State Math Standards Questioned

1/5/2005, The Albany Times, by Rick Karlin:

The Thomas B. Fordham Foundation said, in reference to New York and about a dozen other states it studied, that the state math standards "offer vague and overly simplistic guidelines for teaching K-12 students."

"All of us were awestruck by the levels of ignorance that we saw," in math standards nationwide, said David Klein, a math professor at California State University at Northridge, who headed the math research effort. In general, Klein said, states place too much emphasis on concepts such as probability and the use of calculators at the expense of basic skills like adding, subtracting, multiplying and dividing. "Many state standards don't allow students to learn enough arithmetic," Klein said.

I am completely mystified by the emphasis on teaching elementary students concepts like mean, median, and mode, some of the graphing activities that are included in the curriculum, as well as the probability. These ideas are presented without an adequate context in which to understand and use them, and they lead nowhere--they are conceptual dead ends until students get to Introductory Statistics in college. At that point, we expect them to know these basic concepts (because they were taught in elementary school) but find we are in a quandry because a) if we assume this knowledge, they will in fact not have complete or adequate concepts and b) if we assume they don't know, they are bored and disinterested because they think it's simplistic material. I think statistics and probability should be delayed until a good enough foundation exists to pursue a reasonably complete development of the concepts. Of course, arithmetic must come first. Working out averages is a fine exercise in arithmetic. Is it necessary to call it the "mean" at this point? I doubt it, unless you are going to discuss geometric means or other measures of central tendency too. Students in college-level Introductory Statistics often lack algebra skills and important background concepts like summation notation, unions and intersections of sets, etc. It would be much better to make sure these things are taught well, rather than to teach shallow and isolated portions of statistics before the students are really ready for them.