Battered Blue Wheelbarrow

What It Carries, Still

Your father, whose voice scared me,
whose head loomed a full 14 inches over my mine,
bought us our only housewarming gift;
a bright blue, six cubic foot wheelbarrow.
We laughed at its size, laughed as you gave me
a bumpy ride over the first lawn
we giddily called our own.

He seemed to believe our future
would be one of Paul Bunyan-sized loads.
It was.

In it we hauled firewood, dirt, rocks,
crinkled leaves topped with squealing toddlers.
It held a big block Dodge engine.
It toted rolls of fencing, chicken feed, cow manure.
It carried trays of tender seedlings
out to the garden, waiting
as I blessed each one into soft earthen beds.

Today you mend the rusted body
of our battered blue wheelbarrow.
I wish your father lived to see
its wooden handles smoothed from use
and what it carries, still
on that one sure wheel.

Laura Grace Weldon

Originally published in The Moon Magazine. Find more poems in my collection, Tending.

Listening To People Without Voices

communicate with dementia patients, reading another person,

Image courtesy of polveredigrafite.deviantart.com

I got my first summer job when I was 13 years old.  My official title was “feeder.” This was my first exposure to time clocks and posted schedules. Also my first exposure to quite a bit more.

My grandparents had died a few years earlier after protracted illnesses, and like many others, I associated the sounds and smells of the unhealthy elderly with my own grief.

Before I started all I knew was that was supposed to wear a white uniform to work. On my first day I was informed my only task was to spoon-feed patients unable to feed themselves. The head nurse handed me a list of names with room numbers and told me I had to be done in two hours. “It doesn’t matter if you clock out late,” she said, “We aren’t paying you more than your allotted two hours.” Her swiftly delivered instructions were entirely lacking in useful information.

As I walked down the hall I discovered every resident there thought I was a nurse. Me, a girl who fell over her own feet. Me, a girl who could barely endure the sorrow of driving past a puppy chained to a tree, an unknown puppy whose imagined plight kept me upset for hours. Now I was surrounded by real plight.

Perilously frail people lined the hallway. Nearly every one of them sought my attention. They asked me to get them something urgent like a bedpan or a pill. They asked why they couldn’t go home or lie down or find something missing. They asked to simply to engage in a little conversation. I was overwhelmed.

One woman cried as she begged me to hold her hand. I smiled and nodded. As I listened to her cry I couldn’t help but steal glances at her hand’s bumpy joints and raised purple veins. I realized it had once been as strong and soft as mine. Time’s appetite made me feel as if the walls, floors, and ceiling were already collapsing.  But I had a job to perform. Surely hungry people were waiting for me. She wouldn’t let go. Not knowing what else to do, I crouched by her wheelchair there in the hallway and smiled weakly as I carefully uncurled her fingers from mine.

heart-based communication, transcending speech, speaking with people who can't speak,

Image courtesy of colinharbut.deviantart.com

The patients I was expected to feed lay hostage on narrow beds in identical rooms. Each person’s eyes stared, some directly at me and some at a place well beyond me. Trays of pureed food waited at each bedside. I had to figure out how to lower the metal bed rails in order to reach patients. I held out wavering spoonfuls of meat, potatoes, and vegetables pureed into of a nauseating mush of pale browns and olive greens. After the first patient gagged, I realized it was possible to raise a person’s head and shoulders using a crank at the foot of the bed. Like every other surface, those crank handles seemed to bristle with germs.

I was repulsed by almost everything there except for the people. I found their faces especially compelling. One of the few men on my list was hunched and fierce like a hawk, giving the impression he was ready to fly at any moment. One woman’s deep-set brown eyes were beseeching although she could say only a few garbled words. She looked at me as if she could see much more than those who walk and talk so casually could do. Another woman, whose powdery thin skin and soft clouds of white hair made her look angelic, rarely opened her eyes. When she did I felt strangely blessed. Her awake moments, although silent, felt like moments of expansive awareness.

Maybe it was a 13-year-old’s sense of drama, but I loved these people in a way I couldn’t explain. I wanted them to feel comfort and peace in the minutes we had together. I didn’t know how to accomplish that. But I started, from my first day, to ask them a question. I told them my name each time, that I was there with dinner, and then I asked them what they’d like me to know or asked what it was like to be them. And then I was quiet while I listened to whatever their silence could tell me. I knew most couldn’t hear me or answer me. But I was sure there was a reason I felt something different in the presence of each person. I felt it strongly.

Sometimes an aide would hustle into the room and sharply tell me to hurry. “No use talking to someone stone deaf” or “Ain’t nobody home in there.” But somehow these people, not fully in the stream of life and yet not departed, seemed imbued with more instead of less. They were my elders, far ahead of me in every way, and I hoped for a hint of what they knew. I wished to make my attention into an antennae to pick up whatever they might be sending.

mystical communication with the elderly, speaking to those near death, communicating with the dying,

Image courtesy of carts.deviantart.com

This is a way of communication I have continued to explore. We humans are connected by much more than language and social norms. We understand each other in far less overt ways. We entrain to one another’s heartbeats, synchronize our moods, react to the light each living cell emits, and pick up energy that some call intuition and others call morphic resonance.

It wasn’t anything I talked about then and even now it’s hard to explain. This is hardly a process unique to me, just something I am still trying learn. If I had to put it in steps, here they are.

1. Pay close attention to the other person. You may choose to look at them for as long as is comfortable, or simply to sit quietly nearby.

