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

"I feel it in my fingers..."

Karen James, on math:

I took the leap and we began homeschooling, with me trusting that like walking, talking, reading, writing, and all the other things he had managed to learn through his play and exploration and with our active support, he would come to have a meaningful understanding of math too. When I came to a greater understanding of unschooling, I suspected we had not made a error in judgement. As I have watched Ethan's relationship with math grow and deepen, I knew we had not.

What I didn't realize when I was worrying about how to bring math to Ethan, was that Ethan had already found math. He found it on his fingers. He found it in the seeds of an apple I had cut open. He found it in the peas spread over the tray on his high chair. He found it in every repeated drop of his cup or spoon. He found it in the music we listened to. He found it in the timing between jumps on his jolly jumper. He found it in the balance he needed to take the next step. He found it in the distance between steps. It was everywhere already, and he was already finding the art in it. I just needed to stop my worrying and start having fun.

So I have.

—Karen James

SandraDodd.com/math/found
photo by Belinda Dutch

The title isn't from the quote, it's from a 1967 Troggs song.


In 2023, Ethan James is newly grown up and working at a video game company, at least for a while.

Perspective and math

Two responses to a newcomer's question: "How do you approach math?"

I wrote:

The real answer is not to "approach math," but to learn how to see all of the patterns, measuring, relationships, weights, game play, sports stats, poker hands that are math in its natural environment.

Jo Isaac wrote:

The question you really want to ask is how do you deschool enough that you know you don't need to 'approach math' at all.

The longer answers are on facebook here.
photo by Sandra Dodd

The real problem

Years before we had children, I was telling my young husband-to-be that in school the only math I liked were the "word problems." He said those are the only real math problems in text books. That was the real math. The numbers sitting already in equations and formations were the solutions to unstated problems, with only the arithmetical calculations left to be done.


I remember that moment vividly. I was in my late 20's and hearing for the first time what "mathematics" meant. I had asked my teachers all through school "What is this for?" and "How is this used?" and they rarely had an answer beyond "Just do it," or "It will be on the test."

SandraDodd.com/math/unerzogen
photo by Sandra Dodd

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.

---

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.

---

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

What is this for?

Years before we had children, I was telling my young husband-to-be that in school the only math I liked were the "word problems." He said those are the only real math problems in text books. That was the real math. The numbers sitting already in equations and formations were the solutions to unstated problems, with only the arithmetical calculations left to be done.


I remember that moment vividly. I was in my late 20's and hearing for the first time what "mathematics" meant. I had asked my teachers all through school "What is this for?" and "How is this used?" and they rarely had an answer beyond "Just do it," or "It will be on the test."

SandraDodd.com/math/unerzogen
photo by Sandra Dodd

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

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

Structure and transformation

Mathematics could use a better name. Seriously. School has gone and made that one all scary. In addition (she said mathematically), it's not called the same thing in all English-speaking places. "Math" in some places, and "maths" in others.

But it's about measuring and weighing and sharing. It's about making decisions in video games (buy the watering can? risk danger to collect coins?) and it's about how fast music goes and which ladder to use to get onto the roof. It's almost never about numbers themselves, and it's never about workbooks (except for workbook manufacture and purchase).

I went to look for a different word for "mathematics," and I didn't find one. One Old English word was "telling." For arithmetic: "cyphering," or sums. So I went looking for modern, philosophical definitions of mathematics that had nothing to do with school, and I have collected all these bits and pieces for you: Mathematics is a science dealing with the logic of quantity and shape and arrangement; structure, space, and change; logic, transformations, numbers and more general ideas which encompass these concepts.

Structure and transformations? I use those things. Shape and arrangement? That covers art, and music. Flowers in vases and books on shelves.

Unschooling is simple but not easy, and it's not easy to understand, but when math is a normal part of life then people can discover it and use it in natural ways and it becomes a part of their native intelligence.

SandraDodd.com/math
photo by Holly Dodd, 2010 or earlier

Something about math

Unschooling is simple but not easy, and it's not easy to understand, but when math is a normal part of life then people can discover it and use it in natural ways and it becomes a part of their native intelligence. All that's left is for them is to learn the notation, later, when they need to.

