This bibliography lists reports of research on problem solving in mathematics, with specific regard to experiments, correlations, and other regional studies. The listing supports a research integration, performed by meta-analysis at Adrian College, Michigan, in 1989-1990. Guidelines for including studies were applied as follows: (1) the study…

This yearbook consists of five sections, with samples of children's work appearing between sections. Part 1, "Perspective on Change in Elementary School Mathematics," describes and discusses broad components of change in elementary school mathematics. The central roles of problem solving, communication, and reasoning are highlighted, as is the…

Lists references of 16 research summaries, 152 articles, and 220 dissertations alphabetically by author within each category. Provides the grade or age level for each reference. A brief abstract is presented for most of the references. Journals searched and author index by content are included. (YP)

This article describes a teaching experiment conducted in a seventh-grade classroom. It explores ways that students used four types of problem-solving knowledge through writing their responses to algebraic problems. The problems were presented to students in the geometric contexts of growth and change and size and shape. It was found that writing…

This article discusses the algorithm for multiplication that is referred to as lattice multiplication. Evidence of how the author's preservice students' conceptual understanding of the algorithm grew through the semester is given. In addition, the author extends the conceptualization of the algorithm from the multiplication of whole numbers to the…

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying…

The author examined the potential influence of learning opportunities provided in 1 U.S. and 1 Chinese mathematics textbook series on students' problem-solving performance. Also, the author studied learning opportunities provided in the textbooks by analyzing word problem distribution across various problem types, as well as the potential…

This report describes an investigation in England of some of the problems children experience with fractions. In particular, the restricted view that some children have of fractions is investigated. The methodology involved a large number of interviews with secondary school children (aged 12-14). The results of these interviews led to the design…

Describes methods for teaching able students mathematical problems. Provides four problems and discusses the students' responses to them. (YP)

There are many problems that can be translated into the language of graph theory. Such a problem, discussed in this article is to show that in any group of two or more people, there are at least two people who have the same number of acquaintances in the group. (PK)

Reviews research which indicates that students performed better on problems when extraneous information was absent than when extraneous information was present. However, recommends that teachers embed word problems with realistic contexts, that is, contexts that contain extraneous bits of information to help students transfer their problem-solving…

The material presents an alternative method for arranging proofs, which arranges development in levels. The method is described as triggered by recent ideas from computer science and is intended to increase the comprehensibility of mathematical presentations while retaining their rigor. Several examples using this approach are presented.…

Outlines a possible framework for allowing teachers to explore how children learn mathematics. A mathematical modelling process and three domains, including content, process and pragmatic domain, are described. Twelve strategies for encouraging children to translate between the domains are suggested. (YP)

Including difference equations in the mathematics curriculum is proposed. Some fundamental ideas and examples are presented. (MNS)