2. Be aware of your bodily sensations. Recognize them without making a mental effort to interpret them, at least right away. They are significant.

3. Be aware of seemingly irrelevant things that occur to you—song lyrics, flickering memories, a rush of emotion. Recognize these without making an effort to interpret them. These too are significant.

4. Slow down, staying with your awareness of the present moment. You are allowing your heart’s wisdom to enter your consciousness. Opening to understanding with your most vulnerable self, unguarded by the analytical mind, can be a way to receive such wisdom.

5. Send kindness to the other person in whatever way you can. perhaps as a quiet blanket of compassion or as waves of love. Your heart’s electrical impulse emanates several feet from your body, affecting the electrical impulse of another person’s heart within that distance. A loving heart actually transmits that sensation to people nearby. The kindness you send is received. Trust that.

6. After following this procedure through several visits you may choose to send a request from the deepest part of yourself to the other person. Then pay attention to the sensations in your own body, to whatever images and emotions arise, and to the quiet sense of knowing that seems to come from nowhere. These are a response. You may have to work hard to refrain from inserting what you think into the situation. Stay centered.

7. Honor the other person. Choose to close with a prayer, a kiss, a few minutes to rub lotion on his or her hands, or some other direct contact.

 

mystical communication, silent understanding, heart-to-heart communion, speak to the dying,

Image courtesy of kdustyk.deviantart.com

My summer as a Feeder seemed endless. I wasn’t good at my job. I realize now how badly informed I was in my position. Not only was I not instructed to raise the head of the bed, I also wasn’t told how much to feed each person or how important it was to get them to drink. I remember feeding very little to the people who looked away, closing their mouths against nourishment. I didn’t know what else to do for people who were trapped in small sweltering rooms inside barely functioning bodies. I could hardly eat that summer either. The smell of the nursing home—old urine and cooked cabbage—seemed to reappear in my nostrils at odd moments, leaving me with no appetite.

After my work was finished each afternoon I spent time listening to the patients parked in wheelchairs and those walking along the hallway handrails. They told me of tragedies. Not the wars and poverty they’d experienced but more recent sorrows— children who didn’t visit, pets gone, choices taken away. They begged me to help them in dozens of ways, every one beyond my ability. They cried. Several women there were healthy in body and mind, but had lost their homes and possessions when they recovered from supposedly terminal conditions, leaving them in institutionalized for years. One man, Joe, told me every day that he was afraid of burning in hell. He insisted he was doomed for eternity unless he could confess to a priest. With the hubris of a non-Catholic, I thought I could easily fix the problem. I told him I’d get someone to come from the Catholic church a half mile away. When I called I was told no priest would come, as a layperson conducted all required nursing home ministry tasks. The next day I asked Joe if he would confess to a layperson. He shook his head with sorrow so profound I could barely breathe.

My job was over when school started. I promised myself I would go back to visit. The faces of the people I fed rose up in my idle moments and in my dreams, but I didn’t go back. The silences I held for them became my own silence.

alzheimer's sufferers still communicate, communicate with the dying, listening to silent people,

Image courtesy of jangmai.deviantart.com

What if a man cannot be made to say anything?

How do you learn his hidden nature?

…I sit in front of him in silence,

and set up a ladder made of patience,

and if in his presence a language from beyond joy

and beyond grief begins to pour from my chest,

I know that his soul is as deep and bright

as the start Canopus rising over Yemen.

…there’s a window open between us,

mixing the night air of our beings.

Rumi 

The Land Remembers

There was a small forest behind our house when I was growing up. Stepping from lawn to woods felt like stepping into another world, one teeming with mystery. I couldn’t articulate, but fervently believed, that everything — plants, rocks, water, and creatures —spoke in a language just beyond my understanding. I liked to go alone to a special place, a small rise between two trees next to a tiny stream. I’d sit there silently, hoping creatures of the forest might get used to me, might even come to accept the wilted iceberg lettuce and carrot peelings I was allowed to bring. My offerings were always there the next day where I’d left them, like an answer to a question.

I liked to imagine living in those woods, although I didn’t know how to weave baskets from reeds, how to make a shelter, or what plants might ease illness. I certainly couldn’t imagine eating the creatures I hoped might be my friends. (I was also afraid of the dark and entirely unable to go a single day without library books…)

Of course I returned to the world of mowed lawns and  store-bought food. I’d walk back as if I were part of the forest, trying to keep my footfalls from making a sound despite twigs and dry leaves because I imagined that’s how Native people walked,  when they lived in the same place, when the largest trees might have been saplings.

Every place I stepped then and step now is a place walked by people before me. As Chelsey Luger writes in YES Magazine, “You cannot find a corner of this continent that does not hold ancient history, Indigenous value, and pre-colonial place names and stories. And every place we occupy was once the homeland for other people, most of whom didn’t leave willingly.”

Now, thanks to collaborative mapmaker Victor Temprano’s efforts we can easily find out more about who lived where we now call home. Mr. Temprano is mapping Indigenous languages, treaties, and territories across North America on the website and app Native Land. Simply enter the name of your town or its ZIP code. An interactive map will color-code your inquiry, showing hyperlinked data on the area’s Indigenous history, original language, and tribal ties.

According to the map, I currently live on the land of the Haudenosaunee Confederacy (called the Iroquois Confederacy by the French, the League of Five Nations by the English) and the land of the Potawatomi Nation. These peoples were uprooted by Indian Land Cessions from 1784-1894, and beyond. (See a time lapse map of how 1.5 billion acres were taken from Native inhabitants.)

