You can't just throw maths at someone and expect them to get it. A curriculum is needed. You can't just start with trigonometry without first understanding geometry. And algebra is needed for all variable driven maths.
You also can't teach science without first teaching the scientific method. Without understanding that it's just experimenting for the sake of experimenting.
While there is a logical progression to math, because of it's very nature, a "curriculum" is completely unnecessary. On the contrary, it can disrupt the progression, by forcing certain concepts that a person could achieve an understanding of by another path, their own path.
There are certain concepts that must be understood to understand math. There are infinite paths to achieve that understanding.
You also can't teach science without first teaching the scientific method.
Since you are saying this as if it were in opposition to what I said, I suggest you didn't read what I wrote, since this is almost verbatim what I said.
Once you teach the scientific method (which takes an hour to teach, and a lifetime to master) you have done all the "curriculum" required.
If it is a logical progression, no curriculum is required.
There are many possible logical progressions.
If you force a curriculum, you have to get lucky that you have hit on a "best" one (in an average sense), and that one will almost certainly not be the best for everyone.
The word curriculum is just a word used to describe a progression. Do or do not call it that if you choose but if it acts like a duck... If it wasn't logical none of our kids would graduate. My oldest is on high honor role on the advanced schedule. My second is also on high honor role but not in the advanced schedule. Neither one of them could be doing as well as they are with a logically laid out curriculum.
You can't just throw maths at someone and expect them to get it. A curriculum is needed. You can't just start with trigonometry without first understanding geometry. And algebra is needed for all variable driven maths.
You also can't teach science without first teaching the scientific method. Without understanding that it's just experimenting for the sake of experimenting.
While there is a logical progression to math, because of it's very nature, a "curriculum" is completely unnecessary. On the contrary, it can disrupt the progression, by forcing certain concepts that a person could achieve an understanding of by another path, their own path.
There are certain concepts that must be understood to understand math. There are infinite paths to achieve that understanding.
Since you are saying this as if it were in opposition to what I said, I suggest you didn't read what I wrote, since this is almost verbatim what I said.
Once you teach the scientific method (which takes an hour to teach, and a lifetime to master) you have done all the "curriculum" required.
One hour. Done. Now it's time to get creative.
If a curriculum is setup correctly it IS a logical progression.
Disregard the second half of my comment.
If it is a logical progression, no curriculum is required.
There are many possible logical progressions.
If you force a curriculum, you have to get lucky that you have hit on a "best" one (in an average sense), and that one will almost certainly not be the best for everyone.
The word curriculum is just a word used to describe a progression. Do or do not call it that if you choose but if it acts like a duck... If it wasn't logical none of our kids would graduate. My oldest is on high honor role on the advanced schedule. My second is also on high honor role but not in the advanced schedule. Neither one of them could be doing as well as they are with a logically laid out curriculum.