Describes a student project that enables students to experience problem-solving strategies and construct their own understandings of the problem-solving strategies by researching the problem-solving process itself, uncovering and defining strategies that they can subsequently use to solve problems, and exploring the impact that attitude has on…

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Strategies for teaching general mathematics effectively are discussed. Stressed are the use of calculators for arithmetic, individualized instruction, and teaching mathematics in context. Applications to vocational education are described. (CW)

Discussed are some applications of mathematics involved in actuarial science which may be taught in high school mathematics classes. Described are the importance of approximate solutions, multiple answers, and selling the solution to a problem. (CW)

Presented is a method which may be used to help students start their own original investigations and create their own conjectures about fundamental mathematics concepts. An example of this method is provided. (CW)

Described is an approach to teaching algebra in a meaningful context by using problem solving to motivate students and increase their retention. Examples of this approach are given. (CW)

Two ideas for teaching mathematical Concepts are presented: "Writing Study Cards for Understanding"; and "A Conceptual Approach to Solving Equations." Examples of the applications of these methods are discussed. (CW)

Discussed are several common aspects of teaching functions and statistics including graphing relations, exploring relations, transforming relations, and modeling situations. Examples of each are provided. (CW)

This article explains how this method is done, examines some reasons for including it as a topic in mathematics curricula, and uses modular arithmetic to explore its mathematical basis and its generalizability to computations in bases other than 10. (CW)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Presents three problems that help students develop a repertoire of heuristics and persistence in problem solving: the water-jug problem; the missionaries-and-cannibals problem; and the census-taker problem. Discusses methods to encourage students to persist. (MDH)

Described is a two-week summer residential program designed for students who have been identified through one of several middle school talent searches. Discussed are the assumptions and goals, course content and pedagogy, evaluation, and materials of the program. (CW)

Counterintuitive moments in the classroom challenge common sense and practice and can be used to help mathematics students appreciate the need to explore, reflect, and reason. Proposed are four examples involving geometry, systems of equations, and matrices as counterintuitive instances. (MDH)

Discusses the process of mathematical iteration, its benefits as a problem-solving technique, and how to teach it. Presents a selection of mathematical ideas and problems that can be solved and explored using iteration, along with related BASIC computer programs. (MDH)