This was written for the German magazine Unerzogen, and appeared in their 4/2008 Issue (Fall 2008). It can be viewed in PDF, gratis, here: Unschooler und Mathematik - Wie war das bei uns? (translated by Niki Lambrianidou)

Mathematics

"But what about algebra?"

I think that's the second-most-asked question, after "What about socialization?"

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."

Another ten years passed, and we were starting to homeschool our first child, in the way John Holt advocated, without formal instruction, without a curriculum, but by finding learning all around us. We have three children who have not been to school. As I write this, they are 22, 19 and 17 years old, but when we started unschooling, they were five, two, and about-to-be-born.

I think in words. My husband, now an engineer, has always thought in patterns. We both play instruments, sing and read music, which involves patterns, proportions and complex graph-reading in real time. Genetics do play a part in the talents and intelligences a child will have, but then nurture can enhance or harm his development.

I had been a teacher of language arts when I was young, and in college had studied English, psychology and anthropology. New research has come out affecting the way intelligence is considered, largely by Howard Gardner and his theory of multiple intelligences.

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."

Deductive reasoning was covered early, when I helped them figure out how to pass the bonus round on Super Mario 3 with the charts in the player's guide. What seemed to be a random matching game only had eight permutations, and they were all shown in the book. I copied that page and mounted it on cardboard. We kept it near the TV. They all learned how to choose their first plays in ways that revealed which pattern it was, and then turn all 18 cards without error. It didn't need terminology. When they heard the terms years later, they had something to tie it to.

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.

Meanwhile, in school, children their age have been plowing through rows and rows of solutions to unnamed problems, preparing themselves for the long-gone days when calculations had to be done by men seated in rows doing arithmetic. Half of those in school have been declared below average. A third or so have been declared average. They will fear and avoid math for the rest of their lives. Very few have been told they are "good at math," and most of those probably don't really understand it.

If you took a group of those who made top marks in algebra, for example, and put them in a room and asked them to give you examples of algebra in everyday life, they would probably have no idea. They know what equations look like on paper, but they don't see it in the world. When I overheard my sons at the ages of 9 and 11 figuring out how long it would take them to save both of their weekly allowances to get an expensive game, and how long it would take if they combined their allowances disproportionately as opposed to if both contributed equal amounts, and who would own what percentage of the game if they went the quicker route over the equal-shares route, I knew that mathematics was neither scary for them nor difficult, and later experiences have confirmed that.

Because of the discount Kirby got at the gaming shop, he learned to calculate 30% (and so 70%) of any number. His discount for things he bought for gifts was 15%, which was already what he was using to tip at restaurants.

When he was 15, two notable things happened. He had been sent to a regional Magic tournament to run a sales table for the store. He sold things all morning without the cash register he was used to having. He was figuring sales tax in his head (5.8% or so), and was creating a tax chart on scrap paper. I picked him up at lunch to carry the cash to the bank and to take him back to the hotel, because he couldn't drive yet. He told me in the car that they were going to bring him a tax chart that afternoon. He hadn't known such things existed. They were bringing him a calculator, too. Most people would have said hours before that, "I can't work without a calculator and a tax chart," but Kirby just did it, because he wasn't afraid. He had not gone to school to learn that math is difficult.

That same year, he was overheard explaining to some other teens at the gaming shop how to multiply by 18—to do it by 20, and subtract two for each one you have. No pencil, no paper, and his school-labeled "learning disadvantaged" friend totally understood his explanation. The adults who overheard this expressed amazement. The other home¬schoolers who heard about it were amazed that adults had been amazed (and came and told me about it).

Kirby is now 22 and works for Blizzard Entertainment, in Austin, Texas. I called him about this article and we talked about math's applications in his life. He talked about running Magic tournaments in those game-store years, and the considerations involved in planning to finish a tournament within the allotted time. He talked about things I didn't understand—elimination systems and "Swiss rounds" in which wins and losses all receive points. He talked about the logistics of styles of play, and of the social factors in running tournaments and in teaching karate (which he also did as a teen). "It's not enough to know how it could or should play out, because there are human factors that will affect the time required," he said. "I apply the same things with my job now, helping manage a team."

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.


2014 note: Kirby will be 28 this summer and still works for Blizzard. He has had a couple of promotions. Some of the people he supervises have college degrees and some do not; it doesn't matter, in what they're doing (except that some are paying student loans off, and others are not).

Marty and Holly are grown and competent, have worked with money in jobs and never had any problems. They've both (in separate hobbies and activities) been involved with the financial end of event planning, and seem to think more creatively and expansively than others they've worked with.



Unschooling and Math

Backup PDF in case the magazine reorganizes its webpages