Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students' higher-level skills, and evaluate its learning. While these studies usually study specific aspects of problem solving, further research is needed to understand how to address problem solving from a…

This article examines the role that replication research has played in the development and refinement of mathematics interventions for learners with extensive support needs. By highlighting 16 research studies, we seek to inform stakeholders of lessons learned and knowledge gained through replication. These studies show that when given…

The authors completed a narrative review of studies of mathematics interventions from 1996 to 2010 for helping elementary school students with difficulties in mathematics solve word problems. Key instructional components supported by research are teaching cognitive and metacognitive skills; schema-based instruction focusing on semantic analysis,…

This paper presented various issues about pedagogical and cognitive aspects of problem solving and explored ways to lessen the heavy cognitive load of a problem solving task. It established a problem type schema for students at different levels. It recognizes the role of modern technology as a cognitive tool that promotes learning mathematics with…

Transferring the skills learned in mathematics to other contexts is a problem for many students. A new heuristic model of mathematics instruction is proposed. The model would guard against the adoption of mistaken assumptions about mathematics and foster the learning of problem-solving strategies. (VM)

This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…

The topics of computer-assisted instruction, computer-augmented problem solving, and computer-managed instruction are discussed. In the field of computer-assisted instruction, uses of the computer for drill and practice, tutorial purposes, and simulation are examined. (Author/JN)

Notes that problem solving may become the focus of school mathematics to an extent never before experienced. It is felt much more systematic research is needed. Studies which focus on perception and cognitive processing ability are viewed to have potential for producing important results of wide applicability. (MP)

The needs of mathematics teachers who wish to provide relevance in their lessons, and the need to infuse energy topics into all disciplines in the curriculum at all grade levels, are addressed. It is felt children could be adversely impacted by present energy practice, and education is essential. (MP)

This report, prepared for and published by the Mathematical Association of America's Committee on the Teaching of Undergraduate Mathematics, includes a description of the state of the art on problem solving, lists available resources, and makes recommendations regarding the place of problem solving in the college curriculum and ways to teach it.…

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…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

This document summarizes the research done on calculators and calculator use. It is noted that calculators are now seen as acceptable, with fears about use in school currently infrequent, and the role of such devices much more evident than 6 years ago. The first two sections of this material summarize data on use and availability. It is noted that…

This paper considers the possibilities of using computers not only to amplify, but to reorganize children's thinking and mental functioning. These two different conceptualizations of the transformational role of noncomputer cognitive technologies (such as written language) in human intelligence and cognitive change are sketched, and the different…

This document examines specifically relevant issues and offers useful guidance in making decisions for elementary and secondary school mathematics education in the 1980's. The expertise of 19 authors is reflected in 14 chapters that provide an overview of mathematics today and recommendations for the future. The individual chapters are titled: (1)…