THIS STUDY WAS AN EXPERIMENTAL COMPARISON OF TWO METHODS OF PROGRAMING TEACHING MACHINES. THE BASIC RESEARCH HYPOTHESIS WAS THAT SUBJECTS WHO USED TEACHING MACHINE PROGRAMS WITH EXPOSITORY PRESENTATIONS INTRODUCED BY PROBLEM-SETTING QUESTIONS WOULD LEARN AND RETAIN MORE INFORMATION AND WOULD LEARN MORE RAPIDLY THAN SUBJECTS WHO USED TEACHING…

A set of 58 problems that may be solved by using lists is presented. This set is part of the Mathematical Problem Solving Project. The problems are coded for three levels of difficulty and are designed for students in the intermediate grades. Answers are provided. (MP)

This teacher's guide contains instructions for the use of a booklet designed to teach problem solving through guessing. For each lesson the purpose, an overview, and detailed teaching procedures are presented. The five lessons are: (1) using guesses and computation to solve problems; (2) using guesses to solve two-step problems; (3) using guesses…

Presents six problems from an alternative approach to homework traditionally given to follow-up lectures. Stresses the advantage of longer term exercises which allow for creativity and independence on the part of the student. Problems include: "System Model,""Open-Loop Simulation,""PID Control,""Dahlin…

Six bonuses that students and teachers experience when using calculators are described. Then problem solving and creative problem-making are discussed, followed by practical suggestions for teachers who want to try calculators. Advice on personalizing the use of calculators and recognizing some of their limitations is also included. (MNS)

The author uses Stella the Spider as the main character in a number of three-dimensional geometry problems. Eight of these problems are discussed, with solutions. (MNS)

The skill of asking appropriate intermediate questions during problem solving is discussed. Several problems and other classroom activities are also presented. (MNS)

A one-semester course at the third-year level at York University is described. It tries to legitimize in students' eyes that it makes sense to talk about mathematics as well as do mathematics. Seven course themes are discussed, followed by nine problems used in the course. (MNS)

Fifteen mathematical puzzles and problems are presented. Areas investigated include pentominoes, arithmetic, fractions, and dissections (dissecting) a shape into two pieces that can be fitted together to form a square. Answers for each puzzle and problems are included. (JN)

Examines the relationship between development of logical processes required in deductive reasoning and their use by preschoolers, also considering possible explanations for children's deductive reasoning. The relationship of problem content to real-world knowledge and the sequence of presentation of problem types were found to affect the display…

Motivational classroom materials that provide direct instruction on problem-solving skills are given. The activity highlights and provides opportunities for practice with two problem-solving skills, make a drawing and work backward. (MNS)

A problem-solving approach involving systematic experimentation, one of the most-used problem-solving strategies, is advocated since it is useful beyond mathematics problems. Examples of its use are given, with two problems explored and four others noted. (MNS)

Since early childhood is a critical time to build a readiness for problem solving, 12 specific activities, with problems, are suggested. (MNS)

The theme for the column is composing and solving problems. One section has teacher-developed problems for the primary grades. The other section contains student-authored problems for the upper grades, submitted for a student problem contest. (LS)