During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

The POWERTECH contest in Taiwan was established in an attempt to promote inventiveness and technology to elementary school pupils. The POWERTECH contest is designed as a collaborative learning system for project design. Project design is comprised of technical processes, which include the construction of an artifact and improvement of its…

It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…

A fundamental question in human cognition is how people reason about space. We use a computational model to explore cross-cultural commonalities and differences in spatial cognition. Our model is based upon two hypotheses: (1) the structure-mapping model of analogy can explain the visual comparisons used in spatial reasoning; and (2) qualitative,…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

School superintendents' role has shifted from the traditional emphasis on managerial aspects to one on instructional leadership (on teaching and learning issues) achieved by generating collaborative learning opportunities at the both school and district levels. Whereas collaborative learning processes in schools have generally been associated with…

In this case study a novel educational programme for students in preparatory vocational education was studied. The research questions were: (1) Which teaching/learning processes occur in a simulated workplace using the concept of a "knowledge-rich" workplace? (2) What is the role of models and modelling in the teaching/learning…

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)

This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…

Understanding the ways in which teachers make sense of what they do and why is critical to a broader understanding of pedagogy. Historically, teachers have been understood through the thematic and content analysis of their beliefs or philosophies. In this paper, we argue that discourse analysis (DA) involves a much finer-grained analysis of the…

This article discusses two examples of geometric problem solving suitable for middle and high school students. Both problems are related to students' everyday life experience and allow them to discover deep connections between mathematical properties and nature. With the help of dynamic mathematics software, students have the opportunity to…

Nearly 50 years ago, Henry Bent published his groundbreaking article in this "Journal" introducing the "global" formulation of thermodynamics. In the following years, the global formulation was elaborated by Bent and by one of the present authors. The global formulation of the first law focuses on conservation of energy and the recognition that…

The present experiment examined whether or not the type of associations (close (e.g. apple-pear) and distant (e.g. apple-fish) word associations) and memory instruction (paying attention to the ideas of others) had effects on the idea generation performances in the brainwriting paradigm in which all participants shared their ideas by using paper…

The term "restriction endonuclease mapping" covers a number of related techniques used to identify specific restriction enzyme recognition sites on small DNA molecules. A method for restriction endonuclease mapping of a 1,000-basepair (bp)-long DNA molecule is described in the fictitious experiment of this test. The most important fact needed to…

In an attempt to study the emerging questions about design of mathematical tasks that could support the solving of challenging problems, we designed two settings of interactive diagrams that share an example represented as an animation of multi-process motion but differ in their organizational functions. The interactive settings, each comprising…