This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ?) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + ? or 6 + 4 + 5 = ? + 5). Next, they completed an encoding task in which they reconstructed…

It is proved that if the differential equations "y[(n)] = f(x,y,y[prime],...,y[(n-1)])" and "y[(m)] = g(x,y,y[prime],...,y[(m-1)])" have the same particular solutions in a suitable region where "f" and "g" are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical…

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

Eigenvalue is an important concept in Linear Algebra. It is well known that the eigenvectors corresponding to different eigenvalues of a square matrix are linear independent. In most of the existing textbooks, this result is proven using mathematical induction. In this note, a new proof using Vandermonde determinant is given. It is shown that this…

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

An essential element in successful psychotherapy involves helping clients become more creative in their approach to their problems. While Otto Rank, one of the pioneers of psychoanalysis, loosely alluded to this as a fitting goal, it was the inventor of psychodrama, Jacob L. Moreno, MD (1889-1974), who made this an explicit objective of the…

Solutions-focused role play provides students with structured opportunities to transfer what they have learned to authentic situations they are likely to encounter as peer helpers. Rather than coming up with a single way to solve a problem, students are encouraged to explore multiple possible solutions. Peer training programs have traditionally…

The matrix diagonalization method is used to solve a limit problem.

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

Crisis intervention is a role that fits exceedingly well with counseling psychologists' interests and skills. This article provides an overview of a new crisis intervention model, the Integrated Problem-Solving Model (IPSM), and demonstrates its application to a specific crisis, sexual assault. It is hoped that this article will encourage…

No matter how skilled students may be, those skills will not lead to a job if potential employers do not know the applicant has them. Job seekers--using a strategy of age-old rhetoric--must provide concrete, detailed support to demonstrate the skills they possess. Because many recruiters feel that the best predictor of future performance is past…

The need is often not more resources, but the right resources, delivered when the user needs them. In today's knowledge economy, where job roles and requirements change frequently, resource delivery systems that allow customization of information, functions and contents by users are increasingly needed. Schatz discusses the inherent challenges of…

Minimization of the within-cluster sums of squares (WCSS) is one of the most important optimization criteria in cluster analysis. Although cluster analysis modules in commercial software packages typically use heuristic methods for this criterion, optimal approaches can be computationally feasible for problems of modest size. This paper presents a…

Two young boys with autism who used the picture exchange communication system were taught to solve problems (improvise) by using descriptors (functions, colors, and shapes) to request desired items for which specific pictures were unavailable. The results of a multiple baseline across descriptors showed that training increased the number of…

As a unifying feature of this Special Issue, we have asked proponents of each framework to analyse an empirical classroom account of one student's process of solving a mathematical problem. Here, for the case study of "Frank", we give the main data that were available to all authors.