The paper discusses the boundary in the frequency-amplitude plane for boundedness of solutions to the forced spring Duffing type equation x[umlaut] + x + [epsilon]x[cubed] = F cos[omega]t. For fixed initial conditions and for representative fixed values of the parameter [epsilon], the results are reported of a systematic numerical investigation…

Students learn to use linear algebra covered in their first algebra course to design mobiles like those created by artist Alexander Calder. (Contains 17 figures and 2 tables.)

A clinical task-based interview can be seen as a situation where the interviewer-interviewee interaction on a task is regulated by a system of explicit and implicit norms, values, and rules. This paper describes how documenting and mapping triadic interaction among the interviewer, the interviewee, and the knowledge negotiated can be used to…

We report a dissociation between higher order mathematical ability and language in the case of a man (SO) with severe aphasia. Despite severely impaired abilities in the language domain and difficulties with processing both phonological and orthographic number words, he was able to judge the equivalence of and to transform and simplify…

In this article, we explore the game based on the following problem from the 1st Mathematical Olympiad of Central America and the Caribbean, held in Costa Rica in 1999: Player A turns on the calculator, presses a digit key and then presses the + key. A second later, player B presses a digit key in the same row or column of the last digit key…

A simple experiment can be performed to characterize the relationship between applied voltage and velocity (steady state and transient) for an electric toy train. The results can be used by teams of students to solve a series of challenges in which they attempt to predict the performance of a particular train. Some sample challenges might include…

An attention-grabbing center-of-mass demonstration uses the map of a state mounted on a sheet of heavy cardboard and cut out along the boundaries. The two-dimensional object is hung from a hole punched into a city near the edge, and a string with a pendulum bob attached to it passes through the center of mass. The process is repeated with a…

Three phases of development of self-regulatory skill in the domain of mathematical problem solving were designed to examine students' behaviour and the effects on their problem solving ability. Forty-eight Grade 4 students (10 year olds) participated in this pilot study. The students were randomly assigned to one of three groups, each representing…

Solving problems and creating processes and procedures from the ground up has long been part of the IT department's way of operating. IT staffs will continue to encounter new problems to solve and new technologies to be implemented. They also must involve their constituents in the creation of solutions. Nonetheless, for many issues they no longer…

The contemporary, changing, and globalizing world necessitates the conceptualization and implementation of the ideas of global education on all hierarchical levels, ranging from kindergartens to universities to the programs of educating the adult. As in many countries, the current issues of global education assume great importance in Russia, a…

Non-determinism is one of the most important, yet abstract, recurring concepts of Computer Science. It plays an important role in Computer Science areas such as formal language theory, computability theory, distributed computing, and operating systems. We conducted a series of studies on the perception of non-determinism. In the current research,…

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x-y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with A's chosen x- or y-axis. It becomes necessary in such cases to develop…

Learning from worked examples is an effective learning method in well-structured domains. Can its effectiveness be further enhanced when errors are included? This was tested by determining whether a combination of correct and incorrect solutions in worked examples enhances learning outcomes in comparison to correct solutions only, and whether a…

Speakers routinely gesture with their hands when they talk, and those gestures often convey information not found anywhere in their speech. This information is typically not consciously accessible, yet it provides an early sign that the speaker is ready to learn a particular task (S. Goldin-Meadow, 2003). In this sense, the unwitting gestures that…

Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two-dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics-naive students were administered kinematics problems and…