What is Understanding and Learning Mathematics?

We learn mathematics by DOING not by only by listening or reading. A learner listens to his teacher explaining a math topic, how to graph a function for example, he may fully understand what the teacher explained, but that does not necessarily mean that he has learned how to graph functions. He has to actully start making graphs, then difficulties will appear and the learner start learning through these difficulties. The point is that we may fully understand a math topic but it is not enough, we still need to practice. Also practice on routine questions has a limited effect. The learner should also try challeging questions and persevere.