So, we're 3/4 of the way into our first homeschooling year, and by all accounts, I think it's going well, though I really have no "measure", other than how my children are feeling & acting and how I am feeling & acting.
I can tell you, I feel much freer, not being tied to the public school schedule, and I am pretty sure my daughter feels the same way. She has been able to try so many new things this year, partly because our "school", Self Design, gives her a learning investment (read: loaded Visa card of a set amount) on which to spend on educational pursuits; and partly because she is not tied to being in school and "busy" for 30 hours a week, which frees up lots of time she wouldn't have had otherwise. For example, last year, when she attended public school, we usually opted to stay home on the weekends and any other time she didn't have dance or soccer, which were the 2 extra-curriculars that she was involved in. Instead, this year, we have done several field trips (museums, guided nature walks, art galleries, the local science center, a bee farm, and several out-of-town play dates with like-minded families); she has dabbled in Kung Fu and gymnastics; and volunteered to be a patient for medical students! She reads at least a novel a week because she wants to and is raising a batch of Buff Orpington chicks all on her own (she bought the eggs to incubate with her own money). We do insist that she does some math and English several times a week, to keep her mind learning and current with the BC Grade 4 curriculum , though we do this via several different tools. Math might consist of workbook exercises, puzzles, or books like the "Life of Fred"; English could also be a workbook, but also includes things like mapping out her plans for the chicks or writing to friends.
Now, in contrast, my boy has never been to school. Not even preschool. I wasn't working so I didn't see any point in sending him off when I could hang out with him. How he learns is SO different from his sister. He will pick up a workbook or puzzle book at any time of the day (but enjoys bedtime best) and practice his letters (he's just turned 6 so would be in Kindergarten this year), does word searches or sudoku puzzles - because it's fun. He is totally fine with deconstructing something shortly after he's built it, which tells me he's enjoying the process and not just the end result. His sister, by contrast, is almost completely focused on the end result and needs to keep the thing around for a while. She can get down-right irate if someone wants to use some pieces from her lego building to make a new thing, even if it's been around for a few days.
This could just be personality style or something more. The boy was allowed to finish his projects as he was home in his youngest years. The girl, well, she was in preschool, Kindergarten, and public school to grade 3 where the children are told when they are done, so then don't get to gauge that for themselves.
Something I'll keep watching, for sure.