes...

writing them down...

& putting it all together.

Then, instead of hitting the books right away this morning, we went for a little adventure...

   We found a heart shaped hollow in a tree...

... and a heart shaped rock.

We walked by a little stream, smelled pine needles, listened to the sound of the water...

... and built a fairy house.  

When we got home, it was time for some math.  We've been working on what we're calling "doubles."  (2+2, 3+3, 4+4, etc.)  A. has them committed to memory through eleven now -- so I thought I'd try something new.  I gave her some division and multiplication problems based in the knowledge she's already acquired.  I thought maybe since she knows four plus four, she can figure out eight divided by two and four times two.  It worked like a charm all the way through twenty.  

We've also been working on word families and spelling.  Instead of just writing her words again and again (that would be boring!), we have make-believe spelling bees.  I gave her thirty-two words today (some from the Second Grade No Excuse List, others from the Fry's 300 Instant Sight Words, others just easy word family words like rain, train, and plain.)  She only missed two.  I think that really says something about the importance of keeping it fun. 

Where's Mama Wind?

There She is!

Then it was time for some Social Studies.  Last session we learned the four directions using the wind and a naturally dyed silk ribbon streamer that we found on Esty at the Tan Family's amazing shop, Syrendell.

With that knowledge intact, we started a cartography project today inspired by our Oak Meadow first grade curriculum.  A. created a map of her bedroom using the four directions to accurately depict the placement of her furniture and other big objects in her room.  Next week we'll expand her map to include the whole house.  Once she's successfully mapped our home, we'll expand to include the neighborhood, the whole town, the state, the country, and then the world!  

I think this geography lesson also has a deeper meaning.  Home is where all adventures, great and small, begin.  And when our foundation there is solid, there's no limit to where we might go.

Om Gnomes

Five little gnomes went out one day...

... over the hills and far away.

Mother Gnome said, "Om, Om, Om, Om."

But only four little gnomes came home.

 Four little gnomes went out one day,

Over the hills and far away.

Mother Gnome said,

"Om, Om, Om, Om."

But only three little gnomes cam home.

 

Three little gnomes went out one day,

Over the hills and far away.

Mother Gnome said,

"Om, Om, Om, Om."

But only two little gnomes came home.

Two little gnomes went out one day,

 Over the hills and far away.

Mother Gnome said,

"Om, Om, Om, Om."

But only one little gnome came home.

One little gnome went out one day,

Over the hills and far away.

Mother Gnome said,

"Om, Om, Om, Om."

But no little gnomes came home.

Mother Gnome went out one day, over the hills and far away.  

Mother Gnome said, "Om, Om, Om, Om...."

... and all of Mother Gnome's gnomes came home!

Gnomes by LittleRedWhimsy on Etsy

... a little shop for little people with big imaginations!

Wisdom, Waves, and Water Sprites

We began our W week with twenty-four new words: with, will, which, when, what, where, we, was, walk, warm, write, woman, way, wish, white, where, way, want, would, work, went, womb, waves, and water.  

Rather than memorizing the correct spelling through written repetitions, we've been combining skills by writing complete sentences using our W words.  Our goal is to have A. writing paragraphs by the first day of summer with 3-5 coherent, meaningful sentences that stay on topic, make sense, and use natural vocabulary.  I think she's well on her way to reaching that goal.

We've also been enjoying word problems and found this great resource for first and second grade math games and worksheets.  While I'm not a big fan of worksheets, I have to admit that since implementing a new house rule of at least one per day, A.'s math skills are showing marked improvement.  She actually enjoys the three-minute timed drills; however, I have a rule that, in my classroom, there are no mistakes -- only learning -- and I've banished all red pens in favor of erasers.

