This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

This document consists of three papers. The first, "A Parallel Model of (Sequential) Problem Solving," describes a parallel model designed to solve a class of relatively simple problems from elementary physics and discusses implications for models of problem-solving in general. It is shown that one of the most salient features of problem…

This study investigated the problem representations formed by college students while solving mathematics problems. Problem representation characteristics indicative of understanding were identified by analyzing audio-tapes and written work of sixteen subjects, ages 16 to 24, who solved mathematics problems using the think-aloud technique. These…

Describes operations research as an important management tool that can aid library managers in effectively using available resources and as a set of analytical tools that can enable researchers to better understand library and information services. Early history, definition, models, applications to libraries, and impact are noted. Twenty-five…

An alternative explanation is presented for the pattern of relative difficulty of arithmetical word problems to that suggested in a 1983 article. It is argued, that for many problems, much of the symbolic manipulation is accomplished externally, not internally. (MNS)

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)

Working in groups of three, seventh-grade students were video taped solving an applied mathematical problem. Audio tapes were made of each group discussing their session. Analysis focused on the first stage of Noddings (1984) model of problem solving for school mathematics: Creation of a representation. Some factors identified as impeding…

A model of qualities of mathematical activity was developed within a framework of learning goals. A clinical application of the model is described, in which ninth-grade students were given assignment projects. A hierarchy of effective guidance was established, permitting diagnostic evaluation and progressive development of mathematical activity.…

This study examined the role and development of applied problem solving in mathematics education in the Finnish comprehensive school. The development during the 1980s of applied problem solving in schools was positive in many ways: the changes were cautious and took place more slowly than had been planned; and many obstacles related to the…

Investigated the effect of the choice of a model's medium (algebraic expression or computer program) on the performance of students. Student programers did not transfer the qualities of a computer program approach to their algebraic models. Provides items for five tests. (YP)

Some diverse fields in which the effects of mental representations have been noticed are first discussed, largely through illustrations of differing problem-solving experiences. Then the LAKOS Project (Logical Analysis of Cognitive Organizational Structures) at the University of Osnabruck is described. A central concern is the specification of a…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

Recent research on solving addition and subtraction word problems has resulted in the construction of theoretical models of children's problem-solving processes. Some of these models have been translated into computer programs. Characteristics and predictions of the theoretical analysis developed by Riley, Greeno, and Heller (1983) are discussed…