Early Childhood Education, 1938 version

Preschool learning by doing.

Guest post by Charles Clanton Rogers, pictured here before his blogging days.

“Catch that bird! Don’t let that chicken get away, Charles!”

I was four years old, enrolled in  Grandmother’s Biology & History class.  On that morning we covered the food chain, the hunt, the kill, butchering, anatomy of a hen, and introduction to animal reproduction.

This was 1938 Oklahoma. Money was scarce for everyone. My great inherited fortune was not money, but family. I was an only child and only grandchild of a doting family. I was kind of a “prince” of an infinitely small principality consisting of five adults and one little boy.

I didn’t know it then, but the entire country was mired in the Great Depression. In our state, dust bowl conditions were destroying farms and forcing “Okies” into a desperate exodus in pursuit of California jobs.

vintage unschooling,

Farm equipment buried in dust. Image: americaslibrary.gov

Back to the morning’s Biology & History lesson. Grandma and I were “the hunters.” We caught that chicken, terminated its earthly journey, then plucked and cleaned it. I learned comparative anatomy as Grandmother identified the hen’s internal structures. She talked about the chicken and egg as a circle of life. Then she coated the pieces in egg and flour, and fried it along with fresh okra that we picked from her garden (we were the “gatherers” too). After lunch was my Music lesson, which meant Grandmother sang.

That was just the morning.

My grandmother earned supplemental income by sewing clothes for ladies in the community.  That responsibility couldn’t be neglected.  Her sewing machine was a Singer foot trade model.  She sat with both feet on the treadle. Pumping it back and forth moved a belt from the treadle up to a pulley attached to the needle mechanism. I didn’t realize it then, but observing the mechanical action was itself a Physics lesson.


Image: oldsingersewingmachineblog.files.wordpress.com

Grandmother would spread the material out on the floor and pin the pattern pieces. She trusted me to cut pieces around the patterns with pinking shears. I knew a mistake could cause waste and expense so I took this responsibility very seriously.

While she was making a dress, I had my own little sewing projects. I learned how to thread a needle and sew two pieces of cloth together.  It seemed like a way to pass the time, but that early sewing experience came in handy years later when I became a physician.

When I tired of sewing I passed the time with coloring books and Crayolas . I think I had 8 or 10 colors.

After dinner, Grandmother read to me. (The Little Engine That Could
was my favorite.)

Grandmother had plenty of other things to do, but whatever she was doing I was part of her team.  Often she impressed upon me that I needed to learn my lessons well, because I was going to grow up and have children and students and it would be my sacred responsibility to teach them the things she taught me just as her parents had taught her when she was a girl.

Grandmother’s love was undeniable. She certainly knew, as the poet wrote, “The hand that rocks the cradle is the hand that rules the world.”

Every waking moment was an education. That suited me just fine.  It did not occur to me that the immersive learning of my early years were in any way unusual.  My “preschool/home school” didn’t have any names or labels. It was just Life. I thought it was what everyone did.

George Gershwin and DuBois Heyward wrote Porgy & Bess in 1934, my birth year. The lyrics of its immortal song, Summertime, could have been the theme of my preschool years:

One of these mornings you’re gonna rise up singing,

And you’ll spread your wings and you’ll take to the sky,

But ’til that morning, there ain’t nothin’ can harm you….

hush little baby, don’t you cry.


I came across retired physician and teacher Charles Clanton Rogers through his post Journey of the Human Mind. In it, he describes living with a sense of astonishment. As he puts it,  “I have an idea of what it is like to experience life before a thing is known; and then to witness its deployment. ” Dr. Rogers’ site, The Rogers Post, offers his musings on history, science, art, and much more. I’m grateful he’s sharing this glimpse of a lovingly guided early education with us. Thanks Charles! 

Learning. It’s Not About Education

free range learning, holistic education, natural learning,

Learning is a whole experience of mind, body, and self in relation to the world

When you pick up an orange you feel its texture and weight in your hand. You breathe in scent emitted by the brightly colored rind. If you’re hungry, you peel and section it to savor piece by piece. A fresh orange has phytonutrients, fiber, minerals, and vitamins that promote health. And it tastes wonderful.

It’s possible to purchase the separate nutritional components of an orange. You simply buy vitamin C, vitamin A, flavonoids, B-complex vitamins, fiber, potassium, and calcium in pill form. Of course replacing an orange with supplements is ridiculously expensive compared to the cost of consuming the fruit itself. And isolated compounds don’t work as effectively in the body as the whole fruit. Besides, where is the sensation of biting into an orange bursting with juice? Lost. Divided into a fraction of the experience.

Imagine being told in your earliest years that pills were superior to food and should replace it as often as possible. Even if handfuls of supplements were deemed more valuable than food by every adult in your life you’d still clamor to eat what you found appetizing. If meal-substitution pills became mandatory for children once they turned five years old, you’d never relate to food (or its replacement) the same way again. The body, mind, and spirit reject what diminishes wholeness.

natural learning, education as a pill,

Don’t argue. Just take it.

Yet that’s an apt analogy for heavily structured education, where learning is set apart from the threads that connect it to what has meaning and purpose for the learner. Conventional education separates learning into thousands of measurable objectives. It has very little to do with a child’s hunger to master a particular skill or thirst to pursue an area of interest, in fact such appetites tend to interfere with institutional requirements. It’s not designed for the whole child but aimed at one hemisphere of the brain, doled out in pre-determined doses and repeatedly evaluated. The most gifted, caring teachers are stuck within systems that don’t acknowledge or understand natural learning. In fact, most of us believe, however grudgingly, that schooling is necessary for learning without recognizing that damage is done.

For the very youngest children, learning is constant. Their wondrous progress from helpless newborn to sophisticated five-year-old happens without explicit teaching. They explore, challenge themselves, make mistakes, and try again with an insatiable eagerness to learn. Young children seem to recognize that knowledge is an essential shared resource, like air or water. They demand a fair share. They actively espouse the right to gain skills and understanding in a way that’s useful to them at the time.

Although we have the idea that learning flows from instruction, when we interfere with natural learning children show us with stubbornness or disinterest that it has nothing to do with coercion. Children often ignore what they aren’t ready to learn only to return to the same concept later, comprehending it with ease and pleasure.  What they do is intrinsically tied to why they do it, because they know learning is purposeful. They are curious, motivated, and always pushing in the direction of mastery.

Learning is a hunger too.

Learning is a hunger too.

But schooling irrevocably alters the natural process of learning for every single child.

