Designers of critical mathematics instruction have documented difficulties in simultaneously fostering the development of critical consciousness while supporting students in developing understandings of new mathematics. However, confining justice-oriented tasks to applications of previously learned mathematics limits the degree to which these…

In the spirit of the networking of didactical theories, it is advocated in this presentation in favor of a mixed networking of philosophical theories, namely Husserlian phenomenology and hermeneutics, and didactical theories to produce a fertile interplay between philosophy and mathematics education. The cross-analysis of students' work on a…

This article reports and analyzes different types of problems that nine students in a Master's Program in Mathematics Education posed during a course on problem solving. What opportunities (affordances) can a dynamic geometry system (GeoGebra) offer to allow in-service and in-training teachers to formulate and solve problems, and what type of…

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

Discusses the problem-solving heuristics of examining for special cases, utilizing dimensions to make sense of proposed solutions, and symmetry. Presents examples to illustrate the use of one or combinations of these heuristics. (MDH)

A key to improving urban science and mathematics education is to facilitate the mutual understanding of the participants involved and then look for strategies to bridge differences. Educators need new theoretical tools to do so. In this paper the argument is made that the concept of "boundary spanner" is such a tool. Boundary spanners…

This study, conducted in the Netherlands, examined the effects of a problem-solving program on students' problem-solving and metacognitive skills. The program consisted of four parts involving one or more aspects of problem solving in the content areas of proportions, geometry, numbers, and solving equations and inequalities. The experimental…

Student problem-solving behaviors are analyzed using a four-dimensional framework with related detrimental factors identified for each dimension. General approaches and specific techniques developed to address negative factors are reviewed. Examined are means of developing the components of problem-solving teaching. (KR)

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

Addresses NCTM recommendations regarding nonroutine problem solving. Illustrates general approaches, teacher discourse, and aims of problem solving via three nonroutine problems. Compares expert and novice approaches to problem solving and applies procedures endorsed by Polya regarding problem-solving strategies. Includes nine additional…

Presents three problems that help students develop a repertoire of heuristics and persistence in problem solving: the water-jug problem; the missionaries-and-cannibals problem; and the census-taker problem. Discusses methods to encourage students to persist. (MDH)

Presents a study to determine whether computer use in guided-discovery learning episodes would enhance the problem-solving ability of secondary school students (n=147). Results indicate interaction between low- and middle-level students' mathematical achievement and treatment groups, while high-level students performed well regardless of approach.…

The paper describes the details and use with primary school teachers of a problem-solving activity known as the King Alfred's College Maths Game. The game demonstrates to teachers that problem solving needs to be approached through structured learning experiences that provide material for reflection and questioning. (Author/MDH)

Describes common beliefs of students about the nature of mathematics and discusses the implications of the student beliefs for problem solving and for teaching. (PK)