You just taught me a term, as I had never heard of strewing until now. I suspect that term became popular after 2000 (the year our son began college). We did indeed strew.
I'm not even sure I would call what we did after 4th grade "choosing a curriculum", which would mean to me having things more laid out (a syllabus and such) than I think we had. I just pulled his portfolio down for a period of time when he was 6 to 7, and it has things like this in it:
1) A letter he wrote to Black Dog and Leventhal Publishers, Inc. noting that when he was reading their book "101 More Read Aloud Classics", the book went from page 96 to page 126 (only he described this much more cutely than I am here) and therefore was "missing 16 (or 32, depending on the way you look at it) pages" and he asked if he could have those pages, either in a separate 32-page book or in another complete book (and he received a new hardbound copy, even though his original was paperback, only 10 days later).
2) A list of books read (with start and finish dates)
3) Photos of things like his planning a lemonade stand with a girl, standing next to a Domino creation, riding a bike, using a continuity checker while fixing a hairdryer, taking a tap dance class, playing in a few handchime choir performances, getting an organ lesson (informal at the handchime choir director's home), visiting the Library of Congress and an airport museum, playing racquetball and ping pong, visiting Montpelier and Monticello, painting, working with an adult friend on a circuit for a robot costume, accepting s Multiple Scerlosis Read-a-thon top fundraiser award, singing at a Halloween campfire, attending a physics of flight class at the zoo, studying the steam engine at a railroad museum, visiting the FDR and Jefferson memorials, attending a university physics program, attending a van Gogh exhibit,visiting Savannah, etc.
4. His subtest and composite scores on achievement and aptitude testing at the end of 6th grade (where he hit the ceiling of 9th grade equivalency on reading, vocabulary, math problem solving, spelling, usage, capitalization and punctuation, science, and social students and scored a general aptitude in the 99th percentile (despite being years younger than a typical 6th grade graduate).
5. A list of examples of questions others posed that he knew the answers for, such as: an electrical engineer giving him a truth table to solve and his solving it correctly even though the engineer at first had the wrong answer himself; in a "Physiology of Speed" lecture given at a science museum that was attended almost exclusively by adults, the college professor asked, "What are endorphins?" and our son was the only one in the room to raise a hand (he had read about endorphins on his own somewhere); in a "Physics of Flight" class, where he was the youngest student, he answered "Who are the Mongolfier brothers?" (he said he had learned this from the software program "Museum Madness", a program he used when he was just two or three); when taking a Degas tour at an art museum, he answered so many questions with such clarity and insight that the tour guide and some parents on the tour felt certain he was planning to be an artist; while eating out at a restaurant, I noticed a picture on the wall of a man carving a statue and it coming to life and asked who the sculpture in the picture was and he answered, "Pygmalion"; at Physics is Phun, he helped solve an equation to find the speed of light using metric measurements, and in doing so, used scientific notation and converted nanoseconds to seconds, among other things.
6. Examples of other ways his mind was strong, such as how he continued to play things on the piano that he often had only heard once prior, and could pick up instruments he didn't usually play and start playing real tunes on them instantly (something that came in handy years later at the Media Lab when a graduate student invented an instrument that he thought would only make nonsense but interesting sounds when used to draw, but our son picked it up and showed the fellow student how it could be used to draw/play a real tune), and how when he was told to jump and risk breaking your legs if in a fire while in a second floor bedroom, he noted that this wouldn't be an issue when he was an adult as his home would have ladders that would automatically shoot out from upper floors when the fire alarm was set off.
7. Samples of some calendar (page-a-day) questions he knew right off, like one asked Fermat's theorem and he stated it perfectly (he had read it in one of his father's books).
8. List of classical myths, poems, stories, and speeches read.
9. Topics covered in grammar and literature.
10. Misc. other ways English was "taught" (seeing two Shakespearean plays at the Folger Library, keeping a journal, writing thank you notes, playing games like "The Play's the Thing", attending a writer's workshop, going to performances at theaters in the area, etc.
11. His making three-colored graphs (one made a flower image) on his new graphing calculator (he had to ask politely on and off for two years to get a graphing calculator), and other topics in math such as probability (figuring out median, mode, median, and range), special triangles, etc.
12. Topics discussed in science, such as internal combustion engines, Anton van Loeuwenhoek, Gregor Mendel, curved reflectors, acids/bases/chemical reactions, experiments with different rocks, adolescence and puberty (and it was good we covered this early as he went through it early; he also took the topic in college when he was 11), and a whole lot more.
13. Topics in geography (24 are listed), world civilization (25 items listed), and American civilization (18 items listed)
14. Health education (fire prevention fair at mall, AIDS, newspaper articles on zinc lozenges and cigars, etc.
15. Topics in art (25 listed).
16. Topics in music (things like Scott Joplin, shapes of melodies, how melody works with chords, attending a Peter and the Wolf performance,etc.
17. Spanish class at the elementary school and Italian class at the community college.
18. Good manners worksheet (one I typed up myself where he had to check off if it was a "Do" or a "Don't" (things like asking when a guest at someone else's home if they prefer you to leave your shoes on or take them off, and get this oldie..."rewind videotapes after watching them"!).
19. A letter to a local paper's editor that resulted in his being offered a position as a writer for the paper (not that this was his intent at all when he wrote).
20. The copy of an essay he wrote that won him $300 in U.S. Savings bonds in a national essay contest.
21. Lots of other stuff (I just scratched the surface there).
So it wasn't like we never used any textbooks (we used a few at times where we felt it made sense), but we didn't do much planning in advance, doesn't seem to me, so much as sort of went with the flow of what seemed interesting to delve into at any given time.
