OK, here's my best definition of what unschooling and radical unschooling mean in our family. A lot of plain old unschoolers do the same things, but a lot don't. I'm sure I have more to add to it but this is it for now. There is a bit of overlap for sure. Everyone is different, blah blah blah

This is really just my idea of what parenting is to me, and what my family is striving for. It really has nothing to do with the label because in my real life, I wouldn't use the label, it's just our life.
IS:
Letting go of the standards, guidelines, and lists of 'need to know by age whatever'. Letting go of the idea that there is a list of things that all children should learn at all. Believing that whatever activity they are doing right then and there is a valid learning moment and doesn't need to be interrupted.
Not dividing life into categories, such as educational activities vs. just for fun activities. Accepting and embracing that learning happens all the time, everywhere no matter what, even if you can't see it. Helping your children live a full and rich life, full of whatever is deemed full and rich by your children. Facilitating the learning process by encouraging, providing, discussing, brainstorming and creating. Presenting new ideas and activities without an academic agenda, when they want new ideas.
Having a keen awareness of your particular child. Being really in tune with them so that you know when they need help or when they need you to back off. Helping them discover the world in a meaningful way that has no academic agenda.
Having principles, not rules. Showing them how to function as a respectful, considerate, honest, helpful, loving, kind, mature, reasonable, open-minded, fun person by being one. Accepting them for who they are.
Helping them get what they want, and helping them figure out what they want. Accepting the choices they make. Realizing they are not just miniature versions of you. Breaking down the wall that divides parents and children. They are their own people, now, not in the future. They are people now with thoughts and feelings and opinions and ideas.
Throwing out our ideas of what success means, and letting our children decide what success means to them, for them. Talking, talking, talking and listening, listening, listening.
Re-thinking limitations, and explaining the natural limitations. Not creating an environment that your child will want to rebel against. Creating an environment your child feels safe to express and discover themselves.
The 'radical' side is the part that acknowledges that not only should your child be free to learn what they want, they should also be free to eat what they want, when they want, decide for themselves how much 'screen time' they get, decide for themselves when and where they need to sleep, decide for themselves what toys or other things are valuable to them, and just generally respecting their wants even when, and especially when they don't fall in line with yours. Not assigning chores; instead, doing housework joyfully and letting them come to help as they see it's not an awful miserable task.
Communicating respectfully, as in, not barking orders, making demands, or saying anything negative or demeaning. Speaking to them with the same respect as you would a family member or friend. Sharing your opinions about something without expecting them to automatically agree and comply.
Is NOT:
-letting them run wild
-condoning violent, disrespectful, or un-safe behavior, rather finding the cause of the behavior and helping them work it out. Or finding a way that can do the activity in a safe and respectful way.
-buying anything and everything they want
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