This paper describes how the method of steepest descent can be used to find periodic solutions of differential equations. Applications to two suspension bridge models are discussed, and the method is used to find non-obvious large-amplitude solutions.

CAPTCHAs are images used on the internet by companies that want to block computer programs from their site. This article presents a method for solving some of these puzzles.

This article describes a method of solution that Ramanujan may have used in solving the following puzzle: The number of a house is both the sum of the house numbers below it on the street and the sum of those above it. (The houses on a street are numbered consecutively, starting with 1.)

At each point of an ellipse one can attach a normal vector and a radial vector, the latter defined as the vector from the center of the ellipse. At the ends of the major and minor axes, the two vectors coincide, but at all other points they are separated by an angle [delta]. What is the maximum value that [delta] can attain, and where does it…

The successful communicator is expected to provide communications that are not only complete but also representative of effective thinking (i.e., original). Creating complete and creative communications begins with a disciplined process of discovery--identifying, assessing, prioritizing, and integrating the articulated and embedded purposes.…

Problem-solving is one of the main goals in science teaching and is something many students find difficult. This research reports on the development, implementation and evaluation of a problem-solving heuristic. This heuristic intends to help students to understand the steps involved in problem solving (metacognitive tool), and to provide them…

This article examines issues that arise from learning and knowledge in technology education. The issues examined are, first, the definition of technological knowledge and what the nature of that knowledge should be, where the concern is with "how" we define and think about that knowledge, especially in the context of how students learn and use…

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

The research on worked examples has shown that for novices, studying worked examples is often a more effective and efficient way of learning than solving conventional problems. This theoretical paper argues that adding process-oriented information to worked examples can further enhance transfer performance, especially for complex cognitive skills…

Response to Intervention (RTI) models have attracted great attention as an alternative to traditional methods used for identifying students with learning disabilities. A major feature of this approach is the implementation of academic interventions in general education and measuring the student's response to those interventions. A common question…

Purpose--To illuminate the importance of the communal deliberative process, as a form of collective thinking, in overcoming the growing complexities of schoolwork in uncertain and turbulent environments. Design/methodology/approach-- Introduces the notion of deliberation as evolved from Dewey's moral theory, the essential phases and elements of…

Despite significant progress over the past six decades, a number of obstacles still exist as far as the understanding and application of inventive ideation techniques is concerned. This paper describes the development of a model aimed at simplifying the selection and application of these techniques. Analysis of a diverse range of creative thinking…

In this article, the author talks about Destination ImagiNation (DI), the world's largest creative problem solving (CPS) program, and describes how this program helps students. In many schools and communities, DI supplements or even serves as the talented and gifted program. CPS is also popular and appropriate for homeschool families because it…

We present and discuss three examples of misapplication of the notion of conditional probability. In each example, we present the problem along with a published and/or well-known incorrect--but seemingly plausible--solution. We then give a careful treatment of the correct solution, in large part to show how careful application of basic probability…

The purpose of this paper is to re-examine the relationships between mathematical problem solving and learning mathematics. After introducing a diagram representing the notion of problem solving, four types of problem solving approaches used in mathematics classrooms will be distinguished according to which aspect of that diagram is attended to.…