I would suppose the question, "How do you know if your kids are keeping up with their peers?" is really just part two of the socialization question.
To start with, let’s clarify just who these peers are, and "keeping up" with what? Developmentally? Academically? Socially, the latest styles, technology, or lingo?
My kids’ "peers" are a mix of ages from church, 4-H, homeschool groups, cousins, etc. As I observe the interaction among friends, I see them forming friendships, navigating and learning as they go along, and seem to be "keeping up" pretty naturally. They can certainly text their friends as quickly as the next guy, LOL. But as homeschoolers, I believe one of our greatest freedoms is the lack of need to feel like we have to "keep up with" or compare our God-given talents and abilities with others.
As I speak with other parents, I can "compare" where my kids are with others. However, one of the beauties of homeschooling is really knowing your kids, where they are, how they feel, and understanding that each child is different. My greatest aspiration for my kids is to instill in them a sense of who they are in God’s eyes, not the world.
On a day to day basis I can get a good feel for how my kids "measure up" by listening to other adults at church, parents, relatives who haven’t seen us in a while, or even a stranger at the post office listening in on a conversation my kids are having while standing in line comment on their vocabulary or thinking skills . (They’re never at a lack for using big words or dreaming up big ideas, LOL.) I do feel it’s difficult not to let other’s judgement of our kids and their actions and behavior, good or bad, puff us up or bring us down in reflection of our parenting skills. I think the "keeping up" has as much to do with our attitude of acceptence as parents as it does with the kids struggles to "fit it." I pray for guidance and grace in this very issue of judgement daily!
Academically, I have begun the process of looking at high school graduation credits. In a sense, this is a comparison to peers, as we look at standards for graduation. After printing off the requirements for high school graduation for my state last week, the one thing that concerns me the most is that I don’t see study skills, critical thinking, or character studies of any sort listed. After having spent 9 years in college, I can certainly atest to the fact that while it’s nice to have a good foundation in chemistry, math and composition, what it really takes to get through college (as well as life in general) is a good foundation of hope and character, critical thinking skills (knowing HOW to use your brain, not just how to pass a test), and standing firm in your own beliefs, rather than looking to your peers for answers.
I feel instead of asking "How do you know if your kids are keeping up with their peers?" we should really be asking "are your kids able to stand firm in their beliefs when it comes to their peers?"