I don’t know much about the people whose land I occupy. I don’t understand the language of plants, rocks, water, and creatures. I am still trying to listen.

“I keep having these recurring dreams where I’m on a plane or train and all the people around me, Native and non-Native, are speaking different Indigenous languages. I hear Paiute, Lashootseed, Diné, Catawba, and they’re feeding their babies wild rice and smoked fish. I’m dreaming about a modern world that doesn’t erase its Indigenous intelligence, but rather embraces the rich complexity of Indigenous culture.

This can be actualized if we all bring our hearts and minds together. The land we walk on is Indian Land, whether it be suburban cul-de-sacs or city streets. Echoes of Indian existence are all around us. It’s up to us to listen.” Matika Wilbur

Adults Close To Their Own Parents Is Actually The Ideal

So glad my family likes to hang out together.

When I was a teenager, a rumor spread through our high school. It was said on a senior’s birthday he went home after school to find his belongings stacked in the driveway and house locks changed. His parents had threatened many times over the years that he’d be on his own at 18, even though his birthday was a few months before graduation.

The rumor was true.

This freshly minted adult moved in with my boyfriend’s family for a few weeks,  then stayed with other families as he could. We lost track of him over the years but I’ve thought of him as my own kids moved out of the house on their uniquely necessary timetables.

In every culture around the world, closely connected families are the norm. Grandparents and older children help out with younger children. As young people grow up they move out at ages that vary not only according to tradition  but also by the state of the economy and overall needs of their families. Ideally, adult children stay close — not always geographically but close in spirit, welcoming new members who arrive by love or by birth and, as years go by, helping the oldest members as their needs increase.

Yet today, closeness between adults and their parents is treated as a joke or regarded with disdain. Take just about any holiday movie made in the last 40 years (at least those not geared to young children). Invariably the plot is some variation on the stifling misery of “going back home.” Or consider pundits spewing toxic opinions meant to pit generations against one another. The takeaway? Adult kids and their parents reside in two separate  worlds where real understanding cannot co-exist.

Pshaw.

A survey of 2,263 young adults (ages 21 to 26) and their parents found 60 percent of today’s young adults get together with their parents at least once a week and 79 percent feel comfortable talking about emotional events. Nearly a third stay in contact on a daily basis. Karen Fingerman, professor of human development and family sciences at the University of Texas at Austin, confirms that grown children do better when they are emotionally close to their parents, and believes today’s parent-offspring bonds are improving. She regards the “generation gap” of the 1960’s and 70’s as cultural oddity. “Most cultures have maintained closeness between parents and children,” Dr. Fingerman says. “In America, the middle 20th century was an anomaly — in some way the baby boomers are the odd ones.”

Although stereotypes persistently portray young adults who are close to their parents as less independent, studies show the opposite to be true. Researcher Dr. Irit Yanir conducted in-depth interviews with parents, young adults, and psychologists. She defined a close relationship between adult children and their parents as one in which there is regular communication and time regularly spent together, and in which adult children feel comfortable sharing thoughts and experiences with parents while still comfortably making their own decisions.

Dr. Yanir’s research concluded that young adults who have distant relationships with parents tend to be less independent into their late 20s. In contrast, young adults who have close relationships with their parents are more independent in their daily lives, more financially self-sufficient, more professionally secure, more likely to be involved in a stable intimate relationship, and felt more mature.

“The research found that following adolescence, the familial connection is an important factor in forming one’s identity and living an independent life,” Dr. Yanir explains. “It seems that not only can independence and closeness exist together, but they actually flourish together.”

I know it’s not possible or beneficial in all families, but let’s dispel stereotypes about friction between adults and their parents. Let’s laugh together more often too. Someday our grown kids will need some decent quips to share at our funerals.

 “There’s nothing that makes you more insane than family. Or more happy. Or more exasperated. Or more secure.” ~Jim Butcher

 

 

 

 

 

 

Photoautotrophic Wisdom

Weed I Won’t Pull

 

Some hardship curved it into

a green ampersand. Tendrils sprout

along a resolute stem.

I want to lean close, ask

for some photoautotrophic wisdom.

Listen to the soil’s bacterial choir.

Convert to the worship

plants have practiced since the Beginning.

Laura Grace Weldon

Originally published in The Moon Magazine. Find more poems in my collection, Tending.

Keeping Playfulness Alive Into Teen Years

“When we play, we sense no limitations. In fact, when we are playing we are usually unaware of ourselves. Self-observation goes out the window. We forget…our potential foolishness, forget ourselves. We immerse ourselves in the act of play. And we become free.” ~Lenore Terr

Every other Saturday morning a talkative gaggle of 10 to 14-year-olds get together to create, stage, and film stories they’ve written. Today’s session is taking place on a rainy day in Hailey’s basement where the kids have plenty of room. Hailey’s cousins Dylan and Luke are the prop masters. The boys get what they need from a suitcase packed with hats, belts, jewelry, wallets, stick-on tattoos, sunglasses, a police badge, fake nails, and a few masks. A bigger suitcase will probably be necessary because they keep accumulating props.

Hailey’s dad, Jason, says he found the idea a few years ago in my book Free Range Learning and his daughter took off with it, inviting her cousins and friends to give a playwrights’ group a try. (Here’s more info on starting interest-based groups.)

