This article describes a semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. (Contains 6 figures.)

The purpose of this study was to determine the effect of systematic instruction with a concrete representation on the acquisition of an algebra skill for students with moderate developmental disabilities. Three high school students with moderate developmental disabilities participated in this study. A multiple probe across participants research…

We report on a German-Indonesian design research project, which aims to significantly increase the mathematical skills of secondary school students. Since results of international comparative studies have shown that there exists a relationship between metacognition and learning success, a learning environment for the beginning with secondary…

Learn the 5 practices for facilitating effective inquiry-oriented classrooms: (1) Anticipating what students will do--what strategies they will use--in solving a problem; (2) Monitoring their work as they approach the problem in class; (3) Selecting students whose strategies are worth discussing in class; (4) Sequencing those students'…

This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories…

An exact solution is found for the electrostatic potential of a family of conducting charged toroids. The toroids are characterized by two lengths "a" and "b", with "a" greater than or equal to "2b". They are closed, with no hole in the "doughnut". The results are obtained by considering the potential of two equal charges, displaced from the…

This study concentrates on analysing university students' pre-knowledge of thermal physics. The students' understanding of the basic concepts and of the adiabatic compression of an ideal gas was studied at the start of an introductory level course. A total of 48 students participated in a paper-and-pencil test, and analysis of the responses…

The practical applicability of a semiconductor quantum dot with spin-orbit interaction gives an impetus to study analytical solutions to one- and two-electron quantum dots with or without a magnetic field.

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…

The problem of obtaining the apparent equation of motion and shape of a moving body from its arbitrary given equation of motion in special relativity is considered. Also the inverse problem of obtaining the body's equation of motion from a known equation of motion of its image is discussed. Some examples of this problem solution are considered. As…

Collaborative group work has great potential to promote student learning, and increasing evidence exists about the kinds of interaction among students that are necessary to achieve this potential. Less often studied is the role of the teacher in promoting effective group collaboration. This article investigates the extent to which teachers'…

The introduction of the concept of the variable represents a critical point in the arithmetic-algebraic transition. This concept is complex because it is used with different meanings in different situations. Its management depends on the particular way of using it in problem-solving. The aim of this paper was to analyse whether the notion of…

The present study explored whether first and second order cognitive holding power perceived by children in mathematical classrooms, fluid intelligence, and mathematical achievement predicted their performance on standard problems, and especially realistic problems. A sample of 119 Chinese 4-6th graders were administered the word problem test, the…

This study examined the effects of consistency (relational term consistent vs. inconsistent with required arithmetic operation) and markedness (relational term unmarked ["more than"] vs. marked ["less than"]) on word problem solving in 10-12 years old children differing in problem-solving skill. The results showed that for unmarked word problems,…

In this issue's "Classroom Notes" section, the following papers are discussed: (1) "Constructing a line segment whose length is equal to the measure of a given angle" (W. Jacob and T. J. Osler); (2) "Generating functions for the powers of Fibonacci sequences" (D. Terrana and H. Chen); (3) "Evaluation of mean and variance integrals without…