A group of mathematicians and mathematics educators are collaborating in the fine-grained examination of selected "slices" of video recordings of lectures, drawing on Schoenfeld's Resources, Orientations and Goals framework of teaching-in-context. In the larger project, we are exploring ways in which this model can be extended to examine…

This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…

The Lithuanian Informatics Olympiad is a problem solving contest for high school students. The work of each contestant is evaluated in terms of several criteria, where each criterion is measured according to its own scale (but the same scale for each contestant). Several jury members are involved in the evaluation. This paper analyses the problem…

The general purpose of this article is to shed some light on the understanding of real numbers, particularly with regard to two issues: the real number as the limit of a sequence of rational numbers and the development of irrational numbers as a continued fraction. By generalizing the expression of the golden ratio in the form of the limit of two…

This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

This article presents a mathematical function for measuring the congruence among the strand representation in the enacted curriculum, state assessments, and district pacing guides. Using the Manhattan distance as its basis, this method allows researchers to incorporate the strand coverage of the enacted curriculum (i.e., the curriculum actually…

In this article the problems of functioning algorithms development for system of the automated analysis of educational process rhythm in a higher educational institution are considered. Using the device of experiment planning for conducting the scientific researches, adapted methodologies, received by authors in the dissertational works at the…

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by…

While linear programming is a common tool in business and industry, there have not been many applications in educational assessment and only a handful of individuals have been actively involved in conducting psychometric research in this area. Perhaps this is due, at least in part, to the complexity of existing software packages. This article…

A simple algorithm for computing the partial fraction expansions of proper rational functions with multiple poles is presented. The main idea is to use the Heaviside's cover-up technique to determine the numerators of the partial fractions and polynomial divisions to reduce the multiplicities of the poles involved successively, without the use of…

The online deployment of Technology Engineered online Student Ratings of Instruction (SRIs) by colleges and universities in the United States has dynamically changed the deployment of course evaluation. This research investigation is the fourth part of a post hoc study that analytically and psychometrically examines the design, reliability, and…

Methods courses in teacher education programs often stress the importance of planning and preparation. However, there is no real substitute for experience and ongoing professional development; learning for a mathematics teacher is a continuous endeavor. While university coursework is helpful, the preparation for planning discussed in this…

This note offers a derivation of the Euler-Maclaurin formula that is simple and elementary. In addition, the paper shows that the derivation provides Euler-Maclaurin formulas for a variety of functionals other than the trapezoid rule.