The group didn’t start off all that smoothly. The kids seemed stymied about how to proceed and argued about whose ideas were best. The adults avoided intervening, instead leaving the young playwrights to their own devices. At first the kids decided to keep a list of proposed characters and plots, voting which to use. After a while they dropped the list because fresh ideas kept coming. They still argue sometimes while jockeying to better promote their opinions. (Those verbal tussles are actually an important part of gaining social skills.) Jason says they’ve learned to combine ideas and now more graciously share the glory with each other.

During their first year together the kids would agree on a rough story line, then act it out with improvised lines and actions. They’d climb up the backyard slide to elude kidnappers and perish in dramatically extended death throes, these scenes often mixed into incongruous plots like an underwater fashion show gone wrong. Their audience, mostly parents and grandparents, reliably applauded.

The last two years they’ve developed a more sophisticated process. They write scripts and practice them a few times, work on costumes and staging, set up lighting, then film their performances. They edit the videos to include music and credits. They’re so enthralled by devising and acting out stories that they’re frequently in touch with each other nearly between sessions, eagerly planning and honing their ideas. Recently their parents agreed to let them stay for longer sessions. Now all eight kids in the group arrive with packed lunches so they can work until through the afternoon.

Part of the pain of preteen and adolescent years has to do with a loss of playfulness. Too soon they leave behind the delights of play for a peer culture where being accepted often depends on superficial standards of attractiveness and popularity. Kids feel as if they’re under constant scrutiny by others in their age group; judged by how they look, what they own, what they say and do. When play is stripped away by the pressures of schoolwork and fitting in, something vital is lost.

Some kids manage to keep enthusiasm-friendly spaces in their lives where they’re free to be playful well into their teens. They may find the right circumstances in summer camps, school clubs, music groups, community theater, choir, volunteer programs, youth groups, and pick-up games. Sometimes they’re able to let themselves be playful when they’ve traveled to a new place. Sometimes they look forward to extended family get-togethers where they can hang out with younger relatives.

When I asked online for stories about play-friendly preteen and teen experiences I got all sorts of responses.

Many people said getting together with a specific intent enabled them to indulge in playfulness.

Jennifer Tejada: “My drama club was very helpful, assignments that required playfulness being the great equalizer among students.”

Malik: “There was nowhere to be myself until I started rapping with a few other guys. We let loose all our frustrations and aggravations, and it was like that freed us up to laugh like we’d never laughed before. I didn’t let it go at school or in the neighborhood but with those guys, rapping, I could be myself.”

Some describe a place that gave them the freedom to be playful and expressive. 

Cait : After school, in my middle school and high school years, I would go with my neighborhood friends (all ages, all different cliques) and walk in the conservation land that bordered our property. We would make forts, and as we got older we called them ‘nooks’ because forts were so passé. We would go on adventures, tell stories, climb trees…

And sometimes, play-safe places meant a break from daily routines.

Denise Bowman: “For me it was when I was away from peers, doing a trip with my mom. On vacation, away from home, with just us, I was much more able to engage in playfulness and not be so concerned on how I was ‘coming across.'”

Darren: “I lived for summer camp. For three summers, starting when I was 13, I went to a math camp at an urban college. I showed up nervous, acting like I didn’t care, wham, into a totally different world. I met kids from different countries, kids who were gay, kids who were aspies, all of us math geeks. We had fun I experienced nowhere else. When I’m down all I have to do is remember staying up all night to make a math tower (don’t ask) as a joke for our favorite instructor.”

Over the phone I can hear conversation and laughter spilling over in Hailey’s basement. The preteens have invited a few of their younger siblings to play roles in a production they’re calling “Clones, Inc.” Hailey’s dad Jason says the kids have coated Hailey’s toddler brother with lotion so he’ll look like a “freshly hatched” baby clone. Jason is surprised how eager the two-year-old is to comply. When he’s with the older kids, this toddler demonstrates far more patience than he normally does, even delivering the one line they’ve given him over and over till it’s just right.

Jason, who retreats upstairs to finish our call, says he can tell when they’re filming. The hubbub of enthusiasm gives way to expectant quiet that, even a floor away, sounds full of promise.

Interview: Math Is Child’s Play

One autumn afternoon, the kids who normally rush inside to participate in math circle activities with Maria Droujkova lingered outdoors instead. She discovered them sitting in a large pile of leaves under an oak tree. There the 5- to 7-year-olds were speculating how many leaves were on the ground. Counting them one by one proved futile. So Maria helped the children pile leaves into groups of ten, then measure out 100 piles of 10, fitting them into a small box. Filling that box ten times and then emptying the leaves in a pot gave them approximately 10,000. Ten of those pots filled with leaves fit into a recycling container, for an approximate count of 100,000 leaves. After the kids filled the recycling container 10 times (handily emptying it into a compost pile) they could reasonably estimate that about a million oak leaves had been on the ground.

Maria says the kids were expansive throughout, full of questions and theories, and “kept that first charge of joy from the sun and the leaves for the whole hour.” They never did get back indoors to take part in the activity she’d planned.

Maria is an innovative math educator. She is an expert in building natural mathematical understanding from the earliest years on up through hands-on, open-ended activities. The collaborative site she founded, Natural Math, is dedicated to sharing play-based, deep-inquiry math endeavors through all sorts of resources that empower parents, teachers, and kids to make their own mathematics. Foremost is a series of project-based books for families and math circles. The first title is Moebius Noodles: Adventurous Math for the Playground Crowd, aimed at children from toddlerhood to five years old. The book’s delights include robot commands and mirror books.

