The teacher's guide for the second unit of this SMSG series covers the two chapters in Unit 2 of the student text on algorithms and flow charts and on problem formulation. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed,…

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

This is the second unit in a series of 14 SMSG texts designed to cover mathematical concepts which the general population should know. One chapter of the unit discusses algorithms, flow charts, and computers; the second chapter tackles problem formulation procedures (not actual problem solving) and briefly covers mathematical models. For a special…

The author describes a new graphing algorithm for computing probabilities, and presents problems for these algorithms for use in the classroom. (SD)

The cognitive method, an algorithmic method for transforming verbal word problems into equations, equation systems, inequalities, etc., is presented and discussed. The psychological and mathematical aspects of the cognitive method are also reviewed. (MP)

Explores the use of computers for teaching mathematical models of transposition ciphers. Illustrates the ideas, includes activities and extensions, provides a mathematical model and includes computer programs to implement these topics. (MVL)

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

Student weaknesses on problem-solving portions of the NAEP mathematics assessment are discussed using Polya's heuristics as a framework. Recommendations for classroom instruction are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).