My son once pointed out that he finds math in the "real world" less stressful because you don't always have to get it right the first time; if you find you've made a mistake, you can go back and refigure. On assignments and tests, when it's wrong, it's wrong.
My question is this. How have other unschoolers handled math and what have you seen for the older unschoolers and their experiences around no formal math training. I don't think they need more than they will use out there in the world but are we doing them a disservice by not having them exposed to the possibilities.
The subject of math can be frustrating for unschoolers! ;-)
Math is as easy to get as reading.
But there are two things that get in the way of naturally learning math:
1) Most of us are familiar with school math and that's the only model we have. It seems impossible to get all that by living life.
Well, it is and it isn't. The problem is that schools teach kids to memorize how to do things. They don't teach kids to understand. The hope is that understanding will come from memorization but memorization alone is enough to be testable and show that learning is taking place. And it takes oodles of time to memorize things you don't understand. It take oodles of time to go step by step through something that doesn't make sense.
My favorite analogy is that learning math naturally is like how kids learned to speak English. They picked up and used the parts that they needed to get what they wanted. And they got better at it as a side effect of using it. It works like a charm!
Learning math in school is like how kids learn (or not learn!) a foreign language in school. The process in school is to memorize and acquire an abstract understanding in order to apply it. But it doesn't work.
Kids learn to make plurals by hearing lots of plurals being made in lots of different contexts, not because they're told to add s. They learn to do verb tenses by hearing lots of different verbs in lots of different contexts, not because they've memorized the rules. (Which are broken for lots of the verbs we use most often anyway!) They learn to put sentences in proper grammatical order by hearing oodles of different sentences and without even learning what nouns and verbs and prepositions and so forth are.
2) Most of us don't speak math. We don't point it out. We don't use it in front of the kids in ways they can understand. Mostly because we think math is what's found in textbooks.
So we need to learn to see math in real life to gain confidence that it exists. We need to speak math when they ask us a question. If they want to know how many days until their birthday, figure it out out loud without resorting to paper. Add numbers out loud without paper. It forces you to manipulate numbers to make them easier and kids can see how numbers actually work.
There are some math threads on the message boards at Unschooling.info that might help. If you think of the message we've been inundated with since grade school that math needs to be taught rigorously, it shouldn't be too surprising that most people need to read a lot about naturally learning math in order to counteract that message.
The only subject I can't think of how to do is math. When the kids are interested we measure in different ways and the money thing is on going but how will my kids learn multiplication and division and such?
Real life math probably bears the least resemblance to its schoolish counterpart than any other "subject". Because real life math is about discovering how numbers work rather than memorizing formulas to impose on numbers.
Real life math is, as an example, casually encountering percentages in a dozen different contexts and therefore slowly building up an idea of what percentages are and how they're used.
It's similar to the process of how we acquire new words. Usually when we're reading or listening to conversations we don't run and get the dictionary to look up a word we don't know. Generally we can get a good enough idea of its meaning from the context. And the next time we encounter it we add another facet to our understanding and the fuzzy impression of what the word means gets a bit more clear. And so on. The process probably accounts for our often not being able to define a word for someone else that we've not only read and heard dozens of times but even used.
For some reason people think multiplication and division are such difficult subjects that, after algebra, that's the one thing they question under "how will they learn?" But once a child realizes that multiplication is just a fast way to do repeated addition and that division is just a fast way to do repeated subtraction, a great deal of what causes math phobia in adults disappears. Multiplication and division aren't mysterious at all. They're just addition and subtraction short cuts.
One thing I've found helpful is expressing things in a couple of different ways. When we've come across percents, I've said "17% or 17 out of every 100," or "25% is the same as a quarter."
Another thing is solving problems out loud without pencil and paper so they can see how numbers can be manipulated. So for instance to add 138 + 53. (Hmm, a bit tougher than I normally pull off the top of my head! ;-) but kids do pick up on the process when they hear similar processes dozens of times.) 39 is almost 40 and 53 is almost 50. 40+50 is 90. But we added 2 to the 38 so we need to take away 2 from 90. And we subtracted 3 from the 53 so we need to add 3. That brings us up to 91. Then just add 100. So 191.
Any thoughts about strewing a little more math into our lives?
By being more conscious of math that's around you. And not just numbers! But also patterns, connections, and relationships.
By realizing that what kids need is to absorb the language of math by seeing, for example, percent used in a variety of contexts.
That said, board and card games, computer games, video games, puzzle books.
There's a Dorling Kindersley book that used to be called Comparisons but I think has a different title now?
But above all speak math. Walkthrough solving problems out loud. (Stick to problems he asks, like how long until Christmas, if you can't help sounding like a lesson when you figure out a tip. ;-) Compare things. Pick some standard of measurement to help him grasp relationships. (It's more meaningful to translate 18 feet into 3 Daddy's for instance. Some of the ones I use are a story which is 10 ft, 3000 miles across the US, 600 miles from Boston to Pittsburgh as units of measurement.)
The reason math in school takes so long is they need to substitute drill for understanding. It's really hard to do pages of problems like 7.5% of 182 when you don't know and don't care what percents are, let alone 7.5% of 182. If the understanding is there first, the details are much easier.
I have let go of the math study, confident that they will do it when they are ready.
Perhaps it's more accurately stated that they will acquire math as they need it. And they may study it formally if they find it interesting or want something a formal study could help them get.
Unschooling math looks more like playing games and celebrating Pi Day (March 14 to coincide with 3.14) and saving up for something they want.
If he should decide in 9th grade that he wants to be an engineer will he be able to jump into math and be where he needs to be when he wants to start college.
Math learned in a classroom is like a foreign language learned in a classroom. It's memorization of stuff that isn't being used or understood. Math taught with school methods is all about memorization mostly because it's really difficult to test for understanding and very easy to test to see if something's been memorized. It's hoped that understanding will come from memorization and practice, but that isn't the goal.
Math learned from life is how kids learn to speak their native language. It's just absorbed as they use it. They get better as a side effect. It's painless and effortless.
If he begins exploring engineering type things he'll use math as he used English as a toddler. He'll be able to pull the sense of it out because he'll see the context it's in.
Kids get math by providing opportunity and fun materials. By fun materials in math, I mean things like Tangrams, an abacus, a hand counter (those little clicky things), magnetic marbles, plastic frogs for sorting and counting, plastic magnetic numbers, books, puzzles, chess game.
Video games. Grocery store. Allowance. Computer art programs.
Even better than plastic counters are real things! :-) Leaves. Rocks. Acorns. Hot wheels! ;-) Anything specifically designed for sorting and counting has built-in ways the kids are "supposed" to sort. The counters are deliberately limited so as not to be "confusing". That way when kids come up with the built in right answer teachers can check off that they've demonstrated an understanding of the concept.
Real things allow kids the freedom to explore surprising similarities that may not be obvious. Learning to observe is a much more useful skill to a real scientist or mathematician (or cook or automotive mechanic or ...) than being able to notice what everyone else has already noticed!