  • The very structure of school makes children passive recipients of education designed by others. They cannot charge ahead fueled by curiosity, pursuing interests wherever they lead.  Although interest-driven learning results in high level mastery, the top priority in school is completing assignments correctly and scoring well on tests. Despite what individual children want to learn, value is given to what can be evaluated.
  • Segregated by age, children are limited to examples of behavior, reasoning, and ability from those at a similar level of maturity. They have little exposure to essential adult role models and minimal engagement in community life.  They’re also deprived of the opportunity to practice the sort of nurturance and self-education that happens when children interact in multi-age settings.  Even collaboration is defined as cheating.
  • A child’s natural inclination to discover and experiment is steered instead toward meeting curricular requirements. Gradually the child’s naturally exploratory approach is supplanted by less meaningful ways of gathering and retaining information.
  • The mind and body are exquisitely cued to work together. Sensory input floods the brain, locking learning into memory. Movement is essential for learning. The emphasis in school, however, is almost entirely static, and almost entirely focused on left-brain analytical thinking. Many children ache for more active involvement, but their attempts to enliven the day are labeled behavior problems. The mismatch between school-like expectations and normal childhood behavior has resulted in millions of children being diagnosed with ADHD.
  • Coming up with the correct answer leaves little room for trial and error. Thinking too carefully or deeply may result in the wrong answer. The right answer from a child’s personal perspective may actually be the opposite of the correct answer, but to get a good mark the child cannot be true to his or her experience. The grade becomes more important than reality.
  • Emphasis on the correct answer squeezes out unconventional thinking. The fear of making mistakes squelches creativity and innovation. After years of being taught to avoid making mistakes, the child has also learned to steer clear of originality.
  • Readiness is pivotal for learning, particularly in reading. In school, reading is used to instruct in every other subject, so the child who doesn’t read at grade level quickly falls behind. The subject matter in school, even when taught well, isn’t necessarily what the child is ready to learn. The way it is presented tends to be indirect, inactive, and irrelevant to the child. Schoolwork repeatedly emphasizes skill areas that are lacking rather than building on strengths, or goes over skills already mastered with stultifying repetition. Neither approach builds real learning
  • The desire to produce meaningful work, the urge to make contributions of value, the need to be recognized for oneself, and other developmental necessities are undercut by the overriding obligation to complete assignments.
  • Conventional education takes the same approach to a six-year-old and an 18-year-old: assignments, grades, tests. Self-reliance and independence doesn’t easily flourish in such a closed container.
  • Children must hurry to do the required work, then change subjects. The information is stuffed into their short-term memories in order to get good grades and pass tests, even though such tests tend to measure superficial thinking. In fact, higher test scores are unrelated to future accomplishments in such career advancement, positive relationships, or leadership. Students aren’t learning to apply information to real life activities nor are they generating wisdom from it. The very essence of learning is ignored.
  • Schoolwork clearly separates what is deemed “educational” from the rest of a child’s experience. This indicates to children that learning is confined to specific areas of life. A divide appears where before there was a seamless whole. Absorption and play are on one side in opposition to work and learning on another. This sets the inherent joy and meaning in all these things adrift. The energy that formerly prompted a child to explore, ask questions, and eagerly leap ahead becomes a social liability. Often this transforms into cynicism.
  • When young people are insufficiently challenged or pushed too hard, they do learn but not necessarily what they’re being taught. What they learn is that the educational process is boring or makes them feel bad about themselves or doesn’t acknowledge their deeper gifts. They see that what they achieve is relentlessly judged. They learn to quell enthusiasm and suppress the value-laden questions that normally bubble up as they seek to grow more wholly into themselves. Gradually, their natural moment-to-moment curiosity is distorted until they resist learning anything but what they have to learn. This is how the life force is drained from education.

We’re so committed to structured, top-down instruction that we impose it on kids beyond the school day. Young people are relentlessly shuttled from the classroom to enrichment activities to organized sports and back home to play with educational toys or apps when there’s very little evidence that all this effort, time, and money results in learning of any real value.

Many of us think that education has always been this way—stuffing information into young people who must regurgitate it back on demand. Based on dropout numbers alone, this approach doesn’t work for at least a quarter of U.S. students. So we advocate copying Finland or Singapore, using the newest electronics, taking away testing, increasing testing, adding uniforms or yoga or chess or prayer. We’ve been reforming schools for a long time without recognizing, as Einstein said, “You cannot solve a problem from the same consciousness that created it.”

free range learning,

Figuring something out is itself a delight.

Structured education is actually very new to the human experience. Worse, it actually undermines the way children are primed to advance their abilities and mature into capable adults. That’s because most of the time humanity has spent on Earth has been as nomadic hunter-gatherers, before the advent of agriculture. This time span comprises approximately 98% of human history. Although our culture and lifestyle have changed considerably, our minds and bodies have not. Like our earliest ancestors we are still tuned to nature’s rhythms, cued to react quickly to danger, desire close interdependence with a cohesive group of people, and need in our earliest years highly responsive nurturing that gradually fosters our abilities.

Studies of isolated groups who continue to live in hunter-gatherer ways have shown us that during this era (and throughout most time periods afterward) babies are breastfed and remain in close contact with their mothers for the first few years. This results in securely attached infants who are more likely to grow up independent, conscientious, and intellectually advanced.

Their children play freely in multi-age groups without overt supervision or direction by adults. Such free play promotes self-regulation (ability to control behavior, resist impulse, and exert self-control) which is critical for maturity. Play fosters learning in realms such as language, social skills, and spatial relations. It teaches a child to adapt, innovate, handle stress, and think independently. Even attention span increases in direct correlation to play.

Playfulness can’t be separated from learning. Children watch and imitate the people around them. The child’s natural desire to build his or her capabilities doesn’t have to be enforced. Instruction happens when the child seeks it. The learning environment is particularly rich when young people are surrounded by adults performing the tasks necessary to maintain their way of life. Children naturally learn as they playfully repeat what they see and begin to take part in these real life tasks. Mastering all the skills for self-reliance isn’t easy. Hunger-gatherer children must recognize thousands of species of plants and animals as well as how to best obtain, use, and store them. They must know how to make necessary items such as nets, baskets, darts, carrying devices, clothing, and shelter. They need to learn the lore of their people and pass along wisdom through story, ritual, and art. And perhaps most importantly, they need to be able to cooperate and share in ways that have allowed humanity to thrive. In such cultures, children learn on their own timetables in ways that best use their abilities.

free range learning

It’s about curiosity and awe.

We don’t have to live as hunter-gatherers do to restore natural learning to children’s lives. Homeschoolers and unschoolers have been doing this, quite easily, for a very long time. Our children learn as they are ready and in ways that augment strong selfhood. They stay up late to stargaze or make music or design video games, knowing they can sleep late the next morning. They may fill an afternoon reading or actively contribute to the community. They have time to delve into topics of interest to them, often in much greater depth and breadth than any curriculum might demand. They explore, ask questions, volunteer, hang out with friends of all ages, take on household responsibilities, daydream, seek challenges, make mistakes and start over. They’re accustomed to thinking for themselves and pursuing their own interests, so they’re more likely to define success on their own terms. Because homeschooing/unschooling gives them the freedom to be who they already are, it pushes back against a world relentlessly promoting narrow definitions of success.

This kind of natural learning isn’t just an antidote to the soul crushing pressure of test-happy schools. It’s the way young people have learned throughout time.

Let children sleep in. Let them dream. Let them wake to their own possibilities.

free range learning, holistic learning, effect of school, school mindset,

This is an excerpt from Free Range Learning: How Homeschooling Changes Everything.

Making Memories Through Music

image: pixabay.com

image: pixabay.com

Do you attach any significance to songs that start playing in your mind? I do. Maybe that’s because they often get stuck, becoming earworms that loop around for what seem like hours. Sometimes they even wake me in the middle of the night.

I can’t help but wonder why the underpinning of my consciousness loads a particular piece of music. Sometimes it’s easy to figure out because my husband was whistling it or it was playing at a restaurant or I heard a slice of it when a car stopped next to me at a traffic light. Most of the time it seems too random to be chance. So I try to figure out what the song tells me in lyric or mood or memory.

