I am collecting some of my favorite commentary on learning math naturally, written candidly by real parents of unschooled folk at various times. Joyce Fetteroll wrote:
Wild math looks different than domesticated math It looks more like conversations, using numbers to figure out something the child wants to know, video games, allowance, weighing things in the grocery store, finding the best deal among several choices—that is not as a lesson but what you would normally do—board games, figuring out "how long until?" when she asks, budgets, doing a rough estimation of the items in the grocery cart to see if you have enough money, baseball statistics, crafts, origami, wrapping presents ...
Holly Dodd in her mid-20's, reported by me (the mom):
Sandra Dodd, March 13, 2017:"Your math isn't wrong, it's just NOT math. 'Wrong math' isn't math. You're doing something that isn't math. It's art or something. People can't do bad math, it's just NOT math."
Pam Sorooshian's review and comments on the article "Mathematics: The Most Misunderstood Subject," by Dr. Robert H. Lewis of Fordham University
I wrote an article on How Kirby learned math for the German magazine Unerzogen. It appeared in the August, 2008 issue. 😊 Here is the original English text, and a link to the magazine's site, to that issue, and to a PDF of the article in German:
Mathematics / Unschooler und Mathematik - Wie war das bei uns?
Karen James on Ethan's math interest
An unschooler goes to sixth grade, and how he did in math
Is this page inducing anxiety?
"I don't want to count, I want to think."
Structure and transformation
"Mathematics could use a better name. Seriously. School has gone and made that one all scary. ..." (at Just Add Light and Stir)
Powers of Ten videos
A Tale of Times Tables
"My Son Knows Algebra! (somehow)"
Celebration and speculation,
An Unschooler does someone else's Word Problems!
Julie reports her nine-year-old's first experience with contrived "math problems."
School math in history and school math after unschooling
An odd justification for school math, from 1911, and stories of four kids doing school math after years of unschooling.
Pam Sorooshian's math page
King's X From the Math Monster
Unschoolers and times tables
Pam Sorooshian, on Dice
Pam talks about about all kinds of patterns in dice-play.
Pam Sorooshian: Games and Math
What mathematicians really do.
Math concepts from handling cash.
Games, all kinds, with history and links and ideas and pictures.
Logic (mostly fun writing by Joyce Fetteroll!)
Knots and Knotwork (Celtic interlaced designs)
STATISTICS PAGES TO PLAY WITH
Visualizing World Development (a video)> Baby Name Wizard
MATH GAMES ONLINE
"Want to let me read your mind?"
Joyce Fetteroll's math topics:
"What Special About This Number?" Hard page to describe, definitely worth a look. Something mathematically significant about every number up to 9,999.
I found a great math site that seems like it was designed for unschoolers.... www.mathcats.com
You can mess aroung with polygons and tessellations, explore what you like with no determined path or drills...great stuff." (—dawnofns)
ZOOMBINIS, explained incredibly well.The great news is now the game is available for $10 or $15 now, whereas lots of us paid $40 or more when it was new! Great game. Not a single number in the whole thing, but mathematics to the core.
Dr. Math, a resource for answering math questions! (submitted by Pam Sorooshian, unschooling mom of three, and instructor of statistics at college level)
I was driving today and my 5yodd and her 5yo friend were in the backseat talking. The friend says "I can count all the way to 100" to which dd says "Why?"
I laughed to myself. The funny thing is that dd is learning to count to 100 as well. On her own just for fun. I guess she just didn't feel it was noteworthy enough to mention out of the blue.
A CLASSIC! This is by Linda Wyatt, writing on January 12, 2003, in response to questions from someone skeptical about unschooling:
This subject is near and dear to my heart, so it jumped out at me.
How do unschooled children learn long division? What do they do to practice it?
Linda Wyatt:What do unschooled children need "long division" for? And could someone please explain to me what long division actually is, and is there such a thing as short division?
I know how to divide. Do I use "long division"? Beats me. Quite possibly not, since my elementary school experience was at a "free school" where we didn't have the usual types of "subjects" that most elementary schols have. I didn't take a math class until I was 10 and decided to listen in on a group of kids learning algebra. (Which I immediately LOVED, and have ever since!)
