What knowledge have you gained about how children learn mathematics from this course?

I have gained a lot of valuable knowledge about how children learn mathematics through this course. Before this class, I knew that how I learned math growing up was not how we were supposed to teach it now. I now know some great ways to teach math and I have learned in what ways children learn math best. I have learned that children do not learn best through rote memorization. We should not teach formulas and other mathematic problems to just memorize but we should teach the reason to why they use those formulas, etc. Children learn best through the use of manipulatives with concrete examples and then move into semi-concrete examples and finally symbolic examples. We should not use worksheets and lecture, but we should use hands-on and interactive activities. The children should feel comfortable in taking risks while learning and sharing their answers. This class has taught me some valuable lessons and techniques to use that will help students become successful learners in math.