Through numerical investigations, this paper studies examples of the forced Duffing type spring equation with [epsilon] negative. By performing trial-and-error numerical experiments, the existence is demonstrated of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions. Subharmonic boundaries are…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

This article relates to an empirical study based on the use of mathematical symbolism in problem solving, twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a…

The Positive Deviance Approach promoted by Jerry Sternin suggests that the answer to reform must come from within an organization or community. By identifying the few who have created success already, we can find the means to amplify that success and broaden it to the larger community. Sternin explains how this approach worked to alleviate hunger…

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

The way in which two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students is described. Carolyn and Elizabeth's approach is to pose several problems of various degrees of difficulty and complexity for each aspect of the…

A study examined the way graduate students solved mechanism problems that were far removed from the simple systems in which mechanisms are traditionally presented. One aim is to probe the extent to which the students' experiences with the organic chemistry as undergraduates prepared them to solve mechanism problems they were likely to face as…

The disconnection between what counts as social research (SR) and what serves society's needs and interests results in a way of theorizing which, while useful, does not integrate theory and practice; a form of social theory that is not embodied in real lives and does not help non-academic people understand their contexts and practices. This…

This study investigated factors promoting the use of self-constructed diagrams by examining students' perceptions and daily class activities, and comparing Japanese (n = 291) and New Zealand (n = 323) students. Algebra word problems and a questionnaire were administered. The results revealed that the New Zealand students used diagrams more often…

Teachers need to be multicultural--able to relate to many cultures with the knowledge, skills, and attitudes to better understand growing student diversity. By the year 2010, 40 percent of learners in classrooms will be children of color, while the teaching population will remain around 85 percent white and female (Applied Research Center 2000).…

Middle school teachers realize the value of students playing games in mathematics classes if those games emphasize problem-solving strategies, algebraic reasoning, or spatial sense. This article describes various versions of the traditional game of nim and shows how working backward can be used to find a winning strategy. The link is then made…

This paper describes an in-service professional development course in introducing creative approaches to teach mathematics for teachers from the private-funded schools in Java, Indonesia. The course focused on introducing teachers to problem-solving processes and skills, and samples of activity-based worksheet on problem solving through secondary…

This article presents a scenario in which the dean of the faculty of a fictional college discusses the issue of critical thinking (CT) with other school officials, using their insights into its nature and roots to prepare a course of action to present to the board of trustees. She learns that college graduates need to have strong CT…

Art educators have acknowledged for a long time the importance of the study of images and visual elements in the lives of children and the field of art education. This is even more evident today as the discipline moves to embrace notions of "visual culture," which emphasize exploring and studying all the things that visibly shape lives. In spite…

Background: Studies on rewording word problems can be grouped into two main groups: situational rewording, in which the situation denoted by the text is described more richly, and conceptual rewording, in which the underlying semantic relations are highlighted. Aims: Our aims are to define and distinguish these two kinds of rewording and to test…