I've always believed in the importance of understanding what you learn instead of the traditional process of just memorizing disparate bits of information for later recall on tests. To do this, I try to help students see the relationships and patterns between different facts, concepts and ideas. Almost everything in math fits together in some way just like a tapestry or mosaic. It's also much easier to recall remembered facts if they fit into a pattern of related facts; four threes is just one more three than three threes.
So why is it that our public schools do not teach math in a way that students can understand what they are learning. Why Do Americans Stink at Math, a recent article by Elizabeth Green in the NYT, sheds some light on this dilemma. Green suggests that the Japanese approach to change through lesson study is an effective way of bringing about the adoption of more effective classroom pedagogy. She also suggests that parents and members of learning communities need to be patient with the slower rate of change brought about by genuine pedagogical change. She also suggests that this might be difficult in a culture twice stung before by failed attempts to improve math education.
For my own part, I believe that the study of math at the elementary school level has to be made more motivating for students. The development of young children's mathematical ideas is critical to the way they will be able to use these ideas to solve problems and enhance their appreciation of the world around them.
Perhaps one day students will stop asking why they were not taught math this way but I fear it will be long after I have stopped trying.