Guided by Shulman, 1986 and Shulman, 1987 tripartate model of teacher expertise [subject matter knowledge (SMK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK)], the present study examined 162 U.S. and Chinese 3rd grade mathematics teachers' expertise in teaching fractions. Results show that U.S. teachers lag…

Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel,…

The purpose of this study was to examine the effects of actively categorizing math problems on the math problem solving performance of students with and without attention deficit disorder (ADD). To this purpose, 52 fifth and sixth grade students were involved in actively categorizing or noncategorizing (control) tasks followed by two problem…

Out of the 38 nations studied in the 1999 "Trends in International Mathematics and Science Study" (TIMSS), children in Singapore scored highest in mathematics (National Center for Education Statistics, NCES, 2003). Why do Singapore's children do so well in mathematics? The reasons are undoubtedly complex and involve social aspects.…

This materials guide on mathematics instruction for limited-English-speaking students, contains sample instructional materials for teaching mathematical concepts and word problems, and sample lesson guides for lesson development. The emphasis is on adaptation of existing commercial and teacher-developed materials for use with this population. An…

These proceedings contain the papers presented at the 1995 annual meeting of the Canadian Mathematics Education Study Group. Papers are organized into four sections: (1) plenary lectures; (2) working groups; (3) topic sessions; and (4) ad hoc sessions. Papers include: (1) "The Role of Epistemology in the Analysis of Teaching/Learning…

An emerging focus of elementary and secondary mathematics instruction is on problem solving. This study examined an instructional approach for teaching children with learning disabilities how to solve arithmetic word problems. The study was conducted with 60 fifth and sixth grade students who had previously been identified as learning disabled.…

Research in this project studied cognitive processes involved in understanding and solving problems used in instruction in the domain of mathematics, and explored implications of these cognitive analyses for the design of instruction. Three general issues were addressed: knowledge required for understanding problems, knowledge of the conditions…

This document reports on a project that is examining some of the difficulties encountered in teaching word problems involving multiplication, division, and intensive quantities. Some of the various uses of these operations and their structures are considered. Described are discoveries and assumptions regarding students' cognitive models of these…

A change of emphasis in mathematics education may be needed from a mechanical and computational focus to a problem-solving approach. A first step in facilitating this goal is to place children in situations emphasizing problem-solving skills, requiring them to develop and apply their own logic structures. This paper describes a microcomputer based…

This document contains overviews of current research, insights from teachers and tutors, and considerations of such issues as metacognition, choice of operations, and the testing of problem-solving skills. Papers include: (1) "Historical Perspectives on Problem Solving in the Mathematics Curriculum" (George M. A. Stanic and Jeremy…

This booklet is intended to assist tutors in helping transitional and low-level adult basic education (ABE) students acquire the math skills required to make a successful adjustment to regular ABE classes. The exercises provided are intended primarily for use in student-tutor learning teams, with students gradually completing greater portions of…

This paper investigates prospective elementary and secondary school teachers' understanding of proof in a case where the truth set of an open sentence is broader than the set covered by a valid proof by mathematical induction. This case breaks the boundaries of students' usual experience with proving tasks. The most important finding is that a…

This paper reports on a study of mathematics teachers' thinking in the teaching of contextual or word problems [WP] with particular focus on teachers' conceptions of WP and the relationship to teaching. The 20 participants included Grades 1-12 preservice and inservice teachers. Data consisted of interviews and classroom observations. The findings…

Articles in this companion volume to the "International Journal of Educational Research" discuss evaluation of computerized mathematics instruction for mentally retarded children; conceptions of science learning and instruction by academics; effects of language arts tasks on motivation and learning; and effects of study strategies on learning.…