Well; like I said this is one of the most complicated cultural manifests there can be. Unfortuneatly I appeared to be a little too quick on the draw with the Rudner Study. There is a newer and more inclusive study from 2003 that betrays several distinctions not readily apparent with the study I cited. Evidently part of the problem is the nature of the sample that is represented in that study. One of the big problems that the educational theorists see is the selectivity of the sample. It is apparent that a good part of the sample that shows what level the students attained at each grade is voluntary reportage. Ie when a parent believes their child will not do well on the test; they just don't take it. So the sample consists of many volunteers who obviously were motivated to take the test. I am looking at some other information regarding participation in the surveys used to acumulate the data that lead to these conclusions. I am curious. Let me ask; at what age do the required Math courses begin to utilise sequential math and then algebraic concepts?