On Edspresso, “John Dewey,” a prospective second-career math teacher, describes his ed school class on National Council of Teachers of Mathematics’ standards. He was assigned to compare NCTM standards with his state’s standards.
I got assigned Geometry/11th grade/representation. “What is ‘representation’?” I hear you asking. Expressing things in different ways, I think. You can use a graph to express a function, or a table of values, or a formula, for example. Which one is best to analyze the problem at hand, I think is what they’re getting at but they go on and on in the standards, bringing in all sorts of ways to show things which might be good things to mention as an aside, but to devote so much class time to it supplants the basics that they are supposed to be learning. (And which educationists think is mundane, and mind numbing.)
I was suffering from stomach flu when I was reading NCTM’s standards. My wife asked why I was pushing myself like that. My response was along the lines that as long as I was vomiting anyway, may as well take advantage of it.
Some ed-school classmates defended the state’s algebra standards, which don’t require students to learn the formula to solve quadratic equations.