Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

In online educational systems we can easily collect and analyze extensive data about student learning. Current practice, however, focuses only on some aspects of these data, particularly on correctness of students answers. When a student answers incorrectly, the submitted wrong answer can give us valuable information. We provide an overview of…

Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…

This paper presents a computer based diagnostic tool developed to facilitate the learning process. The developed tool is capable of generating possible error syndromes associated with the answers received. The developed tool simulates the error pattern of the test results and then accordingly models the action plan to help in children's learning…

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…