The problem involves randomly breaking a stick into three pieces and using the pieces to form a triangle. The probability of getting a triangle is calculated using four different solution methods. Two unique problem interpretations are noted, and one solution method involves a BASIC program. (MP)

Mathematical modelling and an example used with undergraduates were presented in part 1 (v17, n5, p212-18, 1982). A second example, Power from Windmills, is provided which has considerable potential for development both as a model and as a series of modelling experiences of increasing difficulty for students with different backgrounds. (Author/JN)

Provides rationale for and description of an acid rain game (designed for two players), a problem-solving model for elementary students. Although complete instructions are provided, including a copy of the game board, the game is also available for Apple II microcomputers. Information for the computer program is available from the author.…

The focus is on suggestions, with examples, for teaching estimation skills. Estimating can be a very enjoyable as well as a very useful part of mathematics, helping to improve attitudes of pupils toward the subject by providing success. Estimation is shown not to be synonymous with mental arithmetic. (MP)

The harmonic mean is defined, and examples of problems viewed suitable for classroom exploration are presented. Such exercises provide many opportunities for students to engage in interesting nontrivial problem-solving activities and practice on many algebraic skills. Class discussion of the arithmetic, geometric, and harmonic means is suggested.…

Reviews an educationally valuable and reasonably well-designed simulation of volcanic activity in an imaginary land. VOLCANOES creates an excellent context for learning information about volcanoes and for developing skills and practicing methods needed to study behavior of volcanoes. (Author/JN)

The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)

Investigated perceptions of effectiveness of religious solutions for personal problems. Subjects (N=160) read a biographical sketch of a female with a hypothetical personal problem and solution. Found religion was viewed as being as effective as an informational solution. Intensely emotional religious experience was valued less than church or…

Investigated the relationship between participation in Marriage Encounter and subsequent marital or family distress. An analysis of 13 case reports suggested that Marriage Encounter weekends can cause marital or family deterioration through increased marital conflict, avoidance of constructive problem solving, or marital enmeshment at the expense…

Presents the results of a study which sought to determine if prior learning of basic problem-solving steps, the practicing of problem-solving skills, and the receiving of feedback during play were important variables in the use of role-playing activities to teach high school students a specific problem-solving model. (Author/JL)

Considers the impact of learning to program upon the intellectual and personal development of children. The excitement of computer mastery, the usefulness of programing as an introduction to "real world" problem solving, and computer programing as an aid to increased understanding of subject matter are discussed. (JL)

Rubik's Cube is viewed as a tool to generate student interest in applying rather sophisticated mathematics to generate some solution algorithms. Discussion begins with the creation of a notation method for the cube and develops into applications of permutations and set concepts. A special "cycle notation" is employed. (MP)

Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

Students' misconceptions in mathematics and how teaching may be directed to diagnose and eliminate these misconceptions are discussed. Four main types of misconceptions during problem-solving are noted. It is also noted that the basic mathematical processes of generalizing, representing, and explaining are used in selected student self-help…

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)