Now with eight titles published and more in progress, the newest book offered is Funville Adventures by A.O Fradkin and A.B. Bishop.  Funville Adventures takes readers along with nine-year-old Emmy and her five-year-old brother Leo to a magical place where beings have the power to transform objects. One never knows when something will be shrunk, copied, erased, even turned into an elephant. The sibling have fun creatively solving problems and learning a thing or two about themselves in the process. The book seems like a fairy tale, yet the powers of the Funvillians are a vehicle for introducing children to the concept of functions. Each power corresponds to a transformation such as doubling in size, rotating, copying, or changing color. The authors bring their own math “powers” to the story. Here’s a little about the co-authors.

Dr. Sasha Fradkin has loved math from an early age, and seeks to share that love of math with others. After receiving her PhD in mathematics from Princeton University, she worked for several years as a professional mathematician and taught enrichment math at the Golden Key Russian School to children ages 4-10. Last year, Sasha became the Head of Math at the Main Line Classical Academy, an elementary school in Bryn Mawr, PA. She develops their math curriculum and teaches children in grades K-5. She writes a blog about her teaching as well as various math adventures with her two daughters, and enjoys pondering about exciting and engaging ways to present the beauty of mathematics to young children.

Dr. Allison Bishop grew up with a passion for writing, and initially disliked math because it was presented as formulaic. She belatedly discovered the creative side of mathematics and science, and now sees it as a vital component of the curiosity that drives her life. She is currently a professor of computer science at Columbia University as well as a quantitative researcher at the Investors Exchange. She remains an avid fiction enthusiast and writer, and is always seeking new ways to expose young minds to creative mathematical thinking and fuel their scientific curiosity.

The paradigm in math education is shifting.

Let’s find out more in an interview with Sasha, Allison, and Maria.

Laura: Can you tell us a bit of your own story and what led you to this work? 

Maria: My story keeps changing. Growth requires better stories, right? It used to be about me, a little girl from a little Ukrainian town who wanted to be a scientist like the cool sci-fi characters, when she grows up. Now I am also a parent, a teacher, and a community organizer, and my story is about many people. It is a story about people’s access to real math and science.

I work on helping my young friends and their adults be mathematicians – not when they grow up, but here, now, in their own ways. Let’s say we make functions and functionals into fantastic creatures that five-year-olds find friendly enough. That’s what Funville Adventures is all about. What other groups of people now gain access to this abstract algebra? Maybe math-phobic adults, or those working in their second language, or people with learning disabilities? Maybe tired people who work long hours and only have a bit of time late at night? That dream of radical access to math is what’s guiding my projects.

Sasha: Growing up, I loved the math puzzles that my dad shared with me but found most of my math classes in school dry and repetitive.  I was determined to share the exciting and creative side of math with my children and their friends from an early age. My older daughter, who loves turning everything into a story, inspired me to think about presenting math through storytelling and that is how the idea for Funville Adventures was born.

Allison: As a young student, I loved creative writing and hated math because it seemed too formulaic. I want to help kids discover the creative side of mathematics and science at an earlier age than I did.

Laura: Let’s start with Moebius Noodles. In the introduction, math is described as an exciting and enticingly exotic adventure that’s too often simplified into rote busy work. “It is as tragic as if parents were to read nothing but the alphabet to children, until they are ‘ready’ for something more complex. Or if kids had to learn ‘The Itsy-Bitsy Spider’ by heart before being allowed to listen to any more involved music.” Tell us more about natural math.

Maria: Natural Math 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. The question of how to mix skills and concepts in learning programs is very complex, and the debates are hot among researchers, parents, and curriculum developers. The Natural Math path integrates the two in the following ways.

Within each context of mathematics, we start with open free play, with inspiring prompts and ideas that gently help children make patterns and rules. This is the stage where concepts are born, grounded in embodied experiences. When kids doodle fractal hands or stick their noses inside mirror books to peek into kaleidoscope wonderlands, they are playing freely at first. Then children begin to notice, tweak, remix mathematical patterns, and we help them formulate and name their math. Fractals have levels, and the number of objects at the third level is traditionally called “the third power”—but kids often name these tiny objects “grandchildren” of the first-level object. At this stage of “patterning” children hone their skills, because they need more precision and structure to carry on the patterns. You could ask a kid at this stage to show you 3 x 4 with the mirror book (possibly using kid’s own terms), and you’ll see mirrors at the 90-degree angle with 3 action figures inside.

The infinite road to mathematical mastery is in comparing, contrasting, and organizing these mathematical patterns, and building structures out of patterns. For example, could you connect fractal with mirror book patterns? You can, if you used two mirror books in front of one another to introduce scale into reflections.

Laura: Maria, you were featured in a popular article in The Atlantic titled “5-Year-Olds Can learn Calculus.” In it you explain that math instruction traditionally follows a hierarchical progression that, as you say, “Has nothing to do with how people think, how children grow and learn, or how mathematics is built.” You point out that the standard curriculum starts out with arithmetic which is actually more difficult for children than play-based activities based on more advanced fields of mathematics. You’re quoted as saying,  “Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture.”  How do books like Funville Adventures approach math differently?

Maria: Stories, pretend-play, and imagination! These are keys to growth. Let’s hear more from Funville authors.