Today, simply walking into a room, my mind’s playlist came up with a tender song I haven’t heard in decades, “Never My Love.”

It took me right back to my childhood home. Most evenings my schoolteacher father sat in an armchair grading papers. I liked to sit on the floor with my back against his chair reading a book in the same warm circle of lamplight. On those nights he played music like  “Only You” by The Platters, “Happy Together” by the Turtles, “Cherish” by The Association, “Both Sides Now” by Judy Collins, “So Far Away” by Carole King, “Close to You” by the Carpenters, and just about anything by Burt Bacharach.

My father loved all kinds of music. In college he was nicknamed “Pitch Pipe” – a play on his surname Piper and an homage to his perfect pitch. When my siblings and I were tiny he’d turn the stereo up so we could dance to big band music, the score from a musical, or a classical standard. He’d sing along, harmonizing against the melody. Without a shred of self-consciousness he’d lift up his arms to conduct a particularly tantalizing portion of Bach or Mozart. And sometimes after dinner a song would come on the radio and he’d dance with my mother, both of them smiling as they swooped around the kitchen linoleum.

My father’s father died when my dad was only five years old. The only thing my dad owned of his father’s was a guitar, which he taught himself to play. Supervising little kids’ baths was one of his chores in the parental division of duties, so he’d sit on the toilet lid singing and strumming that guitar while we played in the tub. My splashy siblings and I sang right along with him to tunes like “You Are My Sunshine” and “Let Me Call You Sweetheart.” We also sang songs he remembered from his college days, lyrics edited for little ears.

I don’t know what it means that I’m hearing “Never My Love.” Most likely something below the surface of my awareness triggered a childhood memory. But I prefer to think it’s a form of connection that lasts even when death separates us.

I’m singing it aloud Dad. I’m singing it for you.

Keeping Creativity Alive



“The world is but a canvas to the imagination.”—Henry David Thoreau

Imagination springs from nowhere and brings something new to the world—games, art, inventions, stories, solutions. Childhood is particularly identified with this state, perhaps because creativity in adults is considered to be a trait possessed only by the artistic few.



Nurturing creativity in all its forms recognizes that humans are by nature generative beings. We need to create. The best approach may be to get out of one another’s way and welcome creativity as a life force.



If we are familiar with the process that takes us from vision to expression, we have the tools to use creativity throughout our lives. When we welcome the exuberance young children demonstrate as they dance around the room, talk to invisible friends, sing in the bathtub, and play made-up games we validate the importance of imagination.



When we encourage teens to leave room in their schedules for music or game design or skateboarding or whatever calls to them, we honor their need for self-expression. Young people who are comfortable with creativity can apply the same innovative mindset to their adult lives.



Creativity is necessary when dealing with an architectural dilemma, new recipe, marketing campaign, environmental solution, or personal relationship. In fact, it’s essential.



Imagination and inspiration have fueled human progress throughout time. Creative powers have brought us marvels and continue to expand the boundaries. The energy underlying the creative act is life-sustaining and honors the work of others.



But there’s a caveat. Creativity isn’t always positive, visionaries aren’t always compassionate, and progress isn’t always beneficial. After all, a clever mind is required to craft a conspiracy as well as to negotiate a peace accord.



Creativity is a life force when it arises as a healing impulse, as a truth-telling impulse, as an impulse to approach mystery.



Tomorrow’s possibilities call out to our inventive, imaginative selves. Let’s answer.



Portions of this post were excerpted from Free Range Learning.

11 Reasons Sing-Songy Names and Rhymes Are Important

benefits of nursery rhymes, chants for preschoolers,

We make up silly songs and even sillier rhymes in my family. Mostly it’s for fun, but I notice that it ushers in all sorts of other positives. It eases tension and creates fond memories. Sometimes it’s even a strangely effective method of shorthand communication.

You probably do this too without even noticing. Maybe you call your partner and kids nonsense names. Maybe you naturally make up tunes to ease a frustrating experience. Maybe you recite the same chants you learned as a child. Here are some reasons why this is so beneficial.

1. Sing-songy names and rhymes span generations. Your great-grandmother may have said “See you later alligator” when she was a girl. She probably also played finger games like “Itsy Bitsy Spider.” Passing along these traditions preserves a language of play shared from oldest to youngest.

2. They are a form of cultural literacy. Many of these simple refrains are hundreds of years old, nearly identical to those recited in Shakespeare’s time. As children get older they’ll will be surprised to learn the historical roots of nursery rhymes like “Ring Around the Rosy” and “Humpty Dumpty.”

3. Playground rhymes and chants are part of what sociologists call “folkways.” Even when children don’t know one another, they know how to settle who goes first using “Rock, Paper, Scissors” or “Eenie Meenie Miny Mo.” These classics have surprising staying power and become norms in a child’s world.

4. Hand-clapping rhymes and songs not only promote motor skills and coordination, they’re also linked to academic skills. Research demonstrates that young children who take part in hand-clapping chants become better spellers, have neater handwriting, and better overall writing skills. A round of “Say, Say, Oh Playmate” anyone?

5. Nursery rhymes, songs, and clapping games can advance social skills and confidence. Young children feel comfortable with patterned singing, dancing, and playing because these activities proceed with a predictable sequences of words and actions.

6. Rhyming ditties can teach basic skills (such as “One, Two, Buckle My Shoe”) and reinforce positive attitudes (such as “Row, Row, Row Your Boat”).

7. Rhymes help young children expand their vocabularies, become familiar with grammatical structure, and use sound patterns such as alliteration. The rhyming words themselves foster understanding of word families—groups of words with different beginning letters but the same ending letters. When children already know that “ball” rhymes with “call” they quickly recognize that “wall,” “fall,” and “small” also rhyme. This establishes a groundwork for later spelling and reading. 

8. Action rhymes like “Head, Shoulders, Knees, and Toes” or “London Bridge is Falling Down” foster full body movement, always a good way to expend energy.

9. Rhymes aid in establishing routines, from clean-up songs to “Teddy Bear Say Good Night.” Familiar tunes and cadences ease transitions from one activity to another in a comfortably upbeat manner.

10. Rhymes are easily customized to fit the moment. Lyrics for “Wheels on the Bus” can be expanded to include such amusements as exhaust on the bus, clown on the bus, and so on. “This Little Piggy Went to the Market” can be played with toes that instead are destined to go to the park where they swing on swings, slide down the slide, drink from the water fountain, and whatever else the child likes to do at the park. The next time it might be played as “This Little Piggy Went to the Beach.” Personalized hand-clapping games, rhymes, and names make play meaningful and memorable.

11. Songs and chants are so essential to our development that we’re coded to recognize them in utero.  Start singing!


Originally published in Holistic Parenting

Public domain image, pixabay.com

Public domain image, pixabay.com


Evoking the State of Flow

state of flow, Mihaly Csikszentmihalyi, rapt absorption, learning through flow, advance learning with flow,

CC by 2.0 Jonf728’s flickr photostream

Flow is “a state in which people are so involved in an activity that nothing else seems to matter; the experience is so enjoyable that people will continue to do it even at great cost, for the sheer sake of doing it.”   ~ Mihaly Csikszentmihalyi

My daughter spent much of this week with a deer skeleton she found in the woods.

