This paper examines part of a set of students who were followed during their first-term, first-year studies in formal definition-based real analysis at a British university. It explores the approaches to problems about convergence of sequences and series made by students who have a tendency to include visual imagery in their reasoning. We explore…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)

A major advance in the field of reading over the past 15 years has been the development and validation of screening measures that can detect with reasonable accuracy those kindergartners and first graders likely to experience difficulty in learning to read. Increasingly, these students now receive additional instructional support during the…

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on…

This study evaluated the effects of a personalized computer-assisted mathematics problem-solving program on the performance and attitude of Taiwanese fourth grade students. The purpose of this study was to determine whether the personalized computer-assisted program improved student performance and attitude over the nonpersonalized program.…

The issue of how to integrate information technology in the teaching/learning environment remains strongly associated with the use of the computer as a tool. While technology based tools such as Logo have been advocated for problem solvers at the elementary level, spreadsheets have a great deal of potential for use at both the junior and senior…

This book presents 129 problems selected from the calendar problem section of the "Mathematics Teacher" to supplement regular mathematics textbook offerings for middle grade teachers and students. The problems are categorized by six topics: (1) Numbers; (2) Computation; (3) "Oldies but Goodies"; (4) Offbeat and Unusual; (5)…

How the self-explanation process relates to learning and subsequent problem-solving performance was studied in two experiments with college students to examine whether students taught to self-explain during a study phase show greater test gains than control group counterparts; this is an attempt to replicate the results of M. T. H. Chi and others.…

This module is the eighth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include comparison of numbers, pure numbers, denominate…

A training procedure was developed to improve (or to encourage) the construction of a meaningful problem representation by mentally retarded and learning disabled children. Children are taught to use an external visual representation for arithmetic word problems, in which the meaning of the problem is reflected. The construction of this visual…

The purpose of this manual is to present a series of lessons on solving word problems, each focusing on a specific concept. The solving of story problems should be incorporated into the daily mathematics lesson so that children can maintain and increase their skills. The lessons are sequenced according to their complexity. Lessons one through…

This study is to explore the potential of Fauconnier's mental space theory in understanding the teaching and learning processes of mathematics. Notions from cognitive linguistics have been introduced to research in mathematics education recently, but there have been little studies about what potential the framework of mental space has in…

This report describes a program for teaching students to use specific strategies to construct meaning from text. The targeted population consisted of elementary and middle school students in a growing urban community in northern Illinois. The lack of reading strategies was documented by data describing the reading behaviors and achievement of the…

Fourteen word problems, half of which were problematic from a realistic point of view, were administered to 332 Belgian preservice elementary school teachers who also saw answers given by 4 students. Results revealed a strong tendency to exclude real-world knowledge from spontaneous solutions and appreciations of student-supplied answers. (SLD)

A growing body of empirical and theoretical work indicates that young children (grades K-3) have difficulties solving word problems because of deficient language and text comprehension strategies. Describes a computer simulation designed to model working memory demands in "bottom-up" comprehension of arithmetic word problems, offering a…