This pilot study examined the form or nature of the more highly organized knowledge structures used by successful problem solvers and whether there are experiences that would encourage their development. Previous related research and a theoretical framework are discussed. The small-group problem solving mode was used, with "A Problem with…

A series of simple games can be analyzed inductively to determine strategies. Students explore possibilities, hypothesize solutions, prove their solutions correct, and then generalize to more complex games. (SD)

Three worksheets provide exercises involving triangular arrays of numbers. (SD)

Indicates that to explore the relationship between the teaching of science and mathematics in the secondary school, it is necessary to examine the basic issues of the curriculum in some depth. Examines the justifications for the school curriculum and the distinguishing characteristics of physics and mathematics. (GS)

In a study of problem solving by primary students, the investigator found that the most important factor was teacher expectation. The conduct of the study is described, with some rationale and sample questioning sequences included. (SD)

Mathematics should be taught in everday terms, not as a series of wispy, bloodless abstractions. (Editor)

Applying and adapting a variety of appropriate heuristic strategies is one of the accepted standards of problem solving (NCTM, 2000). Thinking through a solution to a non-routine mathematical task, experts in problem solving call into play many sophisticated strategies (almost) without conscious efforts, while novices need to be taught how to do…

Fifty-five college students participated in a study investigating the effect of field dependence and time limitations on the solution of mathematics word problems and visual interpretation problems. Field-independent (n=25) and field-dependent (n=30) subjects represented the upper and lower thirds on the Hidden Figures Test. Field-independent…

Some ideas are presented about the ways in which the three domains of metacognition, affective factors, and beliefs influence the cognitive activities of seventh graders as they solve mathematics problems. The research project, initiated in 1981, is first described. Theoretical considerations are then discussed, with sections on affects, beliefs,…

Over the past few years a substantial body of research has yielded evidence that the semantic structure of elementary arithmetic word problems influences children's strategies to solve them. The study reported in this document considered three other task characteristics in addition to semantic structure: (1) the order of presentation of the two…

Summarized are the findings from five studies carried out in Australia in 1979-80. First was a cross-sectional survey designed to determine the memory capacity of a population of children in grades 1-3. The second study investigated performance differences on a variety of mathematically related developmental tasks for the same group. Data from…

The focus of this booklet is on matching, recognizing, and identifying colors, shapes, and sizes. Concept development as well as vocabulary learning are goals. A variety of materials are used in the activities. Activities for children from preschool through grade 2 are grouped by topic. (MNS)

Problem solving that both requires and develops higher-order thinking skills is illustrated in the EQUATIONS Challenge Matches program, which consists of computer diskettes at the elementary, intermediate, and advanced levels plus a multi-level diskette. Samples of computer output are given, with the results of various types of experimentation…

The purpose of this study was to examine the literature to find out if the recommendation by the National Council of Teachers of Mathematics (NCTM) that mathematics education should focus on problem-solving in the 1980s was being implemented or had caused any changes in the approach to teaching mathematics in the school curriculum. The study also…

The theme of the sixth annual meeting of the North American Chapter of Psychology of Mathematics Education was "The Importance of Psychological Models for Research in Mathematics Learning." The conference proceedings contain papers organized around five major topics. In the first section, eight papers on the learning of arithmetic are…