My point is that it's important to understand the concept of division, but HOW you do that is not so important. There are several different ways.
I'm going to say the next bit in all-caps not because I'm yelling at you, but because I really, really mean it and I think it's critically important and most people have no idea.
I HATE THE WAY SCHOOLS TEACH MATH BECAUSE IT TAKES ALL THE MEANING, JOY AND BEAUTY OUT OF IT!!!
People do NOT need to learn math the way it is taught in schools. In fact, they don't need to "learn math" at all. Math is INSEPERABLE from most everything else in life, and if you live a full life, you'll learn all the math you need because you need it. It's there. It's part of everything. You couldn't escape it if you tried really hard.
SOME people will love it and get interested and want to pursue things to a deeper level and learn more advanced math and do all sorts of cool things with it. MOST won't.
If you try to force school math on kids early on, and turn them off the subject- a VERY common thing that happens because most adults are so terrified of math because of their own awful school math experiences- they will likely develop an aversion, and at any rate, they are extremely unlikely to remember what they've "learned" anyway.
How much of the algebra you were taught in school do you remember and use? I'm serious. What do you still use? What turned out to be irrelevant? What could you easily look up and re-learn if you needed to? How likely are you to need to do that?
What about algebra and other higher mathematics?
First, I don't think algebra is "higher math" but I'll let that go. I think it's mind-candy.
But what about higher math?
Who needs it?
That's a real question. What kind of people use higher math? What do they use it for? When and how did they learn it? You might want to find some and ask them.
What I've found is this: most people who use higher math learned some in school, because that's where they were. But MOSTLY, they learned it through using it as they needed it. Like on-the-job training. They took it further than school does because it actually interested them. They had a use for it.
I remember the day I realized that calculus had a purpose. I was stunned! Why didn't they ever tell us this in high school? I had a rocky relationship with calculus in high school (along with a rocky relationship with just about everything, as most teens have!) but once I settled on a career path where I NEEDED it, it was suddenly easy and made sense and I relearned it all in a few weeks.
If I had not had that career path, I never would have looked at calculus again.
I no longer have that career, and calculus is unlikely to be part of my everyday life (although you never know) so I no longer use it and have forgotten most of it. Big deal. (Now, I use a lot more geometry.)
I'm reading a lot about the practical uses of what we learn, and I agree wholeheartedly BUT...the brain work that goes into learning and knowing how to do abstract number exercises like algebra, increases the ability of the brain to think about ANY subject.
YES!!! It does!
But it works the other way around, too. Learning abstract thinking any other way will make it easier to learn algebra, should you need to do so. Algebra isn't the only way to learn it. Just a fun one.
It's GOOD for the brain to "workout" by doing abstract stuff. And so, how would an unschooling family get algebra across to the kids? Or long division, for that matter? LOL
Well, to start with, we don't do "math" at all here. It isn't a separate thing.
But we use it all the time.
Suppose your Dad is coming in the morning to pick you up at 10:00am.
You need about an hour in the morning to get up and shower and eat
breakfast, to be ready to go.
(The cool thing about that particular need is that it includes using base-12 math as well as base-10)
My current favorite real-life mathematical figuring here:
We have a mini-van.
I never made the shift from being 5 people to being 4 people, at least not
in a practical way.
He redesigned the layout of everything in the car.
We changed it.
A simple change that required a large conceptual leap-which he made, but the rest of us had not- and now, life is much simpler.
To really understand this and the effect it had, you should know that I teach fencing, 6 classes per week, plus I give individual lessons. Four different locations for the classes. Several different locations for the lessons. Different groups of people at each class, with different equipment needs. And all three kids fence, but they don't attend the same classes. I have equipment in the car for about 30 people, plus a variety of training equipment and record keeping stuff. We were really having an issue with having the right gear in the car.
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.
I "make" my kids do their math...lying in a puddle of sunshine on the front room floor, wrap-ups in the recliner, Math Minute drills, etc. Right now, the two younger ones are playing dominos...MATH!
No, it's playing dominoes. Why not let it be that?
Why separate math out of everything all the time? Why do people do that?
The way to learn math naturally is to let it be a natural part of everything, like it is, and not make such a point of it all the time.
