Ask around at your next homeschool conference to compare what people answer when this question pops up: "What does it mean to unschool?" Some will answer that unschooling is homeschooling without using a pre-packaged curriculum. Others will say it's simply the degree of freedom that the parents allow the child in his learning. Still others will say that unschooling defies definition because each child is unique and will go at learning in his own way, in his own time. So what's the big difference between homeschooling and unschooling? In homeschooling the parents make decisions on how to best educate the child, while in unschooling the child somehow makes those decisions for herself.
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Marilyn Burns discusses creative and effective ways to use manipulatives to teach math. Much of her information is oriented towards classroom instruction, but there is great information for homeschoolers too. She discusses the seven "musts" for using manipulatives, how to introduce a Geoboard, pattern block activities, and more.