As she searched the site she was thrilled to find most bones intact. I wasn’t at all involved beyond providing toothbrushes and bleach to clean them.

Today she’s reassembling the skeleton in the driveway. She shows me how the back legs fit into the hip sockets, giving the deer power to leap and run while the front legs are mostly held on by bone and connective tissue.

She points out that the spine is somewhat similar to a human spine in the lower thoracic and upper lumbar regions, but very different where the large cervical vertebrae come in.

I know so little about this topic that I forget what she’s telling me while she speaks.

Handling the bones carefully, she faithfully reconstructs the skeleton. She’s so deeply engrossed in the project that she hasn’t come in for lunch or bothered to put on a jacket to ward off the chill.

Her interests are far different than mine, but I know what it’s like to be this captivated.

You know the feeling too. You become so absorbed in something that time scurries by without your notice. Your whole being is engrossed by the project. You feel invigorated.

Skiers call it becoming “one with the mountain.” Athletes call it being in the “zone.” Psychologist Mihaly Csikszentmihalyi has termed it the “state of flow.”

In this marvelous state the boundaries between you and your experience seem fluid, as if you are merging with what you’re doing. The more opportunities any of us have to immerse ourselves in activities we love, especially those that stretch us to our full capacities, the more capable and centered we feel in other areas of our lives.

Photo by Claire Weldon

Children, especially the youngest ones, slide into flow effortlessly. While playing they concentrate so fully that they lose sense of themselves, of time, even of discomfort. They’re inherently drawn to full-on engagement. As Csikszentmihalyi explains in Flow: The Psychology of Optimal Experience,

Contrary to what we usually believe, moments like these, the best moments in our lives, are not the passive, receptive, relaxing times—although such experiences can also be enjoyable, if we have worked hard to attain them. The best moments usually occur when a person’s body or mind is stretched to its limits in a voluntary effort to accomplish something difficult and worthwhile. Optimal experience is thus something that we make happen.

For a child, it could be placing with trembling fingers the last block on a tower she has built, higher than any she has built so far; for a swimmer, it could be trying to beat his own record; for a violinist, mastering an intricate musical passage. For each person there are thousands of opportunities, challenges to expand ourselves.”

Kids demonstrate flow when they’re eagerly drawing, building, climbing, pretending, reading, exploring—-however rapt involvement captures them. Their intent focus makes a mockery of what is supposedly a child’s developmental handicap — a short attention span.

Flow truly puts a person in the moment. No wonder it can be hard for our kids when we call them away from what they’re doing to what we deem more important. No wonder they might be more enthusiastic about playing with Legos than taking part in a structured geometry lesson.

Imposing too many of our grown-up preoccupations on kids can teach them to block the experience of flow.

What do we need to remember about this state?

Flow is typically triggered:

  1. when a person’s abilities are stretched nearly to their limits
  2. during a self-chosen pursuit
  3. when they are looking to accomplish something worthwhile to them.

These characteristics are also the way we’re primed to learn from infancy on. It’s been called the Goldilocks Effect. This means we are attracted to what holds just the right amount of challenge for us. Not too big a challenge, not too little, but something that sparks our interest and holds it close to the edge of our abilities, moving us toward greater mastery.

That’s pretty much the way science, art, and other major human endeavors happen too. Flow may indeed be our natural state.

Public domain by Cheryl Holt.

How do we encourage flow?

It doesn’t have to be complicated. Here are some ways to allow more flow in your kids’ lives (and yours too!).

  • Foster a calm, relaxed environment.
  • Engage in what brings out delighted fascination. If you’re not sure what that is, fool around with something hands-on. Tinker, paint, write, sculpt with clay, take something apart, dance, experiment—-whatever feels enticing.
  • Let go of worry and pressure.
  • Welcome mistakes as well as challenges.
  • As much as possible, don’t interrupt.
  • Remember that flow isn’t really separate from play.

The outcome of flow?

  • Deepened learning and stronger confidence.
  • A drive toward complexity, luring us to increase challenges, broaden our range of abilities, even face anxiety and boredom as we access an ever more profound state of engagement. (As A Playful Path author Bernie DeKoven explains here.)
  • Dr. Csikszentmihalyi’s work tells us achieving the flow state regularly is a key component of happiness.

That’s vital, even if it means you end up with a deer skeleton in your driveway.

Post first published on the wonderful site, Simple Homeschool.

Portions of this post are excerpted from Free Range Learning

The Magic of Fresh Air for Babies & Other Beings

fresh air for kids, outdoors every day, babies sleep better in cold,

CC by 2.0 Abigail Batchelder’s flickr photostream

For centuries it was common wisdom that a few hours of fresh air each day was an absolute necessity. Children from infancy on up were bundled in warm clothes and taken out in all seasons. The practice stemmed from a longstanding belief that time outdoors promoted strength and robust health. It was also believed that it kept various character weaknesses at bay. That is, until the practice was poo-poo’ed as nonsense. Nothing but old wives’ tales.

Fortunately, my parents thought otherwise. My mother knew childish energy is best expended outdoors. It never occurred to her that we required her participation as she sent us out every day. When we were small she told us to stay in the yard, checking every now and then from the window. Soon our range expanded to a few acres of woods behind our house plus pretty much anywhere we could go on our bikes while still making it back in time for dinner.

I learned even more about the importance of being outside from my father. He set a quiet example by paying attention to birds, the weather, the garden. If we went somewhere with him other than a hardware store, it was to go hiking in the Cleveland Metroparks.

It wasn’t until I had my first baby that my father showed me a deeper power of nature, again simply by example. When he held babies he almost always walked outdoors with them, particularly if they were fussy.

“Here’s the sky,” he’d point. “That’s a tree over there, you’ll be running on this grass in no time,” he’d gently tell an infant.

Their eyes would get big and they’d look around, more calm and focused than they were indoors.

I started to follow his example. If I couldn’t figure out my baby’s troubles, I’d go out to lie on the grass during the day, or wrap up warmly to look at the stars in the middle of the night. It nearly always settled a crying baby.

It worked even better for toddlers. They’d get cranky in the house, far crankier in the car. They wanted out in the largest sense possible. They’d stay outdoors as long as I’d let them, on our most glorious days this lasted for hours. When she was a year old my daughter liked to pick up little stones, hold them briefly, then place them in little piles. She’d look at me, shaking her head to remind herself they couldn’t go in her mouth. My little children helped me garden and sweep and rake. They dug in the dirt, made fairy houses out of sticks and leaves, filled their little wagons with the hickory nuts that littered our yard in autumn, stomped in puddles, squatted to watch bugs, climbed on logs, and asked endless questions. All these richly sensory experiences happened simply because we were outdoors. I had no idea at the time that all of this movement helped build essential brainpower.

As Gill Connell and Cheryl McCarthy explain in the wonderful book, A Moving Child Is a Learning Child,

A young child can learn only what her brain is primed and ready for. And in the early years, that’s everything the body has to teach—the tangible, physical, and sensory qualities of the world around her. It’s no wonder preschool learning rarely happens sitting down.

