One can "construct" knowledge without "discovering" it.
ok, so that's the difference between unschooling and constructivism; a constructivist CAN choose to teach a child something, you just don't spoon feed them you put it on their plate and give them the tools. An unschooler would wait for them to ask for it before you offered it to them.
Yes! Constructivism is very different than unschooling. A Constructivist teacher provides lots and lots of facilitated activities for a child to conceptually understand concepts.
First, I need to admit that I haven't read the entire thread.
Yes, constructivism is very different from unschooling. Once a child demonstrates interest in a topic, an unschooler may or may not choose a constructivist approach to helping that child learn. An unschooler may choose a very traditional approach and still be unschooling.
As for the facilitated activities that help a child understand concepts, those activities do not need to be hands on. In fact, I would argue that as you move away from lower level math, it is preferable that they *not* be hands on, as you are trying to develop a more abstract approach to math.
