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

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

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 algorithm is given for computing the cube root of any real number on a calculator. (DT)

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)

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

This is the teacher's guide and commentary for the SMSG textbook Algorithms, Computation and Mathematics (Algol Supplement). This teacher's commentary provides background information for the teacher, suggestions for activities found in the student's Algol Supplement, and answers to exercises and activities. The course is designed for high school…

This is the teacher's guide and commentary for the SMSG textbook Algorithms, Computation, and Mathematics (Fortran Supplement). The teacher's commentary provides background information for the teacher, suggestions for activities found in the Fortran Supplement, and answers for exercises and activities. The course is designed for high school…

Identifying the larger (L), smaller (S) and difference (D) of two real numbers, and then selecting the appropriate relationship between L, D, and S can help students solve algebra word problems. (SD)

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

There are many uses for the shortest path algorithm presented which are limited only by our ability to recognize when a problem may be converted into the shortest path in a graph representation. (Author/TG)

Four different types of problems from graph theory are presented and discussed. (MK)

When two methods of transforming numbers from one base to another were taught sequentially, the first interfered with learning of the second. (SD)

Suggests and illustrates ways in which systematic consideration of selected unary operations can be facilitated by using electronic calculators. Emphasis is placed upon unary operations suitable for exploration and investigation at the pre-algebra level, using calculation algorithms as a basis for generating examples and non-examples to develop…

Problems with apportioning seats within the House of Representatives every 10 years are discussed. The history of the problem and the nature of the politics involved are reviewed, and the current method in use is detailed along with its flaws. A call for a more sensible system is made. (MP)