The article investigates the patterns that arise in the convergence of numerical methods, particularly those in the errors involved in successive iterations, using data analysis and curve fitting methods. In particular, the results obtained are used to convey a deeper level of understanding of the concepts of linear, quadratic, and cubic…

The National Assessment of Educational Progress (NAEP) collects data in the form of repeated, discrete measures (test items) with hierarchical structure for both measures and subjects, that is complex by any standard. This complexity has been managed through a "divide and conquer" approach of isolating and evaluating sources of…

Data from 32 state assessments in mathematics (conducted in 1984 and earlier) are analyzed in this document. The high degree of variability across the states is stressed, with some of the points of variation in the test development, administration, and analysis process noted. Information is then presented on topics on which students are doing well…