The paper argues that a relationship between visualization and mathematical problem solving ability exists. Research suggests that visual imagery leads to increased understanding of mathematical concepts at both the primary and secondary levels. Mathematical potential is not necessarily "born." Potential can be created in the least likely students…

This volume has been assembled to show what can be learned about learning from large groups of children's responses to well-constructed assessment questions. The wide range of information gathered through the Basic Skills Testing Program (BSTP) has been divided into chapters that focus either on key aspects of mathematics or the major concerns of…

The Young Scholars' Program of the National Science Foundation is designed to stimulate and extend the interests in science and mathematics of students entering grades 7 through 12. An additional goal of the program is to encourage them to investigate and pursue careers in science, mathematics, engineering, and technology. The program strongly…

This paper presents two examples in which technology, in this case a fairly sophisticated authoring system--ToolBook, was used as a tool to construct student understandings in mathematics. In doing so, students were able: (1) to successfully identify the variables (unknowns) and the information given (data) in the problem; and (2) to create…

Factor analysis and Rasch measurement are compared, showing how they address the same data with different interpretations of numerical status. Both methods use the same estimation method, with different measurement models, and they solve the same problem, with different utility. Factor analysis is faulted for mistaking stochastic observations of…

This booklet is a collection of 45 problems that have appeared in the Problem Department of the journal "School Science and Mathematics." The booklet is divided into four parts. The first part presents 20 cryptarithms, puzzles in which letters or symbols are substituted for the digits in an arithmetical calculation, that require knowledge of…

Related research suggests that children may show some simple understanding of event covariations by the early elementary school years. The present experiments use a rule analysis methodology to investigate covariation judgments of children in this age range. In Experiment 1, children in second, third and fourth grade judged covariations on 12…

This article presents a novel approach for explaining algorithms that aims to overcome various pedagogical limitations of the current visualization systems. The main idea is that at any given time, a learner is able to focus on a single problem. This problem can be explained, studied, understood, and tested, before the learner moves on to study…

Research findings that indicate the need for greater integration in the development of verbal and mathematical skills for college technical majors are presented in this paper. Although the project discussed was originally designed to isolate language-related difficulties that affect mathematical skills among bilingual Hispanic students, some…

The Preparing Elementary Teachers to Teach Mathematics Project is a cooperative university/school effort to improve the teaching of mathematics by elementary teachers. Although the primary focus of the project is the improvement of the university training of preservice teachers (PSTs) in mathematics, there are two important collaborative aspects…

Children's nonschool learning provides a foundation for school instruction and problem-solving. Examples of nonschool learning are taken from various cultures. This study examines what young children know about written numerals in their everyday environment, how they come to understand the meaning of written numerals, and how they use this…

This study investigated how preadolescents and adolescents solve problems involving three temporal dimensions. Specifically examined was the question of whether speed and space information would influence the time judgments of 90 subjects 9, 12, and 15 years of age who solved 16 word problems describing the displacements of two cars. The problems…

Leaders in mathematics education are calling for a reorganization of the mathematics curriculum around concept development and problem solving. For many elementary teachers, the limitations of their knowledge about mathematics and teaching mathematics constrains their ability to teach conceptually. If prospective elementary teachers are to…

The focus of this paper is on some of the difficulties students experience in learning from texts and in solving other types of academic problems, because of their failure to distinguish between skills needed for everyday thinking and those needed for academic thinking. The paper discusses the types of processing problems children experience when…

The goal of this material is to explore some aspects of social choice theory that are thought to have potential usefulness in the practical design of decision-making procedures. The document is divided into three chapters: (1) Power in Voting Bodies; (2) Voting Methods for More Than Two Alternatives; and (3) Recent Approaches to Voting Using…