Another post:

> OK, let me try again. Does unschooling teach a child to recognize the
> mathematic symbols used in textbooks?

Unschooling doesn't "teach" a child anything. They learn, which is different.

But do unschoolers learn the mathematic symbols used in textbooks? Sure, if they have a reason to do so. If they want to be able to communicate math concepts, then yes, they'll need to learn standard notation, just like if they want to write to someone and have it understandable, they need to learn how to write in the language they speak. Same thing.

> From the unschoolers I've known math
> is mostly mental math - which is great - yet I don't see where they
> experience the math sentence and different layouts of mathematic problems
> on paper. I would think this could potentially cause a problem at some
> point would it not?

I think this is an interesting thing to think about.

In some ways, you may be right. I think unschoolers do a lot more mental math than school kids do. They *start* with mental math, and may or may not do it on paper until much later, instead of starting with written math, and *not understanding it* until later.

But again, I think it's like learning any language- it is more natural to learn to speak before learning to write.

I don't think it's a problem. They learn to write it down when they need it that way. They also see written math quite a lot, at least my kids do.

> OK so what is Real Math?

Math is a language. It is what we use to describe things and their relationships to each other very precisely.

Math is far more than numbers. It is shapes, patterns, connections, changes, movement, color, music, art, logic...

Everything can be translated into or expressed in mathematical concepts- look at artificial intelligence.

Arithmetic is the manipulation of numbers. It's a basic part of much math, but nowhere near the entire thing. It's just the part that schools seem to focus on, at least until you get to graduate level.

Algebra is the art of taking the information you know, and using it to figure out the information you don't know.

Geometry is boring... no, wait. Geometry has to do with shapes and sizes, angles and connections. Things. Objects.

Trigonometry is very cool, once you figure out what it really is used for. Waves. Frequencies. Vectors. Very compact ways of expressing things that change.

And calculus, that beautiful thing... how incredibly cool that you can figure out so much about things that are only dreamt of, by understanding the theories of how they must be.

fractals... infinite series... infinity itself, what a concept

and on and on. All things of fascination, of beauty. Of TRUTH, in its raw form. Where else but in math are things proven facts, irrefutable, perfect forever?

:::sigh:::

I'm rambling, getting emotional. I have friends who laugh at me because I have to put math books down after a while, I get too excited to keep reading.

> So you are saying that ages 13-14 is where math should begin?

Math begins before you are born. Is, was, and always will be. :-)

Understanding math begins at birth.

A babies first mathematic concept: am I, or am I not, the same being as my mother?

> Thus entering into the algebras, trigs, geometry, etc.?

These also begin very young, they are concepts, much to think about and explore with long before any sort of "formal" education begins.

> Then where is the
> child's base? Math like any other subject must have a foundation.

And it does. Life. Life itself is the base of math, or is it the other way around?

Where is a child's foundation in language?

Human brains are designed to use and understand math and language.

> When did they learn multiplication (note I didn't say memorize the entire multiplication table) and division, fractions, decimals, etc.

All along. Time is a big math concept motivator, as is money. Body parts- two of some ten of some, why? Why are bodies mostly (but not totally) symmetrical? Why do some things fit together, others don't? Why do some stacks of things balance, others don't? Why is it that if you want to build a lego thing that is twice as tall and twice as wide and twice as long as the one you have, it takes 8 times as many blocks? Why is it that two glasses can be different heights, but hold the same amount? Why isn't a taller one always "bigger"?

Notation starts when they realize that making a dot for each thing, or using an object to represent a thing, gets a bit tedious after a while, surely there must be an easier way?

Concepts are learned as we need them, as we wonder about them, as we come across them.

What amazes me is the number of people who think there is no math in their lives.

As far as more advanced written math- they'll either need to learn it, and embrace it, or they won't need to learn it. If they don't need it, they don't need it.

How much of the school math that you "learned" do you still use, really? Only those who have a need or an interest retain it. Most people will not need anything beyond basic algebra, some don't need even that.

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