Sasha and Allison: In Funville, kids will encounter math under the surface of an engaging story, which will naturally appeal to some kids who might not connect with the more traditional way that mathematics is often taught. Readers will see examples of problem-solving throughout the narrative, and will have plenty of material as a jumping off point to invent their own characters and stories. Since many kids love coming up with stories already, linking mathematical functions to “powers” that characters can have presents them with a new opportunity to interact with math through storytelling.

Laura: Bringing autonomy and fun to math is revolutionary in an era when parents feel pressured to push math on even the smallest kids via apps, educational toys, and academic preschools. Your books and Pinterest page offer wonderful ideas. Please give us a few examples of advanced yet playful math for kids of different ages.

Maria: 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.

Sasha and Allison: The concept of functions is very fundamental and can be studies/played with on many different levels, starting at a very young age. After reading Funville Adventures, children can play games such as “Guess My Power” where one person comes up with a power and others try to guess it by asking for outputs for given inputs and/or by asking questions about the characteristics of the underlying function such as: Is it invertible? What is the domain? Is it periodic?

Here are more examples:

  • Logic puzzles: Both of us really enjoyed engaging with problem-solving through logic puzzles when we were in elementary and middle school.
  • Sports math: A kid who likes to watch or play a particular sport might be encouraged to discover patterns in the many numbers and statistics surrounding it. Certain point totals in football are much more common than others – why? How many ways can one reach a score like 21? If two baseball teams are evenly matched and play n games, how close to n/2 do you expect the win totals to be and why?
  • Patterns in music and art: Older kids who like music can learn about the basic patterns of chords underlying popular songs. Children can learn the mathematics of juggling patterns, or how to make art based on fractals or tiling.
  • Estimation: Kids of many ages can learn through experiments how to estimate quantities like Pi, or how to guess how many M&Ms are in a jar. They can then learn how to extrapolate estimations to quantities they can’t test experimentally, like how many cars are in a city, or how many workers it should take to do a census, etc.

Laura: On NaturalMath.com, you write about a community of people sharing naturally math-rich and meaningful activities for children from babyhood on. We’d love to hear about math circles and what you mean by math communities.

Maria: It takes friendly local people to support mathematical free play: to provide inspiring prompts, to get the action going, and to know when to stand aside and let kids explore on their own. Making, collecting, and remixing patterns depends on other pattern-drafters even more. Parents and teachers need to meet like-minded people to share ideas and encouragement. That brings us to math playdates and math circles.

There are quite a few math circles for middle and high school students, for example, in the National Association of Math Circles.  It’s harder to find math circles for younger kids, or toddler and parent playgroups. Each circle develops its own flavor, and its own lore—the little patterns of play, sayings, and favorite activities. Some of these treasures have to stay local and intimate, but we believe the ideas, experiences, questions and answers could be shared more broadly. NAMC math circle conferences, Julia Robinson festivals, or the Natural Math network called 1001 Math Circles help local leaders grow together.

Laura: Tell us about the Creative Commons nature of Natural Math books.  

Maria: We need this openness, because families, math circles, and other groups in our community are very diverse. Some use the activities as is, but the point is to change, remix, translate, and modify everything to better fit each unique situation.

Storytelling and pretend-play are modifications almost everyone uses. We believe in compelling reasons behind each math activity, but what story is compelling depends on the child. Parents and caregivers change settings and characters: a function machine can be used to magically grow and shrink heroes in a fairy tale, or it can provide enough feed for animals of different sizes at a zoo, or it can fuel starships in a sci-fi setting.

Another modification is about tools and media. Our original activity might call for painting, but kids who don’t like to paint can use clay, or building blocks, or flower arrangements. We try to give specific hints for different media, for example that a symmetry activity requires a lot of folds, so you are better off with thin paper. But we want everyone to experiment on their own, like in this large crowd-sourced collection of multiplication towers.

After Funville Adventures came out, readers started to create fan stories and art about their own Funvillians. For example, Dylan has a tall hairdo and too-long shirt because his power is dilation. You can see some of fan works in the book’s web tour.

Laura: All sorts of projects are in the works through the community incubator, where teams of authors develop books with crowd-sourced input. Tell us more about this approach and other Natural Math books we can read, use, and share.

Maria: We developed a community support mechanism for producing Moebius Noodles. It boosted the book’s quality, and was a source of morale to us, so we kept it going to help other authors with their projects. The idea is to grow books in the nurturing ecosystem of people who care. Two to three coauthors, or else an author with a developmental editor, make the first draft. That stage is intense and private: brainstorming, building, bouncing ideas. Then a few more like-minded colleagues, who work on similar ideas themselves, join as advisors and reviewers. With their feedback, the draft is ready for “beta reader circle”—a more open field test of activities from the book by parents and teachers, sometimes combined with crowd-funding. More revisions, more discussions with other Natural Math writers and readers—and the book is ready to go out to everyone. We see publishing as a gradual, participatory, ongoing process where ideas grow more and more accessible to wider and wider public.

Our newest book created with this model is Math Renaissance: Growing Math Circles, Changing Classrooms, and Creating Sustainable Math Education by Rodi and Rachel Steinig. It is for teachers and parents of children ages six and up. The authors share their insights on how math experience might be improved at home, school, and math circle.

Check out other Natural Math books at the web site.

