University of Rochester math professor Ralph Raimi listened to a speaker who was pushing what we so-called traditionalists refer to as "fuzzy math". He wasn't impressed.
Read his account of the 6th grade math involved. See how his mathematical approach simplifies and organizes the problem so much more than the speaker's tripe. Even non-mathies will see that Raimi's approach is far superior.
I always tell my students (and their parents) that it's taken the best minds our human race has to offer a couple thousand years to develop the math we have today. It would be ridiculous, wasteful, and futile to expect a bunch of 14-year-olds (or however old) to invent this math on their own over the course of 9 school months. Instead, the school district pays me a moderate amount of money on the assumption that I know more math than anyone else in the room, and I'm expected to transfer that knowledge to the students. My primary method of pedagogy will not be putting kids in groups of 4 and having them invent the math that was invented centuries ago. I will teach the students. Parents love hearing this at Back To School Night.