Yesterday we enjoyed a mindfulness practice and brought a bowl of water to our morning circle.  We wet our hands, turned our palms up, closed our eyes, and tried to feel when the water was dry by focusing our attention just on the bodily sensation of having wet hands.  Then we made ripples by tapping the center of the water and discussed how people are like waves of the same sea and how, when we have peace within, we create peace on earth through our relationships and interconnectedness.  I asked A. to recall the morning not too long ago when the lake was calm and reflecting the sky.  Then I asked, "How is the water like our mind?"  She answered, "When our mind is calm, it reflects how things really are... just like the lake reflects the whole sky. When they're rough, everything looks wonky."

Then we named some of the things we can do to help keep our mind reflecting what is real.  While I suggested eating healthy, organic foods and exercising, A.'s answers surprised me.  Her first answer was, "By doing things where we concentrate."  I couldn't agree more.  Engaging our mind in an activities like music or art requires mindful awareness.  Through practice, we can develop an abiding clarity of mind.  

Her second answer was, "By trusting ourselves."  She went on to explain how she's been learning to make sharp turns on her bike without training wheels.  When she worries, she misses the turn.  When she trusts herself, she succeeds.  I think this is quite an insight for a Kindergartner.

Today we read a Jataka Tale, The Prince and the Water Sprite.  Jataka Tales are folklore-like literature, much like Aesop's Fables, only native to India and relating to the adventures of the Buddha in his former existences.  Today's story was filled with W words and features a mischievous water sprite who captures all who enter his pond except those who give the right answer to one question: "What are the good fairies like?"

The youngest princes answer incorrectly and are carried off to the the water sprite's lair.  The eldest brother, who is wise of heart, answers correctly saying, "The good fairies are like the pure in heart who do no wrong, the good and kindly in word and deed."  His wisdom saves his brothers and the three princes go on to rule their kingdom together in kindness. 

Wisdom is a recurring theme in our home studies.  It's what happens when we learn to send our intellect down into our heart and allow our actions to flow from compassion.  Sadly, it's missing from Fry's 300 Instant Sight Word list  because it doesn't fall into the category of seventy-five percent of the words children are most likely to encounter in literature.  Today we added it to our vocabulary list as word number twenty-five.

Shapes & Forms

My mind has been turned to shapes lately.  My kinder is almost six, so, naturally, she's known the basics for a while now.  Still, knowing the answers and understanding the essence are two different things.

Shapes conjure up feelings and inform both abstract and specific states of consciousness.  For example, circles appear in many cultures with an archetypal symbolism of oneness.  They are round and endless, seamless, infinite, and whole... an expression of perfection, of equality in all directions.  For subtle reasons, circles represent the feminine... they also represent unity and eternity.  

The Ouroboros, a snake or dragon forming a circle with its tail in its mouth continually devouring itself and being reborn from itself, is a symbol of eternity and of the cyclic nature of the universe.  It expresses the unity of all things, which never disappear but change form in a cycle of destruction and re-creation. 

In Zen Buddhism, the circle represents the entire universe in a single, perfect stroke.

The Wheel of the Year is a Neopagan and Wiccan symbol for the Earth's cyclical seasons.  Buddhism's eight spoked wheel, the Dharmachakra, represents the teachings of the Buddha and the cycle of birth and rebirth.  

The square is a symbol of mathematical perfection... it depicts the four earthly elements, the four cardinal directions of physical space and time.  It represents concrete reality, stability, and logic.  Squares are sound, sturdy, pragmatic, and full of right angles.  They represent building blocks, integrity, and dependability.

Triangles represent balance, equanimity, harmony, enlightenment, Ascension, the Holy Trinity, the Triple Goddess, and the three realms of sleeping, dreaming, and dying... of underworld, this world, and the heavens... past, present, future... mother, father, child... love, truth, wisdom... maiden, mother, crone... creator, destroyer, sustainer.

Hearts are love...

Stars are the goddess... but it's not just geometric shapes that conjure up archetypes.  The word, "swastika" comes from the Sanskrit, svástika, and and dates from the Neolithic period as a religious symbol.  "Once commonly used all over much of the world without stigma, because of its iconic usage in Nazi Germany the symbol has become stigmatized in the Western world, notably even outlawed in Germany."(http://en.wikipedia.org/wiki/Swastika).

