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…

Pascal's Triangle is an important numerical table; with its help, a number of computation problems may be solved. Some of these problems are examined and the question of what"solving a problem" can mean is generally considered. (Author/MK)

Presented are six problems from diverse areas of mathematics that are appropriate for students of differing age and ability levels. (PK)

Ten activities that give learners in grades 5-8 a chance to explore mathematics with calculators are provided. The activity cards involve such topics as odd addends, magic squares, strange projects, and conjecturing rules. (MNS)

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

In this study, we examined 139 prospective elementary teachers' solution processes to additive word problems for which the solution is 1 more or 1 less than the answer produced by the straightforward application of the addition or subtraction of the two given numbers. For each problem, five aspects of their solution processes were examined: (a)…

Young children are interested in and capable of building a mathematics foundation at a very early age. Computer software allows children easy access to math. This software consists of seven activities for ages two to five years. These seven activities emphasize numbers, counting, addition, subtraction, patterns, problem solving, size, and…

This book is a collection of teaching strategies and activities for teachers of secondary mathematics. This volume is the product of a workshop that focused on student understanding of directed numbers. Suggested teaching methods include introducing the number concept, using a number line, number strips, monograms, bottle top addition and…

Describes work with kindergarten children to improve their development of estimation, decision making, divergent thinking, directionality, numerical concepts, and creative problem solving skills through learning to program and control the robot Big Trak, a truck which moves along the floor in response to their commands. (EAO)

Several types of problems designed to provide opportunities for mathematically able students to do original and analytic thinking at grades 3 and 4 while reinforcing numeration and computation skills are presented. (MP)

Discusses how students at the end of the French primary school-cycle (10- to 11-year-old pupils) resolve multiplication and related division problems within an assessment perspective taking into account the 3 factors of the problem's representational structure, the numerical values used, and the context of the problem statement. (25 references)…

Discusses opportunities to use nursery rhymes to aid in the mathematical development of young children. Considers rhymes that involve patterns, ordering, and problem solving. (MKR)

This article describes a series of mathematics activities based on the book "A Grain of Rice," which are designed to help students understand powers of 2. Ideas for activities in other disciplines are also provided. (Contains 3 tables.)

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular…

In this article, the authors would like to look at a range of solutions submitted by Year 4-5 teams in the 2003 "Naturally Mathematical Challenge" to a question that involves no more than the numbers 1 to 6 and possible arrangements of them. In the context of other competition questions and in their elaboration of mathematical process,…