The wave equation is a classic partial differential equation that one encounters in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating string. Using a video camera and Wave-in-Motion software to record displacement data from a vibrating string or spring,…

This study, part of a narrative classroom inquiry into the teaching and learning of mathematics in a Canadian elementary classroom, emerges from the three years I was a participant-observer in Janine O'Neil's 3rd/4th-grade classroom at Bay Street Community School. Drawing on the curriculum commonplaces of teacher, social milieu, subject matter,…

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

Cognitive clusters from the Woodcock-Johnson III (WJ III) Tests of Cognitive Abilities that measure select Cattell-Horn-Carroll broad and narrow cognitive abilities were shown to be significantly related to mathematics achievement in a large, nationally representative sample of children and adolescents. Multiple regression analyses were used to…

In this article, data from a study of the mental computation competence of students in grades 3 to 10 are presented. Students responded to mental computation items, presented orally, that included operations applied to fractions, decimals and percents. The data were analysed using Rasch modelling techniques, and a six-level hierarchy of part-whole…

This article demonstrates how a child's invented algorithm about tens and ones generated "transitional thinking" on the way to the construction of a mathematical understanding of place value. The articles also discusses how two important "best practice" classroom strategies, mathematical discourse, and the role of wait time in that discourse take…

A group of seventh- and eighth-grade Italian students with low achievement (LA) in learning English as a foreign language (FL) was selected and compared to a group with high achievement (HA) in FL learning. The two groups were matched for age and nonverbal intelligence. Two experiments were conducted to examine the participants' verbal and…

This technical report provides the results of a study on the calculation and use of generalized variance functions (GVFs) and design effects for the 1990-91 Schools and Staffing Survey (SASS). The SASS is a periodic integrated system of sample surveys conducted by the National Center for Education Statistics (NCES) that produces sampling variances…

This document offers instructional materials for a 32-hour course on math operations involving graphs/statistics, measurement (English and metric), geometry, exponential notation, and scientific notation as applied in the workplace. The course was part of a workplace literacy project developed by Mercer County Community College (New Jersey) and…

This report examines the development of tuition rates and tuition policy in Washington State's public higher education system and provides comparisons to rates and policies in other states. It also explores philosophies regarding the determination of tuition rates, along with the range of potential policy options. The draft report is divided into…

During the 1989-90 school year, the Barrett Math Program was piloted in selected sections of grades K-7 in five Atlanta (Georgia) Public Schools (APS) elementary schools. The Barrett Math Program is designed to improve the total mathematical skills of elementary school students, including computation, concepts, and problem solving, as measured by…

Developed for elementary teachers, this activity unit is designed to teach students the importance of estimation in developing quantitative thinking. Nine ways in which estimation is useful to students are listed, and five general guidelines are offered to the teacher for planning estimation activities. Specific guidelines are provided for…

The National Council of Teachers of Mathematics (NCTM) has stated that mathematics programs should take full advantage of the power of calculators at all grade levels. This recommendation urges that students be provided access to calculators, and that calculator use be integrated into the core mathematics curriculum on a regular basis. This…

The Skill Acquisition Measures (SAM) were designed by the Lancaster (Pennsylvania) School District as criterion referenced tests for mathematics. This manual consists of copies of the student test forms for level 2, with additional information for the teacher's use. Each of the test items is presented with the correct answers and the criteria for…

Presented is the third edition of a textbook designed for pre- and inservice teachers of elementary school mathematics. The content was selected on the basis of its direct applicability to the mathematical ideas usually introduced in grades K-6. The content is presented in conjunction with appropriate teaching strategies, determined by research…