Influential 19th century British educator, Charlotte Mason, suggested children should spend four to six hours a day outdoors. She wrote in Home Education,

…every hour spent in the open is a clear gain, tending to the increase of brain power and bodily vigour, and to the lengthening of life itself. They who know what it is to have fevered skin and throbbing brain deliciously soothed by the cool touch of the air are inclined to make a new rule of life, Never be within doors when you can rightly be without.

Besides, the gain of an hour or two in the open air, there is this to be considered: meals taken al fresco are usually joyous, and there is nothing like gladness for converting meat and drink into healthy blood and tissue. All the time, too, the children are storing up memories of a happy childhood.

In Scandinavian countries, parents believe it’s healthier for babies and children to be outside for a few hours a day in all but the most extreme temperatures (and they mean extreme, as in 0 degrees Fahrenheit). It’s a common practice to dress babies warmly and tuck them in a stroller in the yard, balcony, or outside a shop to nap on a snowy day.

In fact, the Finnish Ministry of Labour specifically recommends it (see page 24 under “naps”).  Does it help babies sleep better? One study showed children took longer naps outdoors compared with naps taken indoors.

Pediatrician Harvey Karp points out, in The Happiest Toddler on the Block, how staying indoors is overstimulating while at the same time boring for children.

Our homes are boring because they replace the exciting sensations of nature (the feeling of the wind on their skin, the brilliant sun, the soft grass, etc.) with an immense stillness (flat walls, flat floors, no wind).

Yet at the same time, he writes, being indoors is overstimulating.

It bombards them with jolting experiences that kids in the past never had to deal with: crazy cartoons, slick videos, clanging computer games, noisy toys, and bright colors everywhere…which can make many little children feel stressed.

There are exhaustive studies showing that time outdoors, particularly in nature, benefit us in myriad ways—from better health to peace of mind.  I think there’s something intangible too, something to do with keeping alive the awe and wonder that is our birthright. That’s something the youngest children can help us relearn.

“Live in the sunshine, swim the sea, drink the wild air.”  ~Ralph Waldo Emerson

fresh air benefits, outdoors every day, cold air good for sleep, babies sleep better outside,

CC by 2.0 pixydust8605’s flickr photostream

Natural Math: 100+ Activities & Resources

math through play, everyday math

image: pixabay.com

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”   ~Stan Gudder

Today’s children are much less likely than previous generations to learn through play, exploration, and meaningful work. Concern about the math scores of the nation’s youth should instead turn to concern about the manipulation of childhood itself. We’ve substituted tightly structured environments and managed recreation for the very real, messy, and thought-provoking experiences that are the building blocks for higher level thinking.

Learning math requires children to link language with images as they work through equations. It helps if they can easily picture the problem being solved before they move ahead into representational and abstract math. Normally a child who has spent plenty of time playing with manipulatives (water, sand, building blocks, countable objects) and who uses real world applications of math (cooking, carpentry, budgeting) has a wealth of experience to fall back on. This child can call up mental images that are firmly connected to sensory memory, helping him understand more advanced concepts.  Applied math, especially as it relates it a child’s needs and interests, is the bridge to mathematical success.

Computational readiness varies widely from child to child. Some are eager to do mental math, memorize math tricks, and take on increasingly complex calculations. Others need much more time before they are ready to tackle math this way. When readiness is paired with self-motivation there’s no limit to what a child can accomplish.

Benoit Mandelbrot is the Yale mathematics professor credited with identifying structures of self-similarity that he termed fractal geometry. His work changed the way we see patterns in nature, economies, and other systems. Mandelbrot doesn’t believe students need to struggle with Euclidean mathematics. Instead, he says,”Learning mathematics should begin by learning the geometry of mountains, of humans. In a certain sense, the geometry of . . . well, of Mother Nature, and also of buildings, of great architecture.” In other words, by focusing on inspiration found everywhere around them before turning to formal equations.

Natural math, according to math expert Maria Droujkova, is about,

people making mathematics their own, by posing their own problems, pursuing their own projects, and remixing other people’s activities in personally meaningful ways. We believe that “learning math” means two things—developing mathematical state of mind and acquiring mathematical skills.

Droujkova goes on to say,

Most parents we talk to, including the ones who work in STEM fields, tell us that their math education wasn’t satisfying. They want their kids to have something better: to see mathematics as beautiful, meaningful, and useful, and not to suffer from math anxiety and defeat. The two major ways the markets respond to these worries and dreams are via edutainment toys and games, and private early teaching in academic settings.

We suggest a different approach, centered on families and communities. We introduce advanced math through free play. Formal academic environments or skill-training software can’t support free play, but friends and family can. Mathematics is about noticing patterns and making rules that describe and predict these patterns. Observe children playing in a sandbox. At first it doesn’t look meaningful. But in a little while kids make up elaborate stories, develop a set of rules, and plan for what’s going to happen next. In a sense, what we do with math is setting up sandboxes where particular types of mathematical play can grow and emerge.

Let’s fling our limiting concept of math education wide open by eagerly using it in our lives.  Math is everywhere. Equations, patterns and probabilities surround us. Sometimes it takes a larger way of thinking about math to celebrate the beauty and perfection it represents.

natural math, math through play,

Applied math (images: morguefile.com)

Here are some of the starting points suggested in Free Range Learning to spark your own math-fueled journey.

 ~Learn more about yourselves. One family hangs a new chart each week to gather data. One week they might mark off where the dog takes a nap, then figure the percentage at the end of the week (40 percent of the time she sleeps in the window seat, 5 percent of the time under the table, etc), another week they might pick a subject like hours of computer use per person. They are also keeping several year-long graphs. One tracks the weight of trash and recyclables they discard weekly and a second graphs the amount of the produce they harvest from the garden. Yet another tracks money they are saving. They notice that in busy weeks, such as holidays, they fall short of sustainability goals they’ve set for themselves.

~Revel in measurement. Investigate joules, BTUs, calories, watts, gallons, degrees, fathoms, meters, hertz, attoseconds and more. Measure your everyday world. Calculate such things as the energy usage to get to grandma’s house in the car compared to taking the train, what angle a paper plane can be thrown and still fly, how much wood it will take to build a shelf for the baby’s toys, how many footsteps are required to walk to the corner. Figure out how to gather measurements and apply data.

~Enjoy math songs. Play them while traveling and sing them casually as you go about your day; you’ll find your children are memorizing math facts effortlessly. There’s something about a catchy tune that helps the mind retain concepts. There are many sources of math songs including Sing About Science and Math with a database of 2,500 songs.

~Say yes. When kids want to explore off the trail, stomp in puddles, mix up ingredients, play in the water, and otherwise investigate they’re making math and science come alive on their own terms. It’ll probably make a mess. Say yes anyway.

~Use wheels. Plan and build a skateboarding ramp. Time relay races using tricycles (the bigger the kids the greater the fun). Estimate how many revolutions different sized bike wheels make to cover the same distance (then get outside to find the answer). Adjust a wheelbarrow load to carry the greatest amount of weight. Use mass transit to get where you are going after figuring out the route and time schedule.

~Make math a moving experience. Instead of relying on flash cards, remember equations by clapping or stomping to them, rhyming and dancing with them, kicking a ball or tossing a bean bag to them, making number lines on the sidewalk with chalk and running to answer them, or any other method that enlivens learning. Games for Math: Playful Ways to Help Your Child Learn Math, From Kindergarten to Third Grade offers many moving math activities for children.