Funville Adventures by A.O Fradkin and A.B. Bishop

Avoid Hard Work! … And Other Encouraging Problem-Solving Tips for the Young, the Very Young, and the Young at Heart by Maria Droujkova, James Tanton, and Yelena McManaman

Socks Are Like Pants, Cats Are Like Dogs: Games, Puzzles, and Activities for Choosing, Identifying, and Sorting Math by Malke Rosenfeld and Gordon Hamilton.

Playing with Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers  edited by Sue VanHattum

Bright, Brave, Open Minds: Engaging Young Children in Math Inquiry  by Julia Brodsky

Camp Logic: A Week of Logic Games and Activities for Young People by Mark Saul and Sian Zelbo

Moebius Noodles: Adventurous Math for the Playground Crowd  by Yelena McManaman and Maria Droujkova

Here’s to more math adventures!

30+ Book Nerd Delights

book nerd, book bucket list,

How many of these do you want to do? Have many have you done? 

Create a hidden room behind a book shelf.

Take a photo of a book title that perfectly epitomizes your day and share on social media.

Read in a cozy retreat like a hammock, tent, yurt, tree fort, whatever sounds cozy to you.

Pay attention to Library Angels. This is the name given to reading materials you aren’t looking for that somehow appear in your life and turn out to be exactly what you need. Here’s a peek at the strange history of book synchronicity.

Regularly exult in the wonder of libraries. In case you’re not aware, library drinking fountains dispense magic water. Really, try it.

When traveling, make a point of visiting an area library. For incentive, here are some of the world’s most beautiful libraries.

Leave a Post It note to the next reader of a library book.  Maybe a simple, “Dear Next Reader, I hope you enjoy this book as much as I did.  warmly, Previous Reader.”

Name a child after a literary character or author. There are plenty of lists online like FlavorwireMomJunction, and Babble but chances are, your name and the names of your family members have probably already shown up in literature. Just do a search for “name fictional character.” (My kids’ names are found in the classics, in Star Wars, and in video games although we actually chose names that seemed wise and gentle.)

Bestow literary names elsewhere in your life. When I was a kid, my pink bike was named after a fictional horse. Over the years we’ve given cows, chickens, and dogs some lofty monikers. I tend to name things around the house too, like our vacuum and our kefir starter…

As you read, drink what the characters are drinking in the book.  Local microbrew with Bill McKibben’s Radio Free Vermont, gin with Anne Patchett’s Commonwealth, locally made wine with any of the Inspector Bruno mystery series by Martin Walker, Prosecco  with Elena Ferrante’s Neopolitan series of novels, hot chocolate mixed with a hint of hot pepper with Laura Esquivel’s Like Water for Chocolate.

Start or join a book club. If you have time, don’t limit yourself to one.

Indulge in poetry-infused movies and movies about writers.

Savor quotes from your favorite books by copying them onto a plate or mughand printing them on a scarf, or writing them on a shirt using a bleach pen.

Go to book fairs. They’re available in every state of the U.S.  and around the world.

Reread a favorite childhood book to figure out how it shaped your life. (I’m pretty sure The Secret Garden saved me.)

Go to a workshop offered by an author you admire.

Go through a book shelf and donate high quality volumes you no longer want to your local library or an area women’s shelter. Or ship them to Books for SoldiersBooks for Africa, or Reader to Reader. (Huzzah, you’ve just given yourself space for more books.)

Try the read and release method with BookCrossings. Once you’ve read and enjoyed a book, simply go online to print out a label, then leave your book in a public place like a coffee shop, playground, or waiting room. The label assures others the book is free to anyone interested. The label also contains a code so readers can track and follow books as they are read, discussed, and released again elsewhere in the world. Currently, nearly 12 million books are traveling through 132 countries.

Make a composition book cover or try simple bookbinding.

Read under a tree or in a tree or anywhere in nature that inspires you.

Stay up all night to finish a book.

Buy a copy of a book you appreciated and send it to a friend, just because. Do this often.

Whenever possible, buy your books from local brick and mortar bookstores. And get to know the people who work there, they’ll have excellent book suggestions. (But beware. I was thrilled to see a bookstore open not far from me. Although it quacks like a bookstore, it doesn’t act like one. It has lots of local authors and locally made bookish crafts with a token array of bestsellers, but it turns out the owner charges “partners” a non-refundable application fee of $75 to have their book or products sold there for a limited period of time. I cannot imagine what will happen to authors if such a model becomes commonplace.)

When you buy books online, consider steering your dollars to an ethical business or non-profit like Better World Books  or Biblio.

Eat what characters are eating in the book. Thick inviting sourdough bread while reading Sourdough by Robin Sloan, hot fish and corn muffins while reading Their Eyes Were Watching God by Zora Neale Hurston, authentic bird’s nest soup while reading The Wangs vs. the World by Jade Chang,  peanut butter bar cookies topped with chocolate while reading Kitchens of the Great Midwest  by J. Ryan Stradal, nachos with cheese sauce while reading The Nix by Nathan Hill, a hearty sandwich of the sort served at The Bistro, in nearly any of Louise Penny’s Chief Inspector Gamache Series (sign up here to get a free download of Three Pines recipes).

Read in the tub. Or a pool. Or the ocean.

When you travel, read a book set in your destination. Heading to San Francisco? Try  The Adventures of John Carson in Several Quarters of the World: A Novel of Robert Louis Stevenson by Brian Doyle.  Off to a small town in Wisconsin? Read Jewelweed by David Rhodes. New York City? Try Tell the Wolves I’m Home by Carol Rifka Brunt.

Shape snacks that look like books out of fruit leather, honey, and chocolate.

