That is the million dollar question. I don't think he is really passionate about math. There are too many other subjects that fascinate him. However, in the past he has come up with some profound mathematical patterns/insights that surprised me and impressed his pre-algebra teacher. We do have a kind of odd situation here as he is very much a "verbal" kid rather than a true "mathy" kid but I only chose to accelerate him in math because I could clearly see the damage in not accelerating in math whereas it was not particularly harmful to not accelerate him in reading/language arts because that curriculum is all about writing, which is completely open-ended and he is free to and certainly does read whatever level he wants outside of the two-hour reading/language arts block.
It's difficult for me to know what he is thinking/doing to cement his knowledge/skill but the online course does require more than multiple choice and short answer problems. For example, he is called upon to summarize/verbalize all the concepts in the curriculum. I am totally in agreement about the sideways approach. DS has done a fair amount of reading adult level math books (not textbooks) touching a broad range of topics. However, his greatest weakness is the inability to take things slow, which is sometimes necessary for deep understanding/mastery.
