I have intended to write more about our home schooling on this blog, so I'm playing catch-up. Education critics (usually outside of the field of education) often throw around terms like "fuzzy math," or "new math," and I wonder if they have ever really examined the curriculum and approaches recommended by the National Council of Teachers of Mathematics (NCTM) . When children are taught using manipulatives, the goal is for understanding of the concept, not just memorization of facts and algorithms. The idea of memorization is not excluded, though. At some point, for efficiency and accuracy, students must memorize their basic math facts. The goal, though, is for the memorization to take place AFTER they understand what those facts really mean. Practice also has its place. Once a student understands a concept, it is important that he practice it, especially in the context of real-world problems. Here's an example from th...