~Learn to dance. The fox trot or the hokey pokey may be funny names to children, but they also describe specific patterned steps. Mastering simple dances are a way of transforming mathematical instruction into art. Choreographers use dance notation to symbolize exact movements. Over the years different methods of dance notation have been used including: track mapping, numerical systems, graphs, symbols, letter and word notations, even figures to represent moves. Choreograph using your own system of dance notation. Draw chalk footprints on the floor to show where the dancer’s feet move to a waltz. Try dance classes. Music and dance enliven math concepts.

~Think in big numbers. Figure out how many days, minutes and seconds each member of the family has been alive. Estimate the mass of the Earth, then look up the answer. Stretch your mind to include Graham’s Number. Talk about why big numbers are best expressed in scientific notation. Check out the Mega Penny Project. Read stories about big numbers, such as Infinity and Me, How Much Is a Million? Millions to Measure, On Beyond a Million: An Amazing Math JourneyCan You Count to a Googol? , and One Grain Of Rice: A Mathematical Folktale

~Fold your way into geometry. Print out paper designs that fold into clever toys and games from The Toy Maker including thaumatropes and windboats. Check out instruction books such as Paper, Scissors, Sculpt!: Creating Cut-and-Fold Animals or Absolute Beginner’s Origami. Although these may seem to be for amusement sake, they teach important lessons in conceptualizing shapes and making inferences about spatial relations.

~Play games. Nearly every board game and card game incorporates arithmetic. Make time to play the games your children enjoy. Try new ones and make up your own. Many homeschoolers set up game days so their children can share games with their friends, this is a worthy tradition for kids whether they’re schooled or homeschooled. Games make strategizing and calculating effortlessly fun. For the latest information on games, check in with the aficionados at Board Game Geek. For educational game reviews, consult Games for Homeschoolers  and The Board Game Family.

~Learn chess. This game is in a class all its own. Research shows that children who play chess have improved spatial and numerical abilities, increased memory and concentration, enhanced problem-solving skills as well as a greater awareness of these skills in action. Interestingly, chess also promotes improved reading ability and self-esteem.

~Get hands-on experience in geometry. Geometrical principles come alive any time we design and build, whether constructing a fort out of couch pillows or a treehouse out of scrap wood. Make models using clay, poster board, craft sticks, or balsa.

~Find out about the math in meteorology. Learn about weather trends and predictions, measurement of precipitation and temperature conversion. Keep a weather log using instruments to measure wind speed, precipitation, temperature, barometric pressure, and humidity: then graph the results to determine average, mean, and median for your data.

~Play with shapes. Enjoy puzzles, tangrams, and tessellations. Notice the way shapes work together in the world around you both in natural and constructed settings. Keep a scrapbook of appealing shapes and designs. Create a sculpture out of toothpicks and miniature marshmallows. Cut paper snowflakes. Make collages out of pictures and three-dimensional objects. Grout bits of tile or broken dishes into mosaic designs. Make mobiles. Cut food into shapes.

~Pick up a musical instrument. Learning to play an instrument advances math skills as well as sharpens memory and attention.

~Learn to code. It’s not only fun, it’s really a basic skill.

~Estimate, then find out how to determine an accurate answer. Predict how much a tablespoon of popcorn will expand, then measure after it has been popped. Before digging into an order of French fries, estimate how many there are or how far their combined length will reach. See how the guess compares with the actual figure. Guessing, then finding out the answer enlivens many endeavors.

~Get into statistics.

  • Kids go through a phase when they want to find out about the fastest, heaviest, most outrageous. Once they’re duly impressed with the facts in such books as Guinness World Records it’s a great time to pique their interest using almanacs and atlases.
  • Sports offer a fun way to use statistics. Player and team stats are used to calculate odds, make comparisons and determine positioning. Children may want to keep track of their favorite teams or of their own activities. The numbers can help them to see patterns, debate trends and make predictions.
  • Data provided by WorldoMeters makes fascinating reading and may lead to further investigation.
  • Collect and interpret your own statistics. You might develop a survey. Or record measurements, weights, and other information about specific data, then analyze the statistics using a graph, histogram, or other instrument.

~Make calculation part of household rules. If children are permitted a certain amount of screen time per week, let them be responsible for charting that time. If children rotate chores or privileges, assist them to create a workable tracking system.

~Learn to knit. This useful skill also provides hands-on experience in basic math including counting, skip counting, multiplication and division, patterning, following a numerical guide, visualizing shapes, and problem solving.

~Make time for calendars. Check out the history of African, Babylonian, Roman, and Egyptian calendars. Learn how our calendar system came into use. Would it make sense to change to 13 equal months of 28 days each, with one remaining “day out of time” set aside? What are the definitions of “mean solar time,” “sidereal time” and “apparent solar time”? Make a homemade sundial to see how accurately you can tell time.

~Make math edible. Cereal, pretzels, crackers, small pieces of fruit or vegetables, cubes of cheese, nuts and other bite-sized foods are excellent tools to demonstrate addition, subtraction, multiplication, division, fractions, percentages, measurement and more. Using food to make math functions visible is a tasty way to solve equations. Your children can calculate recipe changes such as doubling or halving while they learn other useful meal preparation skills at home.

~Use trial and error. This is a fun process, especially when applied to brain teasers, puzzles, and mazes; try making up your own. Other math-related ways to stretch your mind include optical illusions, magic tricks, and drawing in perspective. These activities go well beyond solving equations to figuring out larger concepts.

~Devise your own codes and use them to send messages to one another. Check out the history of codes and code breakers. Set up treasure hunts by hiding a tiny treat and leaving codes or equations to be solved that lead to the next set of hints.


~Enjoy the intersection of math and art. Muse over puzzling visual patterns, for example the work of M.C. Escher. Learn about rug making, sculpture, weaving, basketry and many other art forms to discover the calculation, patterning, and measurement used to create objects of beauty.

~Delve into maps. Look at maps of the world together. Find maps of your locality. As well as road maps, your child may be intrigued by topographical and relief maps, economic and political maps, navigational and aeronautical charts, weather maps or land ownership maps. Draw maps of your neighborhood, home, yard, or bedroom—notice what details your child includes. Make imaginary maps, perhaps to accompany a story or to demonstrate what an eight-year-old would consider a perfect place. Consider mapping somewhere you know well, but from different time frames—how might this place have looked 100 years ago, now, in the distant future? Some children who are reluctant to keep diaries or sketchbooks will cheerfully keep records of places they’ve been by drawing maps. Maps and mapping can teach measurement, spatial awareness, and complex geographical concepts.

~Use logic. Apply critical thinking to current events.

~Compare related things like the weight of a puppy to a full-grown dog, or the size of a pitcher compared to the number of glasses it can fill.

~Use math at the store. While shopping, have children help check prices as part of the process of choosing a better deal. Talk about what other factors come into play—durability, ecological impact, value, overall worth. If you need to make a bigger purchase like a refrigerator, have the children compare the special features and cost effectiveness of running the appliance.

~Try travel math. Traveling is a great time to use math. Children can figure out fuel usage, keep track of expenditures, consult maps, estimate time of arrival, and more. Playing math games also provides excellent distraction during a long trip!

~Talk about math as if you are thinking out loud. “I wonder how many bricks it took to make this entire wall?” then look up a formula for figuring that out; or “If we don’t buy ____ for a whole month do you think we’ll have enough money left over for a ____?”

