The design and empirical validation of a computer-based learning environment for acquiring long division skills, called the long division machine (LDM), are described. The construction of the LDM is primarily based on the didactic method of progressive schematisation. It offers the student a game-like environment for solving division problems by…

Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular…

In this note, it is shown through an example that the assumption of the independence of Bernoulli trials in the geometric experiment may unexpectedly not be satisfied. The example can serve as a suitable and useful classroom activity for students in introductory probability courses.

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

Education within Second Life frequently recapitulates the "sage on the stage" as students sit their avatars down in chairs in the virtual world and listen to or read an instructor's lecture while watching a slideshow. This conceptual article explores alternative active learning techniques supporting independent and collaborative learning…

The article is aimed at a partial problem of science process skills development--the evaluation of educational outcomes. In comparison to evaluation of obtained knowledge, the skills development is not so easy to be objectively evaluated. The article provides a proposal of an evaluation tool and describes the first results of its research…

This article described the methods of media education development of personality (including the audience's individual, "creative critical thinking" corresponding to "conceptual" (knowledge of media culture theory), "sensory" (intentional communication with mass media, orientational experience in genre and topical…

The increasing complexity of technical work, the demand for highly skilled workers, and the vital challenges facing the world at large have combined to create a need for better ways to transfer knowledge, especially expert knowledge. In this dissertation, I attempted to see if an approach to this process that is more holistic than is typical in…

Within the framework of language socialization, this dissertation uses conversation analytic and ethnographic methods to examine the interactional practices used by the adult safe school educator at a progressive elementary school to socialize students into beliefs and practices associated with the school's Cool Tools Safe School Program. Cool…

Changes in engineering practices have spawned changes in engineering education and prompted the use of distributed learning environments. A distributed collaborative engineering design (CED) course was designed to engage engineering students in learning about and solving engineering design problems. The CED incorporated an advanced interactive…

This study brings together two lines of research on teachers' affective responses toward mathematics curriculum reforms: their concerns and their efficacy beliefs. Using structural equation modeling to analyze data on 151 elementary mathematics teachers' concerns and efficacy beliefs 5 years into a mandated curriculum reform on problem solving,…

Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum…

One special characteristic of any exponential growth or decay function f(t) = Ab[superscript t] is its unique doubling time or half-life, each of which depends only on the base "b". The half-life is used to characterize the rate of decay of any radioactive substance or the rate at which the level of a medication in the bloodstream decays as it is…

In this chapter, the authors illustrate on mathematical problem-solving activities within families how the functions and structures of their mathematics at home are dependent on values, and how interacting values during problem situations came to shape what counted as solutions. These values examples from family math illustrate the complex…

Assurance of learning process plays a major role in higher education and has increased the accountability on the part of instructors at all levels. This paper will discuss the role of assurance processes in teaching and the ways to measure these processes of student learning. The research focus will be to determine if student engagement in problem…