Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…

Discusses the issue of math problem solving and the concomitant concept of mental discipline/transfer of learning. Considers if there is any evidence to support the mental discipline theory. Discusses implications of the lack of mental discipline for the curriculum. Comments that "God gave humans two halves of the brain that are supposed to work…

Presents a set of problems for which there is a tendency for students to ignore part of the given information in the problem and substitute some extraneous assumptions. Discusses typical student reactions. (Author/ASK)

Notes how literature has a powerful role to play in fostering children's understanding of mathematical ideas. Discusses 19 books focusing on mathematics. Concludes that children's literature can help restore the story that has often been missing in traditional mathematics instruction. (SG)

An attempt to implement problem solving as a teacher of ninth grade algebra is described. The problems selected were not general ones, they involved combinations and represented various situations and were more complex which lead to the discovery of Steiner triple systems.

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

Strategies that children used to solve a fraction problem are presented, and an insight into how students think about divisions and fractions is described. Teachers can use these strategies to help students establish connections related to fractions.

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…

A special but common type of scenario is one in which a company has a promotion that is designed to make the customer purchase more of their product than they otherwise might. Although this can be aimed specifically at children, it really applies to all persons. The basic premise is that the company issues a "set" of different items or…

The unified approximations reduce the conceptual complexity by combining solutions for a relatively large number of different situations into just two similar sets of processes. Processes used to solve problems by either the unified or classical approximations require similar degrees of understanding of the underlying chemical processes.

A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…

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…

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…

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…

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.