Determined whether 11 third-grade children, differing in cognitive processing capacity, solve addition and subtraction word problems differently. Results, among others, show that children who differ in cognitive processing capacity also differ in strategies they use to solve the same verbal problems and differ in their success in finding correct…

Develops a classification scheme for mathematical problem-solving activities. Presents problems generated in solid and plane geometry and fractions. (JM)

A previous article examined the amount of fuel that could constantly burn each second and achieve a safe landing. This article investigates some ways to burn variable amounts of fuel according to some mathematical function (such as an arithmetic progression). Several assumptions (such as a massless fuel) are made. (JN)

This activity consists of two problem situations, each illustrating how a computer can be used as a tool to assist students in solving mathematical problems. In one, numerous calculations are performed by the computer; the second uses a Monte Carlo model to simulate a physical action. (MNS)

This annotated bibliography contains 12 references on computers in elementary school mathematics. Topics include developing mathematical concepts with microcomputer activities, teaching mathematics with computers in primary grades, microcomputers and problem solving, review for grade 1 software, early learning of logic and geometry using…

Advantages of using flow charts are listed. Flow charts for adding and subtracting fractions and for polynomial division are provided. Rules for constructing flow charts are given. (DT)

Based on a synthesis of the literature, a model for problem posing cognitive processes was formulated, and validated. The major constructs incorporated in this framework were the situations in which problem posing occurs. For each situation, four cognitive processes were established: the editing of problems based on iconic or symbolic stimuli, the…

Our study concerns the analysis of teacher and student activities. Secondary school 6th grade students were confronted, for the first time, with solving equations. We used our cognitive models of students and experts (in algebraic calculations) for analyzing the teaching process and the cognitive functioning of students. Our model led us to…

The purpose of this paper is to share the strategies that children invented to solve problems involving division of fractions in the absence of algorithmic instruction. The data come from two sources, the first being a teaching experiment and the second being the regular classroom practice of this teacher/researcher. It was found that when the…

A case study in mathematics designed to illustrate how the computer may be instructed to solve complicated problems. The problem is to find the volume of a right truncated cone given the altitude and a half angle or the base radius. (RP)

Identified difficulties encountered in spontaneous modeling, as well as strategies, approaches, and language used in this activity. Graduate mathematics students (N=223) were asked to create a mathematical model of a biological process. Their solutions and strategies are analyzed and results described. Significant conclusions for teaching applied…

Results from the third national mathematics assessment are presented. Overall, the performance of nine year olds changed little since the second assessment, while significant gains were made by 13 year olds. Data on whole numbers, fractions and decimals, other basic concepts, and problem solving are discussed. (MNS)

A sequence of activities is presented that has been used to explore powers of numbers and patterns with middle school students. Experiences with use of this sequence are noted. The material is designed to serve three instructional purposes, which are noted at the conclusion. (MP)

Current practices in teaching about distributivity of multiplication over addition and subtraction are reviewed. Then a study is described in which two inventories were administered to 83 eighth-grade students; scores were low. Suggestions for teaching distributivity are presented. (MNS)

An approach to problem solving is described that is based on analysis of how fast model race cars can go. The exercises were used to replace standard time/rate/distance exercises, and were found to be greatly enjoyed by both girls and boys. (MP)