One might argue that this tells us symbols hold inherent meaning AND can evolve to take on drastically different socio-political meanings.  

Think about this...

 The Goddess of Willendorf...

With an estimated origin at 30,000 - 25,000 BCE, she's quite possibly the earliest depiction of the human form and "the first known religious image of the Mother Goddess in all her raw and fertile splendor." (http://www.goddessgift.com/colin-heaney-art-glass/goddess-willendorf-1.htm)   She's probably not the image of yourself you've been taught to honor.  At the same time, she's an exquisite image of the roaring, whole, round, mama, goddess most of us are...  not a stick figurine resembling an augmented, emaciated, pre-pubescent girl.  Our conditioned response to the female form has certainly evolved.

Both our nature, what is born in us, and our nurture, how we are conditioned, define who we are and what we believe.  What we allow into our consciousness, therefore, weighs heavily on what we will become.


Today for Om School we're getting outside and looking for shapes in nature.  Instead of telling A. what I think the shapes we discover mean, I'll ask her to express what they mean to her.  Maybe Jung and Campbell were right... maybe universal archetypes exist in the depths of our consciousness.  Maybe the Buddha was right... maybe all things are empty of inherent meaning and definitions only arise in relation to everything else.  Then again, maybe the only meaning things have is what we give them.  Whatever the case may be, I'm hoping that discovering hidden shapes in nature proves to be an awe inspiring adventure.

S is for Spring

With one week to go, signs of spring abound and, by yet another sweet synchronicity, we began our letter S unit this week.  

We use Fry's 300 Instant Sight Words for our weekly words.  With a total of 30 S Words on the list, we decided to split it in half and give the letter S two weeks instead of one.  This week's words were: spring, said, see, she, so, stand, such, some, saw, say, school, seem, shall, should, soon, and sure.  Instead of a written spelling test this week, we elected for something more fun.  After singing all of the words all week, we had a family Spelling Bee on Saturday.  I'm proud to report that A. is becoming quite a fantastic little speller. 

Some of other S things we enjoyed this week were Spring's Sprung by Lynn Plourde, beautifully illustrated by Greg Couch, learning to play a Samba on piano, Book 10 in Scholastic's Planet Earth Phonics Reading Program - Snakes, and committing to memory eight math facts we called "sister sums" where we matched doubles (like 4+4 and 6+6) with other math facts (like 5+3 and 7+5).

Still, the highlights of our week were welcoming spring in our outdoor classroom.  We've been closely watching the trees in our area give birth to blossoms and baby leaves.  Our neighbor's Flowering Cherry is aflame with pink blossoms, our winter daphne is full and sweet smelling, the manzanita are covered in tiny white flowers, our snow peas are thriving, and our tomato and jalapeno seedlings are now three inches tall with water droplets always glistening on their primary leaves.

With the sun's return, and our studies turned to the letter S, it seemed like a perfect time for sun salutations... a moving prayer of gratitude to the life-giving energy of the sun.  Sun salutation, Surya Namaskar, links together twelve asanas in a dynamic flow.  Beginning the day with a set in each of the four cardinal directions wakes up our bodies, gets out the wiggles, and as Christopher Key Chapple, a professor of Indic and comparative theology at Loyola Marymout University says in this month's Yoga Journal, "calls us to stretch our minds and spirits to the corners of the universe, allowing us to feel the vast expanse of the cosmos within the movement of our bodies."

The ability to sense the cosmos within our body is something I hope my munchkin is cultivating through our at-home studies.  It comes when we slow down, when we put some space between our habitual responses and our actions, and when we take care to spend time with the natural world.  