~Enjoy hands-on projects requiring sequential instruction. These hone logic and spatial skills as well as patience. Model-building, quilting, making repairs, knitting, carpentry, origami, beading and Legos® are examples of such projects.

~Learn how alternative languages relate to numbers. Check out Morse code, semaphore, Braille and sign language.

~Play pool. The sport known as billiards has a lot to teach about angles, trajectory, speed and calculation. And it’s fun.

~Expect kids to participate in household chores. All sorts of mathematical concepts are learned when the youngest children put away silverware, stack plastic containers in the cupboard, and sweep the floor. Even more while older kids help make meals, do repairs, and brainstorm solutions to make the household runs more smoothly.

~Make puzzles a family tradition. They can increase concentration as well as promote spatial learning and reasoning.

~Start or join a math circle. Meet regularly with others who enjoy making the subject fun and intriguing. Most are run by math experts and include projects, games, and field trips related to math. Some resources to get you started:

~Play with math and critical thinking, together.

~Check out learning games suggested by math teachers and math bloggers.

~Read literature that incorporates math.  Find lists of specific math concepts in children’s literature through the National Association for the Education of Young Children as well as the math in children’s literature list on Love2Learn2Day.  Here are some age-related suggestions.

~Read-aloud math stories for children under 8.

~Math Stories for Children 8 and up.

~Math inspiration for older kids.  

Enjoy math-y videos.

~Keep math references handy, you’ll find them endlessly useful.

This post is third in a series on natural math. 

The Benefits of Natural Math. Data that turns turn our assumptions about math instruction upside down. If you read only one in this series, read this. 

Math Instruction versus Natural Math: Benezet’s Experiment. What happened when formal math instruction was eliminated? 

image adapted from livescience.com

image adapted from livescience.com

The Benefits of Natural Math

natural math, exploratory math, hands-on learning,

images: public-domain-image.com

Math as it’s used by the vast majority of people around the world is actually applied math. It’s directly related to how we work and play in our everyday lives. In other words it’s useful, interesting, even fun.

We now know babies as young as five months old show a strong understanding of certain mathematical principles. Their comprehension continues to advance almost entirely through hands-on experience. Math is implicit in play, music, art, dancing, make-believe, building and taking apart, cooking, and other everyday activities. Only after a child has a strong storehouse of direct experience, which includes the ability to visualize, can he or she readily grasp more abstract mathematical concepts. As Einstein said, “If I can’t picture it, I can’t understand it.”

As parents, we believe we’re providing a more direct route to success when we begin math (and other academic) instruction at a young age. Typically we do this with structured enrichment programs, educational iPad games, academic preschools, and other forms of adult-directed early education. Unfortunately we’re overlooking how children actually learn.

Real learning has to do with curiosity, exploration, and body-based activities. Recent studies with four-year-olds found, “Direct instruction really can limit young children’s learning.” Direct instruction also limits a child’s creativity, problem solving, and openness to ideas beyond the situation at hand. Studies show kids readily understand math when they develop a “number sense,” the ability to use numbers flexibly. This doesn’t come from memorization but instead from relaxed, enjoyable exploratory work with math concepts. In fact, math experts tell us methods such as flash cards, timed tests, and repetitive worksheets are not only unhelpful, but damaging. Teaching math in ways that are disconnected from a child’s life is like teaching music theory without letting them plunk piano keys, or instructing them in the principles of sketching without supplying paper or crayons. It simply makes no sense.

One study followed children from age three to age 10. The most statistically significant predictors of math achievement had very little to do with instruction. Instead the top factors were the mother’s own educational achievements and a high quality home learning environment. That sort of home environment included activities like being read to, going to the library, playing with numbers, painting and drawing, learning letters and numbers, singing and chanting rhymes. These positive effects were as significant for low-income children as they were for high income children.

There’s another key difference between kids who excel at math and kids who don’t. It’s not intelligence. Instead it’s related to what researcher Carol Dweck terms a growth-mindset. Dweck says we adopt certain self-perceptions early on. Some of us have a fixed mindset. We believe our intelligence is static. Successes confirm this belief in our inherent ability, mistakes threaten it. People with a fixed mindset may avoid challenges and reject higher goals for fear of disproving their inherent talent or intelligence.  People with a growth mindset, on the other hand, understand that intelligence and ability are built through practice. People with this outlook are more likely to embrace new challenges and recognize that mistakes provide valuable learning experience. (For more on this, read about the inverse power of praise.)

Rather than narrowing math education to equations on the board (or worksheet or computer screen) we can allow mathematics to stay as alive as it is when used in play, in work, in the excitement of exploration we call curiosity. Math happens as kids move, discuss, and yes, argue among themselves as they try to find the best way to construct a fort, set up a Rube Goldberg machine, keep score in a made-up game, divvy out equal portions of pizza, choreograph a comedy skit, map out a scavenger hunt, decide whose turn it is to walk the dog, or any number of other playful possibilities. These math-y experiences provide instant feedback. For example, it’s obvious cardboard tubes intended to make a racing chute for toy cars don’t fit together unless cut at corresponding angles. Think again, try again, and voila, it works!

As kids get more and more experience solving real world challenges, they not only begin to develop greater mathematical mastery, they’re also strengthening the ability to look at things from different angles, work collaboratively, apply logic, learn from mistakes, and think creatively. Hands-on math experience and an understanding of oneself as capable of finding answers— these are the portals to enjoying and understanding computational math.

Unfortunately we don’t have a big data pool of students who learn math without conventional instruction. This fosters circular reasoning. We assume structured math instruction is essential, the earlier the better, and if young people don’t master what’s taught exactly as it’s taught we conclude they need more math instruction. (“Insanity: doing the same thing over and over again and expecting different results.”)

But there are inspiring examples of students who aren’t formally instructed yet master the subject matter easily, naturally, when they’re ready.

1. The experiment done over 85 years ago by Louis Benezet showed how elementary school children can blossom when they’re free of structured math instruction.

2. Homeschooling and unschooling families around the world devote much less time to formal mathematics instruction. Studies indicate their children grow up to succeed in college, careers, and life with greater self-reliance and focus than their schooled peers. Interestingly, two different surveys of grown unschoolers showed that a much higher number of them work in STEM careers than schooled adults. The samples were small but intriguing. More proof? Many of our greatest science, technology, engineering, and mathematics contributors have already emerged from the homeschool community.

3. Democratic schools where children are free to spend their time as they choose without required classes, grades, or tests. As teacher Daniel Greenberg wrote in a chapter titled “And ‘Rithmetic” in his book Free at Last, a group of students at the Sudbury Valley School approached him saying they wanted to learn arithmetic. He tried to dissuade them, explaining that they’d need to meet twice a week for hour and a half each session, plus do homework. The students agreed. In the school library, Greenberg found a math book written in 1898 that was perfect in its simplicity. Memorization, exercises, and quizzes were not ordinarily part of the school day for these students, but they arrived on time, did their homework, and took part eagerly. Greenberg reflects, “In twenty weeks, after twenty contact hours, they had covered it all. Six year’s worth. Every one of them knew the material cold.” A week later he described what he regarded as a miracle to a friend, Alan White, who had worked as a math specialist in public schools. White wasn’t surprised. He said, “…everyone knows that the subject matter itself isn’t that hard. What’s hard, virtually impossible, is beating it into the heads of youngsters who hate every step. The only way we have a ghost of a chance is to hammer away at the stuff bit by bit every day for years. Even then it does not work. Most of the sixth graders are mathematical illiterates. Give me a kid who wants to learn the stuff—well, twenty hours or so makes sense.”