Mathematics (written for a German magazine; the translation is linked there)
photo by Sandra Dodd

Three children

Writing from early 2002,then 2012:

And now I have three children who are 10, 13 and 15. They have never been to school. They have never had a math lesson. But today Holly asked me to help her with 7/18 plus 5/18, for a video game she was playing. Kirby has a job and will do his income taxes soon for the second year. Marty was discussing odds and probability earlier with three other teens and his little sister.

Ten years and some later, Holly's about to turn 21, Kirby has done his taxes for years, and all three have taken math classes as young adults, for fun.

SandraDodd.com/unschoolingworks
photo by Sandra Dodd, of three fleeting flowers

Mathematics

Mathematics could use a better name. Seriously. School has gone and made that one all scary. In addition (she said mathematically), it's not called the same thing in all English-speaking places. "Math" in some places, and "maths" in others.

But it's about measuring and weighing and sharing. It's about making decisions in video games (buy the watering can? risk danger to collect coins?) and it's about how fast music goes and which ladder to use to get onto the roof. It's almost never about numbers themselves, and it's never about workbooks (except for workbook manufacture and purchase).

I went to look for a different word for "mathematics," and I didn't find one. One Old English word was "telling." For arithmetic: "cyphering," or sums. So I went looking for modern, philosophical definitions of mathematics that had nothing to do with school, and I have collected all these bits and pieces for you: Mathematics is a science dealing with the logic of quantity and shape and arrangement; structure, space, and change; logic, transformations, numbers and more general ideas which encompass these concepts.

Structure and transformations? I use those things. Shape and arrangement? That covers art, and music. Flowers in vases and books on shelves.

Unschooling is simple but not easy, and it's not easy to understand, but when math is a normal part of life then people can discover it and use it in natural ways and it becomes a part of their native intelligence.

Unschoolers and Mathematics
the image is a Holly photo

A tool, a toy, a game

My kids think math is a tool and a toy and a game. Why would they want to be saved from it?

"We don't have to know that" isn't anything I have ever heard my children say. Because there is nothing they do "have to learn," there is nothing that is off their learning list either. In artistic terms, without the object there is no field. In math-lingo, they have the infinite universal set. In a philosophical light, they avoid the dualism of learning and not-learning.

SandraDodd.com/timestables
Photo by Sam Baykus

Real vs. acting, or practicing

Writing done in school is practice writing, mostly. That "math" done in school is the calculations of other people's math. It's all at least two steps from "real world," while saying "this is the real world."

---

That is from a discussion about the depth of being, rather than of acting like a child's partner. Examples were used, and tangents were taken. The longer collection is at:
"Partners," examined

photo by Holly Dodd

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

---

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

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

Math without numbers

In thinking of mathematics, I operated on the assumption that our children might be more pattern-oriented than I am (spatial and logical intelligences) and that they might be more word-dependent than my husband. We provided games involving patterns–board games, video games, dice, cards, and singing games–and played them with the children. One of the most memorable games was Bazaar, a game with exchange rates and values but requiring no numbers or reading. (In Germany there is a similar game called Bierbörse.) Math was a fun part of the fabric of life. It was the structure of games and of music and of Lego and Ramagon. We talked about proportion and perspective in art and construction, but only in words, not with numbers. They found patterns; I found patterns, and we shared them without me saying "this is mathematics."

Games     /     Geography without maps
screenshot by Holly Dodd, of the game FlipPix

A beautiful mystery

"I want to see Lucas Sven Leuenberger's math rock band. But where? When?

"The future is a beautiful mystery."

—Holly Dodd            

One doesn't need to know what math rock is to appreciate the comment about the future.

SandraDodd.com/holly
photo by Colleen Prieto

"...don't have to know..."

My kids think math is a tool and a toy and a game. Why would they want to be saved from it?

"We don't have to know that" isn't anything I have ever heard my children say. Because there is nothing they do "have to learn," there is nothing that is off their learning list either. In artistic terms, without the object there is no field. In math-lingo, they have the infinite universal set. In a philosophical light, they avoid the dualism of learning and not-learning.

SandraDodd.com/timestables
photo by Holly Dodd

Learning everything

If you think of knitting as “good for learning math” it isn’t good for knitting. 🙂

EVERYthing is good for learning everything.

Chat with Sandra Dodd on Mommy Chats, 4/25/07
photo by Ida Maria Stenild Coltau