Watching tiny blossoms sprout from barren winter branches reminds me that spring is a promise the earth keeps each year.  Sensing the birth of that promise within myself gives me a deep peace -- a trusting feeling in my heart.  There is a surrender, a certain acceptance, in this trusting... a calmness of spirit that informs each day with joy.


Tomorrow we'll begin eight more sister sums, fourteen new S words, sing a silly swan tongue twister, and continue seeking spring.  Tonight, I'm settling down with my family for a Sunday night in stillness.

Socially Conscious Math

Today was a Math and Social Studies day and our Main Lesson was the number ten.  After writing "t-e-n" and "10" on the board a few times, we used wooden blocks to answer math facts with sums of ten.  We also outlined our hands, numbered our fingers one through ten, and counted by fives and tens. Then I read a sweet tale about generating good karma, The Little Caterpillar's Stripes, from the Oak Meadow Kindergarten Syllabus.  Introducing math concepts through archetypal stories integrates Math with Social Studies and Language Arts.  For a great article on the significance of integrating subjects, read Why Integrate?: A Case for Collating the Curriculum.

In our socially conscious math story, a fuzzy caterpillar must do ten good deeds in his bug community.  After each act of kindness, he earns a yellow stripe.  After the tenth stripe is earned, he makes a soft nest called a pupa and drifts off to sleep.  When he awakens, he discovers the consequences for his kindness: he's transformed into a beautiful butterfly.  I had Amelie take picture notes while listening, then answer questions on content, characters, sequence, and moral.  We finished in her Main Lesson Book by writing the number ten a few times and drawing a picture from the story.

Wooden blocks are a great tool for nurturing creativity.  Amelie shared these today during Circle Time and asked to name some of the things about them that were the same and different.  Some of our observations were: they are all the same size and shape, there are different patterns in the wood grain, they all have light and dark colors, they all have faded  spots, and, like Friday's snowflakes, no two are the same.  Later, Amelie took a few minutes for building.

Next up, we kept up the social consciousness with a short discussion about the earthquake in Haiti.  We found Haiti on the globe, lit a candle, and had a few moments of silence.  I think we'll do this every day this week. While we certainly don't want our kids feeling scared about events like these, I think acknowledging what is happening in the world is essential to raising conscious, compassionate kids. 

After lunch, it was time for Art-Social Studies integration. This is the last week of our December-January thematic unit, Bringing Back the Light.  To honor the winter season and the various holidays, we've been discussing the return of the sun and what it means to feel full of light.

A dear friend just sent us, You with the Stars in Your Eyes: A Little Girl's Glimpse at Cosmic Consciousness, by Deepak Chopra.  This little treasure fit our thematic unit perfectly... "the stars gave us eyes so they could see themselves."

After five minutes of mindfulness with Susan Kaiser Greenland on mindfulness together, we finished our day with a little dancing and yoga stretching.  Tomorrow we'll see some friends, sign up for the new ballet term, and have a piano lesson.  On Wednesday, we'll revisit the number ten, explore it's essence, march and sing our math facts, and maybe start the letter P.

Music, Math, & a Wise Heart

Today was a math and music day so I set my mind to seeing numbers everywhere this morning.  In the process, a Social Studies lesson cropped up organically and reminded me that real wisdom is greater than knowledge.  

This week our Riverdog Farm veggie box contained about ten mandarin oranges. I noticed this morning that they were beginning to look mushy so we started the day with math.  First we counted the oranges -- ten.  Then I sliced them each in half -- twenty.  Only six halves fit on our cutting board and this created a great illustration of the number six as 3+3 and 3x2.  I juiced and Amelie handed the halves to me... this is subtraction.  Six pieces minus one piece equals five pieces. 

To a young one, making juice by hand demonstrates the amount of labor that goes into bringing just one glass to the table.  As we were juicing, I was reminded of a passage from Touching the Earth by Thich Nhat Hanh and our Social Studies lesson began.

