Grizzled Veterans of America's Math Wars

You're just plain wrong on a whole lot of things. Not all triangles add up to 180 deg, certainly those on a spherical or hyperbolic surface don't. There are NOT two parts to learning maths, there are three. Knowing HOW to perform procedures (which you call understanding). Knowing WHY things work - understanding the concept. Knowing WHEN to use the concepts and procedures (which means being able to make decisions about when to apply your knowledge in various contexts and problems) How can maths NOT be about inventing new ways of doing things? What century do you live in? While maths is certainly not about feelings it seriously is about confidence!!