I'm not even sure I would call what we did after 4th grade "choosing a curriculum", which would mean to me having things more laid out (a syllabus and such) than I think we had. I just pulled his portfolio down for a period of time when he was 6 to 7, and it has things like this in it:
1) A letter he wrote to Black Dog and Leventhal Publishers, Inc. noting that when he was reading their book "101 More Read Aloud Classics", the book went from page 96 to page 126 (only he described this much more cutely than I am here) and therefore was "missing 16 (or 32, depending on the way you look at it) pages" and he asked if he could have those pages, either in a separate 32-page book or in another complete book (and he received a new hardbound copy, even though his original was paperback, only 10 days later).
2) A list of books read (with start and finish dates)
3) Photos of things like his planning a lemonade stand with a girl, standing next to a Domino creation, riding a bike, using a continuity checker while fixing a hairdryer, taking a tap dance class, playing in a few handchime choir performances, getting an organ lesson (informal at the handchime choir director's home), visiting the Library of Congress and an airport museum, playing racquetball and ping pong, visiting Montpelier and Monticello, painting, working with an adult friend on a circuit for a robot costume, accepting s Multiple Scerlosis Read-a-thon top fundraiser award, singing at a Halloween campfire, attending a physics of flight class at the zoo, studying the steam engine at a railroad museum, visiting the FDR and Jefferson memorials, attending a university physics program, attending a van Gogh exhibit,visiting Savannah, etc.
4. His subtest and composite scores on achievement and aptitude testing at the end of 6th grade (where he hit the ceiling of 9th grade equivalency on reading, vocabulary, math problem solving, spelling, usage, capitalization and punctuation, science, and social students and scored a general aptitude in the 99th percentile (despite being years younger than a typical 6th grade graduate).
5. A list of examples of questions others posed that he knew the answers for, such as: an electrical engineer giving him a truth table to solve and his solving it correctly even though the engineer at first had the wrong answer himself; in a "Physiology of Speed" lecture given at a science museum that was attended almost exclusively by adults, the college professor asked, "What are endorphins?" and our son was the only one in the room to raise a hand (he had read about endorphins on his own somewhere); in a "Physics of Flight" class, where he was the youngest student, he answered "Who are the Mongolfier brothers?" (he said he had learned this from the software program "Museum Madness", a program he used when he was just two or three); when taking a Degas tour at an art museum, he answered so many questions with such clarity and insight that the tour guide and some parents on the tour felt certain he was planning to be an artist; while eating out at a restaurant, I noticed a picture on the wall of a man carving a statue and it coming to life and asked who the sculpture in the picture was and he answered, "Pygmalion"; at Physics is Phun, he helped solve an equation to find the speed of light using metric measurements, and in doing so, used scientific notation and converted nanoseconds to seconds, among other things.
6. Examples of other ways his mind was strong, such as how he continued to play things on the piano that he often had only heard once prior, and could pick up instruments he didn't usually play and start playing real tunes on them instantly (something that came in handy years later at the Media Lab when a graduate student invented an instrument that he thought would only make nonsense but interesting sounds when used to draw, but our son picked it up and showed the fellow student how it could be used to draw/play a real tune), and how when he was told to jump and risk breaking your legs if in a fire while in a second floor bedroom, he noted that this wouldn't be an issue when he was an adult as his home would have ladders that would automatically shoot out from upper floors when the fire alarm was set off.
7. Samples of some calendar (page-a-day) questions he knew right off, like one asked Fermat's theorem and he stated it perfectly (he had read it in one of his father's books).
8. List of classical myths, poems, stories, and speeches read.
9. Topics covered in grammar and literature.
10. Misc. other ways English was "taught" (seeing two Shakespearean plays at the Folger Library, keeping a journal, writing thank you notes, playing games like "The Play's the Thing", attending a writer's workshop, going to performances at theaters in the area, etc.
11. His making three-colored graphs (one made a flower image) on his new graphing calculator (he had to ask politely on and off for two years to get a graphing calculator), and other topics in math such as probability (figuring out median, mode, median, and range), special triangles, etc.
12. Topics discussed in science, such as internal combustion engines, Anton van Loeuwenhoek, Gregor Mendel, curved reflectors, acids/bases/chemical reactions, experiments with different rocks, adolescence and puberty (and it was good we covered this early as he went through it early; he also took the topic in college when he was 11), and a whole lot more.
13. Topics in geography (24 are listed), world civilization (25 items listed), and American civilization (18 items listed)
14. Health education (fire prevention fair at mall, AIDS, newspaper articles on zinc lozenges and cigars, etc.
15. Topics in art (25 listed).
16. Topics in music (things like Scott Joplin, shapes of melodies, how melody works with chords, attending a Peter and the Wolf performance,etc.
17. Spanish class at the elementary school and Italian class at the community college.
18. Good manners worksheet (one I typed up myself where he had to check off if it was a "Do" or a "Don't" (things like asking when a guest at someone else's home if they prefer you to leave your shoes on or take them off, and get this oldie..."rewind videotapes after watching them"!).
19. A letter to a local paper's editor that resulted in his being offered a position as a writer for the paper (not that this was his intent at all when he wrote).
20. The copy of an essay he wrote that won him $300 in U.S. Savings bonds in a national essay contest.
21. Lots of other stuff (I just scratched the surface there).
So it wasn't like we never used any textbooks (we used a few at times where we felt it made sense), but we didn't do much planning in advance, doesn't seem to me, so much as sort of went with the flow of what seemed interesting to delve into at any given time.