A response I posted to someone:

> Math is a combination of basic memorization, drill, and processes.

No, it most emphatically is NOT.

Arithmetic may be, and even that can be done without rote memorization or drill of any kind. But you are maligning the subject of math by suggesting that's all there is.

Math is a language, a way to describe and measure and compare things with a great deal of accuracy. It is a way of looking at things. A way of organizing information so as to make the most sense out of it and figure out the parts you don't know.

Math can be learned the same way any language is learned- by *using* it. By hearing it around you day in and day out. By being exposed to it *in context* constantly.

Why? What does age have to do with any of it?

People need to understand enough math to do the things they want and need to do, whatever age they are. For some people, this will always be at a basic level. For others, they will crave and be fascinated by quite complex concepts from an early age.

> I know that there is absolutely nothing we as a family do in the
> course of the day, unless contrived, to cover math functions that
> my 4th grader does on a daily basis.

Really absolutely nothing?

That may well be, in your family. It's true in many families, because the adults see math as something separate from life, as a subject to be studied and drilled, something boring and tedious. That's not an environment conducive to learning math in a natural way.

If you truly do no math in your lives, you are *missing out*, and I'm very sorry to hear it. I have a hard time seeing how that's even possible.

We do *lots* of things every day that surrounds us all with math, none of it contrived. It's how we live. We haven't separated ourselves from the math in the world to the point that we no longer even see it- which is exactly what most people do.

> But, without a math text, I know my 4th grader would not be doing
> pre-algebra, mixed numbers, complicated fraction problems, etc.

*How* do you know? Because you don't provide any other access than textbooks?

There are many, many games which have these concepts as important parts, and unless you get those games *so that* your kid will learn math, playing games is not contrived. There are many things in the world to talk about, experiment with, examine, describe, play with. Most kids play with pre-algebra concepts in their heads, all the time. No one tells them that's what it is, so they may not realize it, but it's there.

> Without the daily work, he wouldn't get enough practice and reinforcement
> for there to be serious understanding and the ability to spring forward
> to the next level concept. (ie, fractions> common denominators>
> subtraction when there is no common denominator> subtraction with
> mixed numbers, etc)

Why do you consider it "work"? I'm serious. Your own language shows that you find the subject to be something that is not done for fun.

> (Not in constant unnecessary repetition, but just sure we
> progress daily to higher and more complicated math processes.)

How do you know how to progress? Do you believe that math is a totally linear subject, that it must be taught in sequence? Not so. Most people think it must be, because that is always how schools teach it, but actually, a lot of it can go in any order, even the basics. You don't *have* to understand addition and subtraction before multiplication, but most people will. It's quite possible to learn to add and multiply first, before subtraction- why wouldn't it be?

Around here, we dabble in math. A lot. We may be using fractions one day, geometry the next, then thinking about how to figure out square roots, then off to see how the fibonacci sequence works. My 5 yr old might show us how she has figured out how to count in base 2, the 9 year old may be playing with fractals, who knows?

As we dabble, and as they pull in bits of information from more and more areas of math, it comes together for them. The dabbling is *constant*, it's not like they get a tiny bit once in a while.

> Liberal arts areas and math are just totally different to me in how
> they should be taught.

I think everything should be taught the same way: based on what the learner wants and needs to know, following what fascinates them, and doing the fun stuff. That will lead them everywhere.

> I'd be curious as to how you gauge progress without a formal curriculum
> and how confident you are that they are covering all areas in a math
> level.

Well, I don't measure "progress", because we aren't on any certain path. And I don't even know what "all areas in a math level" could possibly mean. We don't do levels.

But. I'm completely confident that they are learning lots of math, because I see them use it, all the time, every day. We talk about math, a lot. We ponder age old puzzles and problems, we build and design and create all manner of things. We share the beauty in mathematical discoveries. We help each other figure stuff out (most recently, converting RGB codes expressed in decimal into the usual hex code). I'm familiar enough with math to be able to see which concepts they are getting, which they are struggling with, which they have an affinity for. Just like with any language, as their understanding grows, the ways in which we can discuss things also increases.

> I'm open to understanding....just doubtful.

Most people are. The thing is, unless you are fluent in math, and comfortable with it to play with, you may never understand how anyone else could be. You may always see it as "problems" and "work" and drill and repetition and progressing from one specific topic to the next, one by one, day by day.

*That* is contrived. By schools. For many, many years.

But it isn't what math *is*.

Please don't make math boring. Please.

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