A while back Jake S wrote the following in the School Leaving Age diary.
Teaching arithmetic requires a great deal of drilling, because to be truly useful it has to be almost a conditioned reflex. Similar to reading, in a sense. Reading should come so naturally to you - be such an integral part of how your brain works, if you will - that when you see a signpost, you should start reading what it says even before your conscious self catches up to what's going on. Similarly with arithmetics. When you see a problem, you should start solving it automatically, with the same instinctive part of your brain that makes you snatch your hand away from a heated cooking pot.
In the same thread, kcurie wrote:
So a more proper solution will be a 13-15 (3 years) compulsory of pure language and math for everyone (langue means understanding gramming and memorizingg vocabulary and comprehensive reading.. yes.. memorize is GOOOOOOD.. no matter what a stupid pshycologist will tell you... the good ones already chnged their opinoon at least on this one) and basic logic and math for any mature life...
A question for yez
What are the fundamentals of mathematics no fifteen year old should be without?
Now, maybe that is a list too far. (I really don't know.)
Let me try....a quote from Migeru.
if people want to teach themselves you are just a facilitator
It's in the edge--the wide valley bottom--where learning occurs.
The slope yonder is called, "Can't, no, boring, too hard, I'm not good enough, it's not worth it, I don't like you" etc....
And that other slope, the one that people climb up and sometimes never come back, is called "Perseverance, weak!, do it again, wrong, you shouldn't have bothered, I'm afraid not, I don't think Max will make it" etc.
But also...ach..."Almost there!" and "Not right now, thanks", and "There are other slopes", "Sit down and look around", and "Who's going your way?"
What I'm thinking is: I understand the "reading words" part, more or less. It's a case of words being readily present (in my life), and the way words relate to situations around themselves, such as "EXIT" when you leave a place, and "ENTRANCE" when you go in. Or "Yes" and "No", or "Where's" in the various Spot the Dog adventures.
("Where's Spot? Is he in....the hedge?"
No! It's Mr. Squirrel!
(That's not written in the book....so the repeated words that appear are recognised...heh!)
The hard thing is to teach how to read critically--what does that mean?
So I'm thinking there must be a maths evquivalent. I can do the "How much is X?" maths (Spot the Mathematical Dog--"Is it more than one hundred? No! Is it more than ten? Yes!"); I see that basic logic must be applied...
I'm thinking of a not-overly-tiring list of things that, if a person can do them, they can call themselves "numerate"....hmmmm....now I wonder if I could write a similar list to demonstrate that a person is literate...
Heh! Maybe it's just me; 'twould be good though, I think, to list out the basics in all materials--we have a lot of knowledgable people here at ET, and they are knowledgable because they have embraced their subject, and so here I am, maybe I'd like to embrace it a bit too, but I can't be a professor of everything, so some subjects...I'll be happy with the basics, but with an element of rigour, where I can say, "I understand the basics of econmics" and therefore I can follow economic conversations...for example.
There are maybe divisions among folks deeply immersed in their areas of interest; but okay....if I had six months free time to learn "the basics" of, say, arithmetic; is that long enough? Or maybe I don't need six months; maybe I can learn the basics in a month?
The very basics, I mean.
A silly example. I declare (regularly) that it is possible to learn to touch type in three weeks, as long as you practice for half an hour every day, and you won't be able to do the numbers along the top, and you may be a bit sloppy with the shift key...but you'll know the basics.
Pythagoras - Wikipedia, the free encyclopedia
Pythagoras' religious and scientific views were, in his opinion, inseparably interconnected. However, they are looked at separately in the 21st century. Religiously, Pythagoras was a believer of metempsychosis. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became moral. His ideas of reincarnation were influenced by Greek Mythology. He was one of the first to propose that the thought processes and the soul were located in the brain and not the heart. He himself claimed to have lived four lives that he could remember in detail, and heard the cry of his dead friend in the bark of a dog.
One of Pythagoras' beliefs was that the essence of being is number. Thus, being relies on stability of all things that create the universe. Things like health relied on a stable proportion of elements; too much or too little of one thing causes an imbalance that makes a being unhealthy. Pythagoras viewed thinking as the calculating with the idea numbers. When combined with the Folk theories, the philosophy evolves into a belief that Knowledge of the essence of being can be found in the form of numbers. If this is taken a step further, one can say that because mathematics is an unseen essence, the essence of being is an unseen characteristic that can be encountered by the study of mathematics.