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

What knowledge have you gained about how children learn mathematics from this course? I have learned that children truly learn in different ways and those ways have to be met the best way possible. There is more to mathematics than showing students "this is how to do it" and then hand them a worksheet to work out similar problems. This procedure or way of teaching makes future math teachers to underestimate their students abilities because they only know how to think of a problem one way. Teachers need to become aware of what their kids know and then go further indepth on the topics that need to be. Children are really curious at different ages and I think teachers need to take that into consideration as well. When using manipulatives, question the students about them and about how they are thinking. Who knows how many ways will turn up to solve one problem.