Abstract: Considering the importance of science and mathematics achieve ments of young students, one of the most well known observed phenomenon is that the performance of U.S. students in mathematics and sciences is undesirable. In order to deal with the problem of declining mathematics and science scores of American high school students, many strategies have been implemented for several decades. In this paper, we give an in-depth longitudinal study of American youth using a double-kernel approach of non parametric quantile regression. Two of the advantages of this approach are: (1) it guarantees that a Nadaraya-Watson estimator of the conditional func tion is a distribution function while, in some cases, this kind of estimator being neither monotone nor taking values only between 0 and 1; (2) it guar antees that quantile curves which are based on Nadaraya-Watson estimator not absurdly cross each other. Previous work has focused only on mean re gression and parametric quantile regression. We obtained many interesting results in this study.