"reform (or discovery) math" vs traditional math.

Thanks for sharing. It looks to me they are not teaching math, they are teaching physics ( actually more like engineering). It is an important skill to extract a proper mathematical model from a real domain. But this in itself is a not math,and should not be a major focus of math education. The following article may be of interest to you.

Education Panel Lays Out Truce In Math Wars

http://online.wsj.com/article/SB120465579132610785.html

excerpt:

For two decades, advocates of what has come to be known as "reform math" have promoted conceptual understanding over drilling in, say, multiplication and division. For example, to solve a basic division problem, 150 divided by 50, students might cross off groups of circles to "discover" that the answer was three. Some parents and mathematicians have complained about "fuzzy math," and public school systems have encountered a growing backlash.