I'm seeing the same result as I observe my children as they work on projects that they themselves have initiated. Today, Brayden and Annacie are working on a Nocilla family version of Monopoly. It has required planning, creativity, and cooperation. Writing is a huge part of it as they are creating the board and cards themselves. They're writing numbers, determining size and dimension, and will be using paper money to play, so they're doing Math. I'm guessing I could think of more if I tried but I assume you get the picture.
This is how children learn best. What they're doing is interesting and relevant to them. I'm here to make suggestions but the idea to do it was theirs. This fact alone makes it far more likely that it will actually be completed. We have enough incomplete school projects laying around on shelves as proof that the inverse is true. If it's Mommy initiated, their passion tends to fizzle out.
I remember a time before I had kids, wondering what they were going to look like, what their personalities would be like, and so on. I'm so thankful that homeschooling provides endless opportunities for me to embrace who they are, and to be here supporting their learning, each and every day.
I wouldn't be happier if I was a queen in a palace, most days anyway. : )