Or heck, help your area library or bookstore run an Edible Book Festival.  Here are some images from the annual festival at Cleveland’s own Loganberry Books.

Cancel plans, then read.

Make altered books.

Connect with your favorite authors on social media. Link to them with a meaningful quote or the way their work changed your outlook. Want more suggestions for showing authors your love? Here are 17 ways.

Let what you read inspire your own work. As Austin Kleon, author of Steal Like an Artist says,  “Read deeply. Stay open. Continue to wonder.”

Superhero Plunge

My mother was born much too late to be a Victorian but she never once, in all the time I knew her, wore anything but a dress. No pants, no jeans, certainly no shorts. An earlier era’s propriety had its grip on her. (She was also affectionate, occasionally hilarious, and a wonderful storyteller.)

Because of my mother’s preoccupation with politeness, I was raised in a family where anything related to human elimination went unspoken. (For example, intestinal gas was neither heard nor discussed. Only once, when behind a closed door we heard my father’s gas amplified by the toilet bowl, did my mother acknowledge it, saying, “Poor Daddy doesn’t feel well.” We all hung our heads to acknowledge misery so great it could be heard.)

Still, the shadow wants to be known. Perhaps that’s why our bathroom rebelled. Faucets leaked and toilets gurgled in the night as if ghostly hands pulled on the handles. And far too often, the toilet seemed unwilling to swallow our refuse. A few wipes, a flush, and suddenly the angry toilet’s water would rise in an increasingly threatening manner to tremble at the top of the bowl. Sometimes, sheets of water cascaded onto the clean tile floor. I developed a terror of mutinous toilets pretty early in life.

The plunger was of no use to me because, as a child, I didn’t have enough arm strength to create the necessary suction. I learned to grab the toilet brush and clear the toilet’s unwilling throat any time it seemed to swirl a moment longer than usual.  If that didn’t work, I’d cry out in desperation, “Mom, the toilet is overflowing!”

Keep in mind, before I was in first grade, my mother taught me to set a proper table with salad fork, entrée fork, table knife, butter knife, and spoon. She taught me to “sit like a lady” when company visited. She taught me to write thank you notes; always say “please” and “thank you;” and when treated badly, to “kill them with kindness.”

But she was no cliché. My mother broke records in school with her high grades. She broke rules as an RN to better serve her patients. And when our toilet threatened to overflow, my mother morphed into some kind of superhero. No matter where in the house she was, she responded to my cry before I finished the first syllable. I swear she flew through the air, arriving in time to grab the plunger and heartily convince the toilet to behave itself.

(In her last years, she used a walker to get around. Even then, my children were amazed to witness their grandmother levitate to their sides at the mere hint of trouble and unclog the toilet before a single germ-laden drop of water touched her floor. )

I grew up and moved out into a world where my mother could not unclog threatening situations for me. This became obvious when I took my own precious two-year-old to the bathroom in someone’s home. It was a lovely home, with a bathroom far more precious than bathrooms I normally frequented. Everything was stark and shining. I wiped my toddler’s adorable bottom to find that he had, somehow, crapped out a substance thick and unwipeable as tar. I ruminated on what he’d eaten as I cleaned him up, lifted his adorableness from the toilet and flushed it, then pulled up his tiny underbritches and tiny pants.

The toilet rebelled in a slow, menacing way. Water swirled. It rose. It made no gurgling digestive noises as toilets do to let us know our digestion is being taken care of. I felt the hamster wheel of panic start twirling in my chest. I looked for a toilet brush or plunger, but of course this fashionable bathroom did not display such utilitarian tools. Water rose even higher. I could picture it trembling at the lip of the bowl, then pouring out onto the beautiful floor as I fled with my child — ruination flooding out the door behind us.

Every cell in my body wanted to cry out, “Mom, the toilet is overflowing!”

My mother was nowhere in sight.

I saw no other choice. In one rapid move, I pulled up my sleeve and plunged my arm into the icy depths. I grabbed the offending clog away from the opening. The water happily swirled down. With a gurgle, everything was gone.

I washed my arm ferociously as I assured my child that, no, he should never put his hand into a toilet. It was Mama’s job and only in an emergency. I did not tell him that he should never speak of it again, lest that might inspire him to announce it to everyone for months.

It has been a very long time since I was forced to commit this act. I still remember the icy plunge, but I don’t remember the horror. Instead I remember realizing that it was up to me.

I was the Mama. It was time to be the superhero.

Foretold

Foretold During A Sleepover With 12-Year-Old Girls

 

Ghost stories and gossip, forgotten

when she showed us the Ouija board

filched from her older sister’s room.

Outside, dry leaves scraped fingertips

across pavement as wind swirled them

in patterns that may, too, have been messages,

but we clustered over the board’s dark formal script,

giggling, nervous, accusing each other

of willfully steering the plastic indicator,

denying we steered it ourselves, calling out

letters forming words forming prophecies.

 

I asked my future husband’s name

and was given the letter M

followed by A, then R, finally C.

No one by the name Marc in our classes,

so I wasn’t teased like girls who got

Tim or Michael or Kyle.

 

When I met you two years later

your name ended in a K.

Teasing, I nicknamed you Marcus,

sometimes call you that still.

After all these years,

I see what I couldn’t then.

Mark, my love, your name

was already spelled

by every letter on that board.

Laura Grace Weldon

Originally published in Verse-Virtual.  Find more poems in my collection, Tending.