Yesterday I read Knowing and Teaching Elementary Mathematics by Liping Ma. I know this book is way outside of the norm of what I usually read, but I had seen it mentioned on a forum and thought it would be interesting.
The premise of the book is comparing the knowledge and teaching of math between U.S. teachers and Chinese teachers. After reading it, I am shocked and ashamed at the poor performance of the U.S. teachers particularly as they interviewed teachers were selected for being above average. These teachers could not adequately explain why math problems were solved in a particular manner and in some instances could not even solve the problems discussed. On the other hand, the Chinese teachers were able to solve the problems and describe why they chose the methods they did. It seems that a great deal of the "why" is because of a Chinese proverb which states "Know how, and also know why." The Chinese teachers were fluent in the mathematical laws that governed why you take a certain action whereas the U.S. teachers were focused on "well this is the procedure and that's the way you do it because that's how I was taught to do it." One instance also related to linguistic difference in how we say the teen numbers which then impacts how math facts and procedures are taught which was quite fascinating.
What next: I'm not sure what I'm going to do with the information I learned in this book. I'm certainly going to continue to afterschool in the area of mathematics although it is the one area in which dd fights me the most. In particular, she emphasizes "that's not how we learned it at school." Now, I'm going to emphasize that there is more than one way to solve problems and that it is important to be fluent in a variety of methods. I want to go back and become more familiar with the mathematical laws and principles and then make sure I use those terms when discussing mathematics with my daughter. I also think it will be good for my noggin to do math problem solving on a more regular basis.
I wish there was something I could do with this information on a more curricular level at my local elementary and even at the institution where I work but I'm not certain what that would be or how to go about it.