A context-based approach to education aims to improve students' meaningful learning and uses authentic situations in which scientific concepts are applied. The use of contexts may contribute to the learning of abstract concepts such as algorithms. The selection of appropriate contexts, however, is challenging for teachers. It is therefore…

Offers a simple classification of problems and seeks to explore the many factors that may be important in the successful solving of problems. Considers the place of procedures and algorithms. Solving open-ended problems is extremely important in education and offering learners experience with this in a group work context is a helpful way forward.…

Presents recently developed generalizations to the sieve of Eratosthenes, showing the principles underlying these improvements, which increase its efficiency without changing too much of its simplicity. Offers several possibilities to propose good investigations for students to explore, find patterns, and make generalizations. (JRH)

A method for solving inequalities of degree greater than one is described. (MK)

Early calculating methods and devices are discussed. These include finger products, the abacus, ancient multiplication algorithms, Napier's bones, and monograms. (MP)

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Describes a study with the main objective of constructing models based on strategies students use to solve chemistry problems and to show that these models form sequences of progressive transitions termed "problemshifts" that increase the explanatory/heuristic power of the model. Results implies that the relationship between algorithmic…

Presents an approach for illustrating, on an intuitive level, the significance of loop invariants for algorithm design and analysis. The illustration is based on mathematical games that require the exploration of regularities via problem-solving heuristics. (Author/MM)

An alternate method for factoring quadratic equations is presented as being quicker and easier to use than the trial-and-error method. (MP)

Circuits are described, with discussion on how to help students find the algorithms to solve a variety of problems involving circuits. (MNS)

A generalized method of synthetic division where the divisor polynomial may be of any degree equal to or larger than 1, and the dividend polynomial may be of equal or larger degree than the divisor polynomial and a generalization of the familiar remainder theorem, are presented. (Author/MK)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Presents alternative equation-solving procedures that emphasize an examination of the steps or operations necessary to perform a calculation, followed by the inversion of those steps. The approach is especially attractive to students with limited mathematical skills. (Author/MKR)