"Looking into my bowl of rice, I see clearly that this is the gift of the earth and the sky.  I see the rice field, the vegetable garden, the sunshine, rain, manure, and the hard work of the farmer.  I see the beautiful fields of golden wheat, the one who reaps the harvest, who threshes the grain, who makes the bread.  I see the beans sown in the earth becoming the beanstalk.  I see the apple orchard, the plum orchard, the tomato garden, and the workers who are cultivating the plants.  I see the bees and butterflies going from flower to flower collecting pollen to make sweet honey for me to eat.  I can see that every element of the cosmos has contributed to making this apple or this plum that I am holding in my hand or this leaf of steamed vegetable that I am dipping into the soy sauce.  My heart is full of gratitude and happiness."

I asked Amelie to think about all of the work that went into bringing these oranges to us and we talked while we squeezed.  "Looking deeply into our golden orange juice, what do you see?"  "I see the the seed that grew into a tree!"

The world is full of people who have accumulated information; however, a person who thinks with their mind and heart in alignment is a gem and often a real asset to our global community. Integrating core subjects helps develop a wise heart and honors the whole child. This encourages our kids to honor themselves and the world around them.  Since Kindergarten is a time for developmental play, awe and wonder, the last thing we want to do is override the senses, over-pressure a young mind, or put to much emphasis on the intellectual process.  If a child is directed into academic thinking too often and too soon, we risk getting them stuck up there in their head. 

One way we keep it fresh and fun is by making music.  Piano is a regular part of our curriculum and the benefits of music on the mind and body have been recognized since the days of the great Greek philosophers. Plato said music “gives soul to the universe, wings to the mind, flight to the imagination, a charm to sadness, gaiety and life to everything.” Visual and performing arts have a way of tapping into that part of us that is more than mind and, at the same time, music begins with math. 

According to the PBS Independent Lens documentary, Music from the Inside Out, A 1997 study by Rauscher and Shaw revealed that preschoolers who studied piano performed 34 percent better in spatial and temporal reasoning ability than preschoolers who spent the same amount of time learning to use computers. Preschoolers who took singing and keyboard lessons scored 80 percent higher on puzzle tests than students at the same preschool who did not have music lessons.

After Circle Time, we moved right into piano practice and got her mind working in sequences, repeating patterns, and thinking forwards and backwards.  Then it was time for her lesson and a little socialization with her music teacher.  The focus today was learning about intervals. Up and down the keys she went naming notes, repeating patterns, accessing both sides of her brain, and lighting up that part of us that is more than mind.

Back home, we reviewed the four processes of math with an art project and used watercolors to paint brightly colored sets of bugs.  This was great quality time together and we both enjoyed painting and then using colored markers to write out the math sentences. Three ladybugs plus three ladybugs plus three ladybugs equals nine ladybugs.  This emphasized what we'd done in the morning with our oranges.

After playtime and dinner it was time for cookie math.  Three rows of cookies with three cookies in each row equals nine cookies.  Add one more row and you've got three times four.  Our cookie math was another repetition of what we'd done this morning with oranges and before bed we added the finished product to her portfolio and reviewed the equations one more time. 

While the art supplies were out we returned to today's Social Studies lesson, Looking Deeply into the Orange Juice.  I asked Amelie to think back to this morning and draw all of the things she can see looking deeply.  She drew the tree with oranges, an orange falling from the tree, the veggie box they came in, the halved oranges, the compost bowl, a hand-squeezer, a half-full pitcher, and a glass with a straw.  She numbered the steps one through eight which told me that her math hat was still on and that she's still thinking in sequences.

Kids don't need to sit at a desk for hours memorizing math facts on a worksheet to become good at math.  Boring a child with written work isn't going to spark their curiosity in the subject and, from my experience, is likely to turn them away from it for good. Too often we praise dry academics and test scores over actual learning and overlook the inner-lives of our children.  When we include and integrate art and music with other core subjects, our kid's inner light turns on.  This nurtures both compassion and creativity rather than just intellect or memorization. 

