This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.

This paper, part of a series of working papers published to provide documentation of research and development efforts associated with the Indigenous Mathematics Project of Papua New Guinea, discusses the role of problem solving in the mathematics curriculum and types and characteristics of good problems, with illustrations. Reasoning by analysis…

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)

Problems and activities are presented for which "I can't do it" or "It can't be done" are the correct responses. Including problems of this type in the curriculum adds a new dimension to students' learning and helps to develop better problem solvers. (Author/MK)

NINETY FIRST GRADE CHILDREN WERE RANDOMLY SELECTED FROM 3 SCHOOLS (WHICH EACH USED A DIFFERENT ARITHMETIC PROGRAM) TO PARTICIPATE IN A STUDY TO INVESTIGATE THE EFFECTS OF 2 VARIABLES ON THE CHILDREN'S ABILITY TO SOLVE ADDITION PROBLEMS. THE VARIABLES WERE (1) THE PRESENCE OR ABSENCE OF AN EXISTENTIAL QUANTIFIER PRECEDING THE START OF THE PROBLEM,…

The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)

Methods of instructing students in problem solving are suggested that get pupils to view mathematics as a tool. The author states students should look beyond the numerical answer to the other components and highlights areas of the mathematics curriculum that afford an opportunity to explore these many facets. (MP)

This analysis of 44 research studies concerned with word problems contains: (1) a brief overview; (2) 44 major findings and conclusions; (3) 64 suggestions and questions for further research; and (4) a reference list. The author suggests that the experimental research of the 1980s seemed to focus on the children, the instruction, and the word…

This paper describes the research program of the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The major interest is in the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children. Three factors…

Described is a two-week summer institute with 57 Ohio teachers in grades K-12. The teachers were given experiences in problem solving to help them broaden perceptions of real problem solving. Sixteen problem-solving strategies and four illustrative problems are included, and teachers' evaluative comments are discussed. (MNS)

Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)

Presents three reproducible worksheets which contain verbal problem situations in which numerical quantities have been omitted and represented by geometric shapes. The objective of the material is to develop the students' ability to analyze the mathematical structure in verbal problem-solving situations. (PK)