A discussion on the general equation of a line shows how students can be lead to discover mathematical properties, find how one discovery leads to another, see how different branches of mathematics can lead to a solution, and be provided with a starting point for studying special mathematical topics. (MP)

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)

Graph theory is presented as a tool to instruct high school mathematics students. A variety of real world problems can be modeled which help students recognize the importance and difficulty of applying mathematics. (MP)

Cross-number puzzles are presented as both learning devices and as means of student evaluation. (MP)

Ideas that students can use in generating their own problems are discussed and suggestions are made for implementing this type of activity in the classroom. (MK)

Four K-12 studies and one for grades 3-4 considered which math topics could be taught most effectively with a hand-held calculator, which new mathematical topics could be successfully introduced when using such calculators, and what the implications might be for problem solving. (Author/LS)

A sophomore-level course in applications of mathematics was designed to introduce students to the diversity of situations in which mathematical models are used. The course precedes the study of the calculus, and is composed of a sequence of modules. A problem-solving approach is used. (SD)

Determining which whole numbers can be expressed as the difference of two squares and which as the sum of two squares forms the basis of two discovery exercises. (DT)

A journal called the Ladies' Diary published from 1704 to 1841, presented mathematical problems, and solutions to the problems. The purposes of the journal are compared to those of Scientific American today. (SD)

Describes the nature of investigations and their uses in mathematics education. The three types of investigation described, whimsical, real, and mathematical, are defined and illustrated. For each type of investigation, mathematical content and problem-solving strategies are identified, and a solution method is presented. (SLD)

Describes the use of math journals in one kindergarten classroom. Asserts that use of the journals, in which children record their problem-solving processes, makes them think about and use various symbols to represent their thoughts; keeps them actively involved in reasoning, comparing, counting, and other mathematical concepts; and encourages…

Presents historical mathematics to students. Suggests allowing students to have two methods of problem solving with a graphing calculator to allow for a visual result. Indicates that students should have more than one opportunity to experience a solution to a problem, a variety of contexts for the problem, and an opportunity to communicate. (ASK)

Profiles a middle school mathematics teacher and examines her use of two problems from a pilot version of a 6th grade unit developed by a mathematics curriculum project. Reports that problem-solving-oriented curricula provide opportunities for students to make mathematics connections and leads to student confusion and uncertainty. Contains 35…

Presents an activity illustrating the role that technology can play in modeling real-world problem situations and making connections across the curriculum. Includes using a graphical model to answer the questions. Lists related programs for TI-82 and TI-92 graphing calculators. (ASK)

Identifies factors affecting problem solving strategies in the case of a multiplicative comparative situation involving three unknown quantities whose sum is known, and in which comparison relations between two pairs of the quantities are given. Proposes a model of the complexity of a word problem about such situation to analyze solution…