Poker chips

One of our best math tools is a revolving holder full of poker chips. Babies discovered and continued stacking-patterns started by a parent or sibling. They were counted, stacked, rolled, spun and thrown. Older kids use them as coins in adventure games, or try to make patterns too hard for parents to guess.

SandraDodd.com/supplies
photos by Sandra Dodd

Magic gopher

Someone once asked:

My son (14) asked how Magic Gopher works. He tried several times to stump them, with no luck. He wanted to know the mathematical method for "guessing" the numbers. I'm sure it's a very simple and logical process, but I have no answer. Can anyone help? Thanks.

Joyce Fetteroll knew and explained it at length, so I saved it here: SandraDodd.com/math/answers
Maybe play the game first, before looking behind the curtain. Have fun!


SandraDodd.com/math
image capture of "Magic Gopher" starting screen

Math from My Little Pony

Dr. Christine Alvarado, a science professor at UC San Diego, on how playing with My Little Ponies moved her toward math and engineering:

When I started, I took the hair on the Pony's tail and divided it into three pieces for braiding. Soon I became bored with a single braid. I then divided the tail into nine pieces and made three groups. I braided each group of three until I had three braids, then took these three braids and braided them together.

Soon I was up to starting with twenty-seven pieces (nested down to nine braids, then to three and then one) and then on to eighty-one. All the while I was learning about math: I saw that division is the process of taking a large number of things and grouping them into a smaller number of groups. In order to end up with one even braid at the end, I had to be able to divide the initial number evenly by three, then by three, and then by three again, until I ended up with just one braid.

The day after that page was made, I took a photo of some of my daughter's ponies, to use as an illustration at an announcement post, Sleep, Teens, My Little Pony & Science.

Holly, 18, had been away from the house. She came in and saw the ponies out, so I showed her the photo and read her a bit of the Christine Alvarado article. Holly got another pony to show me, told me about the plan of the braids and the angles to get them to cross and stay crossed, and what could be done with those braids, but that she usually twists them into a bun, and had left some unbraided hair out at the bottom of the mane to fasten that bun up with.

I couldn't even keep up with the explanation. Just sayin'... 🙂

There's more of what Christine Alvarado wrote here:
SandraDodd.com/mylittlepony
photos by Sandra Dodd, but Holly did all the braiding

A new kind of change

Joyce Fetteroll wrote:

Unschooling is *much* harder than school at home because it takes a great deal of self examination and change in ourselves to help our kids and not get in their way!

—Joyce Fetteroll

SandraDodd.com/math/phobia
photo by Christine Milne

A puzzle to play with

Linda Wyatt wrote:

Algebra is the art of taking the information you have, the things you know, and using that to figure out the information you don't have, that you need to know. It's a puzzle. That's all. You "expose" kids to it by doing it, by playing with it freely and uninhibitedly. By finding things fascinating and wanting to figure out what you don't know. By experimenting. By needing it.

—Linda Wyatt

SandraDodd.com/math/
photo by Shonna Morgan

Clarity and understanding

Deb Lewis wrote:

Sometimes people who come to unschooling think they have it. They think they get it. When their child shows an interest in insects, they run right out and buy that unit study. They let their kid play all day except for those two hours he has to sit down with the math text book. That is not unschooling, and if a person wants to understand I don't think it's helpful to let them go on thinking it is.

I wouldn't know how to define unschooling so clearly and precisely that everyone would have real understanding. But it only seems reasonable to try to make it clearer for those who are trying to understand.

—Deb Lewis

SandraDodd.com/gettingit
photo by Jennifer Fletcher

Trusting and seeing

Joyce Fetteroll wrote:

Unschooling is trusting in a child's natural curiosity to teach them what they need to know. The parent is there to answer questions, talk, infect the kids by their own curiosity about life! (though curious about what you're interested rather in what you think would be good for the kids to be interested in!), bring in cool resources (that the kids can feel free to ignore if it just isn't the right moment for their interest to ignite).

The hard parts are:

trusting natural curiosity to draw your child to what they need to learn when. (Math is fascinating. Kids only get turned off to it by the boring way school approaches it.)

trusting a child's natural schedule rather than the school imposed one (eg, that the child will read eventually even if they aren't doing so at 7 because reading is always a pleasurable activity not an imposed tedious one, they will multiply even if they aren't doing it at 9)

trusting that it's okay for kids to learn things out of order! It doesn't bother kids at all to pick up interesting tidbits about Thomas Jefferson, knightly armor, Egyptian mummies, WW2 combat planes. They make their own connections as they get more and more things in place. (Later, an orderly approach will be fascinating to them as they can make even more connections.)

seeing real learning that is right there all around you, for example, the things that need sorted, the cookies to divide, the planning for a party that are all real live math. And it's especially tough to trust that those few minutes of real engaged figuring are worth 20 pages of worksheet practice.

—Joyce Fetteroll

SandraDodd.com/unschool/moredefinitions
photo by Sandra Dodd, in Liverpool

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Joyce and I got to visit Liverpool in 2013, thanks to Julie and Adam Daniel.