I agree with Einstein.  Imagination is more important than knowledge... but greater than the imagination is the content of one's heart.  This can't be measured by standardized testing and it is the one thing most central to the continuation of a humane society.  Before we send our young learners out into the world, let's make sure they are ready.  The first step is honoring the whole child.

Romanesco Fractal

The first time my daughter asked, "Mama, what does “infinity” mean?" I stumbled over a technical answer and botched an opportunity for something magical like, "It is how much I love you."  Today, an opportunity to revisit the subject arose as organically as the box in which it came.

We support Riverdog Farm, a certified organic CSA and Thursdays are our veggie box day.  Eating seasonally is an integral part of our curriculum and opening the box on veggie day feels like Christmas morning to my whole family.  We’re always surprised and delighted by the wonders inside.  What’s more, eating seasonally and locally helps us feel our connection to the earth and her rhythms.  As a homeschooling parent and a mother endeavoring to teach her child environmental responsibility, I’ve come to honor and rely on this rhythm.

While picking up our veggie box today, I felt especially grateful for the opportunity to belong to a CSA and reflected on the values this is instilling in my little one.  We talked about how the produce at the grocery store comes long distances on trucks that use stinky fossil fuels and how that affects the environment, we talked about the importance of supporting our community, and how food tastes better when it’s fresh from the farm.

By the time we got home, I felt satisfied with the organic lesson about supporting our CSA.  This was just the beginning of today’s homeschooling highlights.  We opened our box and discovered a fractal vegetable, Romanesco Broccoli (Brassica oleracea).  The bright green flower is composed of spirally arranged segments that are identical copies of the whole flower.  The copying process continues ad infinitum as a three-dimensional fractal form.  The mathematical beauty and simplicity of this flower never ceases to amaze me.  School was now officially in session.

Discussing infinity with a Kindergartner might seem daunting but it becomes magical when demonstrated on the dinner table.  Since botching my first attempt at explaining infinity last year, I’ve gotten a little better at seeing through my child's eyes.  Last summer, we even had some fun growing Fibonacci Sunflowers in our Edible Classroom.  While grasping an abstract idea may be a stretch for most kids, understanding something they can see, touch, taste, smell and feel usually works.  Today, we literally held infinity in the palm of our hand.  This is nature-based learning.

Looking at the Romanesco, we can see that it’s cone-shaped.  Each of its cones is a replica of the whole flower.  Each bud is composed of a series of smaller buds; all arranged in yet another logarithmic spiral.  I hear Jefferson Airplane singing, White Rabbit.  “Go ask Alice, when she’s ten feet tall.”  It’s a pretty psychedelic vegetable!

After eating all of our math, we popped open the laptop and looked at a few other images of fractals.  Two more from nature are the fern and snowflake pictured below.  All of nature is alive with language, math, and music.  We just need to slow down and look more closely.

Later, we'll draw some of our own fractals -- a big shape with of each of its parts as identical copies of the whole.  Maybe I’ll dig up some literature on the universe as fractal and work on a Parallel Worlds Thematic Unit.  We've read (and seen!) so many archetypal stories with the “magical worlds” premise (Chronicles of Narnia, Wizard of Oz, and Golden Compass) that stepping through magical gates into other worlds has become part of my daughter’s regular imaginative play.  Eventually we will discuss the many-worlds interpretation of quantum physics but we’ll have to schedule a field trip to the Exploratorium for that one.  For now, just keeping her mind wide open and pointing her towards math and science is enough.

It takes an open mind to see the magic in the world.  We can't be so full of ideas that we're not open to the infinite possibilities before us.  This is the magic of childhood.  Nurturing that creativity is exactly what I hope to do when I introduce concepts like fractals to my five year old.  One of my most important jobs as her teacher is to pique her curiosity in all subjects.  If I can do that and get her to eat her vegetables at the same time, I think we both get an A+ for the day.