I was unschooled, and fully plan on unschooling DS (as long as finances allow). Having been HS/US'd I suspect I have a farily unique view of it... I was probably among the first generation in the US in many years to have been
While I say I was "unschooled" I suppose we weren't total USers - I did have to do one thing every single day. Math. We used Saxon Math and so every day (mon-fri), I had to do one chapter. I wasn't thrilled but I understood why and am grateful for it now. Saxon Math was the only way I was going to learn math, and so it was what I did. Aside from that though I did whatever I wanted.
As for the function of a gerund - I think I know what a gerund is now, though only because of learnign spanish (I'm guessing its the 'ing' on the end of things, like.. jump-ing?). Despite not having a clue what a gerund is when I entered college, despite not really knowning (then or now) what a noun/verb is, I can write very well. How is that possible? Because of how much I read. Reading is the best teacher of grammar there is - you learn how sentences should look, sound, flow, etc by reading.
Aside from that, I learned most things in time - I became interested in one thing which lead me to an interest in others. My mother was always very good about directing my interest and helping me find books in the library to read. About taking us on field trips to museums, gardens, parks, factories, plays, workshops, etc related to what we (the HSing group), were interested in, or what the moms thought would be 'cool' or 'interesting' or 'neat'. They usually picked pretty good.
In reference to the "you cant learn what you don't know about" - well, I suppose thats true. But I didn't know squat about world war 2 - untill I read biographies and then ather book in the same series-type called "30 seconds over tokyo" and then another called "flying tigers" - between those two books, my interest was sparked. And I proceded, at the age of 11-12 to read everything that our libraries had on the subject. I still have a bookshelf full of books on ww2 and am still fascinated by it. I also became fascinated by airplanes and so learned about flight, aerodynamics, etc. Flight lead me to an interest in astronomy and from there I became interested in physics.
All of that was thanks to unschooling. Thanks to being aloud to read about world war 2 to my hearts content - and then to switch to astronomy - and then to physics. Unschooling works great - moms and dads can help by suggesting something. If your kids interested in bugs let'm read about them to their hearts content. At some point, something else will spark their interest (or not. Maybe they'll become an entomologist