We know all too well that students can be educated for the test, yet not understand how to apply that information. They can recite multiplication tables without knowing when and how to use multiplication itself in the real world. Rote learning doesn’t build proficiency let alone nurture the sort of delight that lures students to higher, ever more abstract math.

Conventional math education may also limit our concept of what math can do. As Stanford mathematician Keith Devlin notes in a post titled “Most Math Problems Do Not Have a Unique Right Answer,”

One of the most widely held misconceptions about mathematics is that a math problem has a unique correct answer…

Having earned my living as a mathematician for over 40 years, I can assure you that the belief is false. In addition to my university research, I have done mathematical work for the U. S. Intelligence Community, the U.S. Army, private defense contractors, and a number of for-profit companies. In not one of those projects was I paid to find “the right answer.” No one thought for one moment that there could be such a thing.

So what is the origin of those false beliefs? It’s hardly a mystery. People form that misconception because of their experience at school. In school mathematics, students are only exposed to problems that (a) are well defined, (b) have a unique correct answer, and (c) whose answer can be obtained with a few lines of calculation.

Interestingly, people who rely on mental computation every day demonstrate the sort of adroitness that doesn’t fit into our models of math competence. In a New York Times article titled “Why Do Americans Stink at Math?” author Elizabeth Green (who defines the term “unschooled” as people who have little formal education) writes,

Observing workers at a Baltimore dairy factory in the ‘80s, the psychologist Sylvia Scribner noted that even basic tasks required an extensive amount of math. For instance, many of the workers charged with loading quarts and gallons of milk into crates had no more than a sixth-grade education. But they were able to do math, in order to assemble their loads efficiently, that was “equivalent to shifting between different base systems of numbers.” Throughout these mental calculations, errors were “virtually nonexistent.” And yet when these workers were out sick and the dairy’s better-educated office workers filled in for them, productivity declined.

The unschooled may have been more capable of complex math than people who were specifically taught it, but in the context of school, they were stymied by math they already knew. Studies of children in Brazil, who helped support their families by roaming the streets selling roasted peanuts and coconuts, showed that the children routinely solved complex problems in their heads to calculate a bill or make change. When cognitive scientists presented the children with the very same problem, however, this time with pen and paper, they stumbled. A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. Similarly, when Scribner gave her dairy workers tests using the language of math class, their scores averaged around 64 percent. The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.

And Keith Devlin explains in The Math Gene that we’re schooled to express math in formal terms, but that’s not necessary for most of us—no matter what careers we choose. People who rely on mental math in their everyday lives are shown to have an accuracy rate around 98 percent, yet when they’re challenged to do the same math symbolically their performance is closer to 37 percent.

We have the idea that memorizing, practicing, and testing is the only way to higher achievement. It’s hard to imagine why we still believe that when studies show that high test scores in school don’t correlate with adult accomplishments (but do line up with interpersonal immaturity).

There are all sorts of ways to advance mathematical understanding. That includes, but isn’t limited to, traditional curricula. It’s time to broaden our approach. Let’s offer the next generation a more intrinsically fascinating, more applied relationship to math. Let’s foster analytical and critical thinking skills across all fields. The future is waiting.

This article is one in a series of three on natural math. 

Math Instruction versus Natural Math: Benezet’s Experiment. What happened when formal math instruction was eliminated? 

Natural Math: 100+ Activities and Resources. Finding and learning from math in daily life. 

Portions of this article are excerpted from Free Range Learning.

Understanding Children Through Imitation

follow your child's example, what it feels like to be a child, child's experience,

Mirror a child’s movements. (morguefile)

So much of a child’s experience, from infancy on, is constantly being shaped by adults. Their behavior, posture, movement, and sound are restricted by structured activities, confining seats, and grown-up expectations . If we allow ourselves, we can drop into a child’s world for few moments by replicating his or her movements. It’s a form of listening at the bodily level that can be instructive as well as enlightening.

I’ve admitted to trying this the very first time as a new mother, imitating my newborn’s movements in an experience so profound it felt like a ceremony.

I didn’t try it again until I was the mother of three kids under six. I’d dashed over to a friend’s house to drop something off, feeling rushed to get back to my nursing baby. My friend’s children were asleep. I stood in her quiet kitchen telling her how much I wanted to sit down and chat, but couldn’t spare the time. She answered my complaint with mock outrage, “Don’t you dare relax! What were you thinking?”

In my best imitation toddler voice I said, “WANT TO!”

She wagged her finger. “That’s enough out of you. Do what you’re told right this minute.”

Then I dropped to the floor in a full-on act of defiance; lying on my back, kicking my legs, and squalling, “You can’t maaaaaake me!”

By this time our hilarity was well out of proportion to this brief moment of improv. When I got up I felt different—wonderfully de-stressed and energized.

I insisted my friend give it a try. She resisted, until I admonished her with the same phrases I’d heard her use on her kids. I even flung out her full name accompanied by finger wagging. That did it. She twirled around whining “Noooooo. No no no!” till she was out of breath, with hair in her mouth and a smile on her face.

We both agreed we felt incredible.

I don’t for a minute suggest you do this, ever, in front of any child. Self-expression should never be ridiculed. But if they’re not home, give it a try. What this did, for me as well as my friend, was let us fully express strong emotions through our bodies as our children do, as we used to do when we were children. We may have been well-educated, reasonably sophisticated women but the need to indulge in some primal venting hadn’t left us. A little method acting gave us both new insight into what our children experience.

After that, I looked for ways to learn from my children through imitation. We adults do this all the time when we play with our kids. We chase and let them chase us. When they pretend to be an animal or make-believe character we join in. We’re the big bad wolf blowing down a child’s fort made of cushions. We’re the sotto-voiced doll talking to another doll or the train engine struggling up an imaginary hill. Playing is a window into a child’s experience, and remarkably restorative for us as well.

But what truly let me honor my children’s world was letting them choreograph my movements. Sometimes we’d play what we called “mirror”— standard actor training done face to face. The child is the leader, the parent the “mirror.” As the child makes gestures, facial expressions, and hand movements the parent tries to duplicate the movements exactly. Then we ‘d switch so the child got a turn being the mirror. I always ended up laughing first.

Sometimes we played a variant of this, making each other into emotion mirrors. One would call out a feeling like “surprised” or “angry” or “wild” and the other would try to convey the word through facial expression. (This is also a great way to advance emotional intelligence.)

My favorite imitation was through dance. We’d turn on some lively music and I’d try to copy my child’s dance moves. This is much more difficult than it sounds. It’s nearly impossible to keep up with a child’s energy level for long!

My kids are past the stage where they want me to imitate their dance moves. But I haven’t forgotten how much letting my kids choreograph my movements taught me. Even now, they’ll catch my eye across a crowded room for a brief moment of mirroring. It’s funny, warm, and lets us both feel understood.

Don’t miss this wonderfully expressive choreography by Zaya, imitated by real dancers.