Teaching methods often promote fact gathering and memorization rather than the use of those facts to solve complex, realistic problems. Students easily memorize basic facts, steps and procedures, repeating them flawlessly from memory when asked. The problem, however, lies in teaching students how to use these facts and procedures creatively in…

The US Department of Education designated T. C. Cherry Elementary School in Bowling Green, Kentucky, as a Blue Ribbon School, an honor awarded to only few schools across the nation. The same became possible because they changed the culture of the school from rowdy to calm, from irresponsible to responsible, from noncooperative to cooperative, from…

The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

The strategies that expose learners to the large volume of knowledge, enables them for creative thinking, self-management and deep reading. The different ways of creating knowledge with the help of creativity, communication, organization, problem solving and decision-making are discussed.

The Conflict Resolution Model was formulated by a group of Australian psychologists who set about integrating the literature on achieving mutually beneficial outcomes in a conflict situation in order to create a best-practice prescriptive process for conflict resolution. A number of experimental studies conducted at the University of Tasmania with…

As society grows more cooperative, the importance of finding emerging leaders has become incrasingly crucial. Not only should these potential leaders be identified, but their talents need the opportunity to develop. Leadership education continues to be a concern in gifted education but remains an abstract concept that is often ignored in school…

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…

In a well-known calculus problem, an open top box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. The task is to find the dimensions of the box of maximum volume. Typically, the length of the sides of the corners that produces the largest volume turns out to be an irrational…

In terms of modern pedagogy, having visual interpretation of trigonometric functions is useful and quite helpful. This paper presents, pictorially, an easy approach to prove all single angle trigonometric identities on the axes. It also discusses the application of axial representation in calculus--finding the derivative of trigonometric functions.

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…

Math-education reformers encourage the incorporation of mathematical modeling activities into K-12 curricula. Many of the purported educational benefits derive from the authenticity of the activities-how well they reflect the everyday and occupational mathematical practices of adults. But a paucity in the literature of observational descriptions…

This brief article describes how classroom group time can be "talk central" for children to discuss problems, imagine solutions, even role-play hypothetical situations. It is often in the safety and support of the large group that children develop the tools they need to learn how to resolve the inevitable conflicts that arise throughout life.…

One of the most important review topics the author teaches in middle school is the use of metric measurement for problem solving and inquiry. For many years, she had students measuring various objects around the room using the tools of metric measurement. She dutifully taught hypothesizing, data collecting, and drawing conclusions. It was…

From the start of the year, the author's goal is to teach his students to be metacognitive thinkers. This means that they will think about what they are doing during each step of the inquiry process. The author uses a variety of methods to enculturate students into using the thinking processes and developing the dispositions necessary for them to…

The Framework for School Leadership Accomplishments (FSLA) is designed to facilitate thinking about, developing, and implementing school outcomes that improve student learning. The FSLA at once provides a means to organize knowledge in educational administration, an approach to practice that frames what schools can do to improve student learning,…