Teacher should strive to be more than the authority in the classroom identifying right versus wrong relating to problem solving. Identifying and emphasizing what aspects of an answer are mathematically correct improves students' confidence to tackle challenging problems and they view themselves as mathematical problem solvers.

Students were given the problem: Given a deck of cards in a certain order, after how many shuffles will it return to its original order? They worked with small decks of cards to develop a general formula, but were unhappy with the results. (SD)

This project addressed the question: What knowledge and processes enable individuals to construct and modify representations of novel, nonroutine problems? The theoretical goal was to extend the information-processing theory of problem solving to include processes that have been characterized as restructuring of problems and productive thinking by…

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

Presented are twenty essays related to applications in school mathematics and aimed at the classroom teacher. The essays use numerous examples and illustrations that provide the teacher with something tangible for immediate use. Four thematic areas are addressed: (1) What are applications?; (2) Why include applications in school mathematics?; (3)…

Using a great variety of word problems drawn from many contexts can make multiplication and division rules more relevant to the student's needs. (SD)

Examples from almanacs are used to provide real-life problems that involve estimating, computing, and thinking. (MP)

An elementary knowledge of geometry is shown to be helpful in problem solving, especially in that the shortest distance between two points is a straight line. (MN)

Describes the differential equation solution to the mechanics problem of the motion of a free mass subject to a harmonic force which can also be illustrated by a simple analogue computer. (SL)

A series of interesting mathematical applications for the greatest integer function are presented. (JT)

Reviews the application of population balance mathematical treatment to transfer operations in chemical engineering. (SL)

Solves the quantum mechanical problem of the bound states corresponding to a sum of several delta-shell potentials. (SL)

A course is described which gives students experience in creating practical mathematical models of "real" problems, relating the mathematical solutions of the model to the original problem, and recognizing non-mathematical constraints on possible solution approaches. The students assume the role of industrial mathematicians while their tutors play…