Values

"Meredith Meredith" wrote:

If you value something, make it part of your life. If you value music, play music, listen to music, dance and sing. Invite the people you love to join you—maybe they will. If you value scientific thinking, think like a scientist. If you enjoy math, play with numbers and relationships. The catch is to live your own values without trying to foist them off on other people—because that's not a very good way of sharing what you love, and because personality matters. All your singing and dancing won't make your kids musicians if they're not so inclined—but they'll know a few things about music. If you push music at them, they may associate what they know with drudgery and unhappiness—and then you've failed and failed more utterly than if you never sang a note in their presence.

—Meredith Novak

Meredith
photo by Sandra Dodd, of Marty kid-art

Real learning is bigger

Pam Sorooshian wrote:

The idea that learning to read is learning to sound out or recognize words, that learning to write is learning to draw the letters correctly, that learning math is learning to carry out algorithms by rote—such ridiculously low goals. As if that is what kids are capable of. Those are not real reading, writing, or math.

—Pam Sorooshian

What Teaching Can Never Be (chat transcript)
photo by Cátia Maciel

When to say no

Sandra Dodd, response in 2000 to: Can anyone explain to me "unschooling"?

It's like "just say no."

Just say no to school years and school schedules and school expectations, school habits and fears and terminology. Just say no to separating the world into important and unimportant things, into separating knowledge into math, science, history and language arts, with music, art and "PE" set in their less important little places.

Most of unschooling has to happen inside the parents. They need to spend some time sorting out what is real from what is construct, and what occurs in nature from what only occurs in school (and then in the minds of those who were told school was real life, school was a kid's fulltime job, school was more important than anything, school would keep them from being ignorant, school would make them happy and rich and right).

It's what happens after all that school stuff is banished from your life.

Several Definitions of Unschooling
photo by Rosie Moon

"I told him already."

Not lately, but once upon a time...

...When the triangles come up on Math Arena, I have to think "isosceles" and then look for one (or "right" or "equilateral" or "obtuse" or whatever). Holly doesn't have to.

So my strewing plan was this: The next morning I would wake up early, make tea, and get out the geoboards. We have three. I would set up three basic triangles. When Holly got up and noticed these out, I would point at the hypotenuse on the right triangle. Either she would say "huh!" and "Would you make Malt-o-Meal?" and it would be over, or she might ask "And what are these other two?" Maybe it would be a couple of days of playing with triangles and maybe it will be one little "huh!"

That was my whole plan. I was going to be fine with however minor or glorious it was, because I knew she would have something to tie it to in her head, another dot to connect, and all that internal triangulation would be more valuable than any vocabulary study and formulaic recitation we could do.

But what happened was that I forgot to check back on my geo-board kid-trap. When I remembered in the early afternoon, Marty and Holly were working on fancy designs with colored rubber bands, and making "how many triangles?" puzzles for each other to count triangles within triangles. I came over and said, "That is a hypotenuse," and I pointed right at a green rubber hypotenuse. Holly said, "I know, I told him already." Not only had I missed my big chance to review it with her, she (at twelve) had already explained it to her brother (the fifteen year old).

SandraDodd.com/dot/hypotenuse
photo by Julie Daniel, of Adam, also not recent
(I couldn't find a geoboard photo)

Conversations and interactions

The middle of a longer article:

They grew up with exposure, context, experiences and knowledge of those things mathematics is designed to describe. Our oldest son, Kirby, worked in a games store from the time he was fourteen, and was running tournaments for Pokemon, Magic the Gathering and other such structured strategy games, in the store and at hotels in town for several years. The knowledge required to play those games and even more to organize, judge and score tournaments, is huge.

When Kirby was 18 he took his first math class, at the community college. Like a musician who can't read music, he was baffled at first, but once he understood the notation, he soared, and had the highest test score in the class.

To some people reading this, it might seem there was no "higher math," but what we have done is create a home in which algebraic thinking is a standard part of conversations. Our interactions are analytical and involve factors and projections. They see the concepts and they use them.

SandraDodd.com/math/unerzogen
(There's a link there to the published German version.)
photo by Belinda Dutch

Embrace curiosity

Joyce Fetteroll wrote:

Some people hold onto the fear that kids need schoolish math to learn math. They need to experience their kids learning math by living life to pry those virtual textbooks from their mind's grasp.

But some people are so damaged by math in school, the idea that they don't ever have to do math with their kids because kids will learn math by living life is like a great weight lifted.

That's not good either! For unschooling to flourish we should embrace a curiosity about the world—and the world includes relationships, comparisons and other uses of math.

Unschooling is *much* harder than school at home because it takes a great deal of self examination and change in ourselves to help our kids and not get in their way!

—Joyce Fetteroll

SandraDodd.com/math/phobia
photo by Denaire Nixon

Odd combos

The connection between humor and learning is well known. Unexpected juxtaposition is the basis of a lot of humor, and even more learning.

