Well, I don't think any book/teaching method would entirely dismiss linearity, it would just make things less linear (as compared to the current way of teaching).
As a start, I suppose you could have a topic in algebra... then use that to discuss probability. From there, you can view something as geometry and teach some of that, etc...
Maybe that doesn't work. So maybe, you teach math by asking a question and exploring to find an answer. As you explore, you inspect different approaches to a problem. Later questions can use earlier points as analogies.
To be honest, I don't know quite enough math to even give a list of questions/topics. But, I imagine a good math teacher could do something of this sort.
Its probably best to start at the University level and move your way down as you learn lessons about teaching these things.
As for your idea, CYA-Math, I like it in some ways. "To see how this connects to this, go to page 34. To see an analogy to something else, go to page 54." I agree though very tough to build.
A robust cross-reference system could keep the page numbers automatically up to date. I'd edit the textbook in a wiki style interface, then use some automated software to commit it to a specific order with page numbers.
This is one area where a digital textbook would be incredibly useful.
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I also agree, but how would you write a nonlinear book? "Choose your own adventure - Math" would be a tricky textbook to produce.
Well, I don't think any book/teaching method would entirely dismiss linearity, it would just make things less linear (as compared to the current way of teaching).
As a start, I suppose you could have a topic in algebra... then use that to discuss probability. From there, you can view something as geometry and teach some of that, etc...
Maybe that doesn't work. So maybe, you teach math by asking a question and exploring to find an answer. As you explore, you inspect different approaches to a problem. Later questions can use earlier points as analogies.
To be honest, I don't know quite enough math to even give a list of questions/topics. But, I imagine a good math teacher could do something of this sort.
Its probably best to start at the University level and move your way down as you learn lessons about teaching these things.
As for your idea, CYA-Math, I like it in some ways. "To see how this connects to this, go to page 34. To see an analogy to something else, go to page 54." I agree though very tough to build.
though very tough to build
A robust cross-reference system could keep the page numbers automatically up to date. I'd edit the textbook in a wiki style interface, then use some automated software to commit it to a specific order with page numbers.
This is one area where a digital textbook would be incredibly useful.