For example, what if, in writing and speaking, you had to stop and make a point of every time you used the letter "e"?
Look, I'm writing an e-mail... USING THE LETTER E!
How ridiculous is that?
Yet people do it to math all the time.
But would unschooling REALLY say not to give them seat work to practice their basic number skills, and on a consistent basis?
I wouldn't necessarily say it, but I also would NEVER do it. SEATWORK?!???
What on earth for?!?
And who came up with a term like that anyway? I find the very concept nauseating, I really do. Sit here and do this. Whether you like it or not. Whether you have any use for it or not. Stay in your seat, do your seatwork. YUCK.
This does not mean that we don't have a zillion math books around here, including workbooks and such. We do. I probably have more math books than most schools do. But it's because I enjoy them. I NEVER make or even ask my kids to have anything to do with them. It's my special interest, not theirs. Once in a while, they'll pick one up, look through it, put it back down. Sometimes, they'll use computer software that has math games on it- more so when they were very young, not so much now. But I have never and will never require it.
I will, however, discuss with them when I'm working on trigonometry for fun. It's interesting to me, and they might also think it is. So far, mild interest, no real excitement. That's fine. They know it's here. And they know something about what it's for. They can ask if they need to.
The best thing for my kids having to do with math is that I love it, and they know it. No math anxiety here. (Except for when my daughter had an issue with girls in her scout troop telling her she's not learning anything because she's homeschooled, and she came home wanting to "do math" and we had a little talk about that.)
People learn best by having resources available, and interesting things to do.
Learning is interest-driven. Joy-driven. Need-driven.
But please don't make it a command performance. ESPECIALLY with math, which is already handicapped by a national phobia about it.
The best thing you can do for your kids with math is to learn to love it yourself. Play with it. REALLY learn it. Not just how to calculate, but why it works that way. Why does borrowing work? Why does carrying work? What is the real meaning of "place value" and why? Why do we use base-10 math. Learn some other system. Learn to multiply in binary. Play with numbers. Play with shapes. Why are "odd" and "even" called that? Is it important? How many math words do you know? How many math words do you use every day? (Count them! Make a list!) How much math is there in your life that you are so comfortable with you're not aware of it?
And my very favorite math question:
How, exactly, do you know when it's safe to cross the street?
Play with patterns. Play with sets. Go outside and throw rocks and pay attention to the paths they travel. Drop stones into a pond and watch the ripples. Figure out why buildings don't fall down- or why they do. Ponder why the wind off Lake Michigan travels through the city of Chicago the way it does. And Oklahoma, where the wind comes sweeping down the plains... what's different in very windy places? How do you need to change things to accommodate that? Or other weather? Why are most of the roofs in places that get a lot of snow not flat?
I could go on and on and on and on. You can, too.
Question everything. Figure some of it out. Don't worry about whether you are learning math or not. You are. It's there. It's ALWAYS there.
If I waited for them to come to me asking how to divide...well, I sure wouldn't hold my breath!
Why would they not ask you?
If they needed to divide and couldn't figure it out, they woudn't ask for help?
Or is it that you believe they'd never need to?
Sometimes, we buy a box of popsicles. In our family, treats like that are portioned out by shares, so each kid gets a fair share. They're into this. But the youngest used to have to ask me how to figure out what her share was. She very specifically DID come to me and ask me to help her figure it out- to learn how to divide.
Then she thought it was cool, and figured out shares of practically everything in the house.
But NONE of my kids, as far as I know, can do division on paper, using the method taught in schools. They've never needed to. They do it in their heads. They estimate, when that's good enough for what they need. They use calculators.
And honestly, that's what almost everyone does in real life when they need to divide big numbers anyway, because few people trust their own figuring enough to use it without checking. I used to freak people out when I ran a food buying club and did all the invoicing and such by hand, no calculator.
Truly, just wanting to figure it out.
And that's what it's all about. Figuring stuff out that you need to know. Remember that.
Well. I kind of got going on this, didn't I?
Linda sent an update in 2008 and there's a 2014 update below that!
In March, 2008, Linda wrote to ask me to ask my sons about a video game her son was considering. This came from that correspondence, and I was eager to add it here!
Just got home and spent a few minutes looking around on your site.