Yes, children can certainly learn a great deal independently, but for most children that is not the case for advanced subjects.
And please don't get me started on the Saxon series. That series was a product of 60's thinking that children could learn merely by absorption, without learning in an incremental, concrete manner, moving from more basic topics to more complex. I used Saxon up until 11th grade and hated it. Once I got different textbooks my grades shot up. I have talked to numerous other students and every single one of them despised the Saxon math series. Why on earth anyone recommends them is beyond me.
I wholeheartedly agree with this part of your quote. Saxon Math is USELESS and confusing, and there's no rhyme or reason to it. The person who put this series together made a boatload of money keeping children ignorant in a logical progression of mathematics.
The most useful place for a Saxon Math book is a book burning party.
Don't get me wrong: this whole thread is very interesting, but here an off-topic
theme has me very intrigued. What is
this "Saxon Math" thing you are all worked
up about? Can you briefly describe it? Or is there some other thread that goes
into detail on it? How would I know if any particular curriculum uses it? I raised
children and never heard of it. Is it possible that one of my children was subject
to its influence and suffered in Mathematics classes as a result without my
knowing it?
How does "keeping children ignorant" happen "in a logical progression of
mathematics?"