Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 3-5 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…

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…

An angles teaching sequence was designed, in which students were guided to abstract a general concept from physical activities with concrete materials. The three design principles used were familiarity, similarity recognition, and reification. The resulting teaching sequence was tested in a field study involving 25 teachers of Grades 3-4. The data…

A minicourse designed to teach fourth and fifth graders about computers included decoding computer cards, a "race" against the computer, a field trip, flow charting, and writing computer programs. The course was limited by the students' ability to understand abstract mathematical concepts. (MP)

The effectiveness of an experimental mathematics teaching program was investigated. Observational measures revealed that teachers implemented the treatment. Analyses of product data showed that students of treatment teachers outperformed those of controls. Thus, teachers and/or teaching methods exerted a significant difference on student progress…

Investigated the relationship between peer-tutoring interactions of dyads and experience in a reciprocal peer tutoring (RPT) program in mathematics. Analysis of 40 at-risk fourth- and fifth-grade students indicates that RPT participants displayed significantly higher rates of mathematics achievement, social acceptance, and other favorable measures…

Studies the co-emergence of teaching and children's construction of specific conceptions that support the generation of improper fractions in a constructivist teaching experiment with two fourth-grade students posing and solving tasks in a computer microworld. Reports that examination of the teacher's adaptation of learning situations (tasks) and…

Investigated development of turn and turn measurement concepts within a computer-based instructional unit. Written assessments, interviews, and interpretive case studies of third and fourth graders found that turns were less salient for children than forward and back motions; students evinced a progressive construction of imagery and concepts…

This paper reports the results of a special urban study of the 2005 National Assessment of Education Progress which indicates that city school districts may be seeing some payoff from years of work to improve mathematics instruction. However, similar initiatives to raise reading achievement have not led to significant gains. While, most of the 11…

Of the 1,828 grade 6 students who received accelerated instruction outside of the regular classroom, 27% participated in both reading and math interventions. Of the 1,872 grade 7 students who participated in accelerated instruction outside of the classroom, 26% participated in both reading and math interventions. The overall state test results for…

Findings from two studies of fourth grade children learning the concept of mathematical equivalence are presented. The questions studied were: (1) Can knowledge conveyed in gesture but not in speech be tapped by a recognition technique; and (2) Does having implicit knowledge that is expressed in gesture but not in speech have implications for…

Through timely questioning, teachers can estimate a child's understanding of mathematical ideas. Hence, the type of question asked by the teacher must be connected to the student's present thinking about a solution. This paper illustrates and analyzes how timely questioning on the part of teachers helped third, fourth, and fifth grade students…

This is the teacher's manual to accompany part 1 of the workbook for grade 4 pupils in the Comprehensive Instructional Management System, a teacher-designed unified mathematics curriculum for kindergarten through grade 7. It is composed of a curriculum, a testing component, and a computer-managed reporting system. The curriculum is organized into…

This investigation of the possible effects of using calculators in mathematics teaching was based on an analysis of the cognitive and affective aims of mathematics education in the nine-year comprehensive school in Finland attended by all children aged seven through fifteen. The experiment consisted of a comparison of two fourth-grade classes…

The purpose of this study was to compare achievement and attitude of low achieving students grouped for instruction and provided with special texts (E-group), to those grouped but not using special materials (S-group), and to those who were neither grouped nor using the special texts (C-group). Chosen by their cumulative record and their…