It can be physical, musical, verbal, mathematical, but basically what it means is that unexpected combinations or outcomes can be funny. There are funny chemistry experiments, plays on words, math tricks, embarrassingly amusing stories from history, and there are parodies of famous pieces or styles of art and music.

SandraDodd.com/playing
photo by Sandra Dodd, one day at Goodwill

Triangles and rows

I had a Shakespeare professor who said "Three trees make a row," to confirm a pattern when a student noticed that something had appeared three times. I remember thinking, but not saying, "Not if they're making a triangle." But it wasn't a math class, and I understood his point.

There's something strong and fun about three. Two parents and a baby. A tripod for a camera or a telescope. A three-legged stool (a tripod to sit on). Three versions of a song. A book or movie trilogy. Counting by threes with its elegant stops at 33, 66, and 99.

European folklore has many sets of three, in bears, goats, wishes...

Here are other posts with photos of three things. It's a fun collection. Three (image label)
Three
photo by Lydia Koltai

The sky stays up

This is from a discussion of speech therapy, once upon a time:

I think the hurry on the part of the therapist is based on school- based assumptions—that his age means being in a certain grade, and that not "catching up" fast means a life of failure and working bringing in the carts at WalMart. It's simple, in this culture, and common, for people to chart a course to a failed future on the basis of ditching school one day, or of a kid getting drunk and missing a football practice, or not studying for a math test one time, or of missing more than some number of days of school in one year because of illness.

The sky is ALWAYS falling for professionals associated with the schools. . . . .
The sky doesn't need to be falling on unschoolers.

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SandraDodd.com/being

Original, on Always Learning
photo by Amy Milstein

Better expectations

Joyce Fetteroll wrote:

What gets in the way of so many new unschooling parents is unreasonable expectations. They think kids must learn to read, spell, do math by a certain age, do chores, do what they're told, not eat more sugar than Mom thinks is right, bathe and sleep when Mom wants... They think unschooling parents have a magical way of getting kids to do those.

Some parent expectations come from how they were parented. Some come from school. Some come from friends and other parents. Some are accepted as truths just because the message is ubiquitous.

For unschooling to flourish, parents need to look directly at their kids. What does *this* child need? What is *this* child reaching for? If a resource helps a parent let go of unreasonable expectations and look directly at their child, then that's supportive of creating a learning environment. If a resource helps a parent understand their child better, that's a good thing *if* it removed a barrier to directly looking at their child. It's not a good thing if it puts a new filter between parent and child. (It's funny how parents who fear TV see addiction in their children. When they let go of their fear, they see engagement.)

—Joyce Fetteroll

SandraDodd.com/waldorf
photo by Sarah Peshek

Determination, focus and interest

Hema Bharadwaj wrote:

I can't begin to say everything I feel about video games... from my beginning ambivalence / aversion / annoyance / fear / more fear, etc. all the way to today's complete acceptance of my child's love and devotion to figuring out a game, his determination, his focus, his interest, his ability to explain it, talk about it passionately, willingness to give Ravi and me tutorials/workshops on a game etc.

He is currently playing a game that is about a guy in school. And the classes need you to figure out games/words/math etc. Then you pass the game. I help him out with certain parts when he asks for it. Been very interesting to watch his intensity in figuring out those puzzles/tests that the school teachers are throwing out to this character. The character gets bullied and keeps getting detention. And Raghu is wondering why this is so. Leads to conversations about the way the video gamer designed the game.

—Hema Bharadwaj
2010

SandraDodd.com/game/benefits
photo by Penny Clarkson

Learning the OTHER things

Sylvia Toyama wrote, in 2004:

This week Andy has figured out money, and it's happened in spurts all week... . . . .
He has learned all this through his own observations. He figured it on his own, when it made sense to him, because it was now important to him to know. And he has the pleasure of knowing he did it without being 'taught' by someone else. He's learned that he's capable and smart — something you just can't get from a worksheet with some arcane facts memorized.

And that's how they reach the point of 'wanting to learn' — when it matters to them, not when it matters to you or anyone else.

—Sylvia Toyama

You can read the details I left out
at SandraDodd.com/math/money
photo by Cátia Maciel

If mathematics is easy for a person...

Disclaimers: Unschooling doesn't ensure mathematical ability.

I wrote this before Marty got a degree in economics. They were 18 or older before taking any classes, and only needed to pay for the books.

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My kids all caught up with formal math in a semester or two of community college. Marty did up to calculus. Kirby only took one class but makes use of math all the time in his work and play, and is good with money and loans and banking and all that practical life stuff.

Holly took three classes, I think. Maybe two. Liked it; it wasn't difficult. There were people in class with her bemoaning the difficulty, and they had been in school for twelve years or more, taking math classes.

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That was written in 2014. Their paid employment and their hobbies, since then, have involved some or all of logistics, statistics, financial accounting, coding/programming, inventory and cash handling. What they learned in class was the notation used to communicate mathematical ideas "on paper" in our culture.

Some of their facility might have been inherited genetically from their mathish dad. That's fair, too.

SandraDodd.com/math/schoolmath
photo by Shawn Smythe Haunschild