Many counting problems can be modeled as "colorings" and solved by considering symmetries and Polya's cycle index polynomial. This paper presents a "Maple 7" program link http://users.tamuk.edu/kfdrc00/ that, given Polya's cycle index polynomial, determines all possible associated colorings and their partitioning into equivalence classes. These…

Translating numerals into number words is a tacit task requiring linguistic and mathematical knowledge. This project expanded on previous number production models by examining developmental differences in children's number naming errors. Ninety-six children from grades one, three, five, and seven translated a random set of numerals into number…

In education, the term "metacognition" describes thinking about thinking. Within mathematics, the term "metacomputation" describes thinking about computational methods and tools. This article shows how Dr. Edward de Bono's Six Thinking Hats can be used to demonstrate metacognition and metacomputation in the primary classroom.…

In this article, the author presents the results of a state project that focused on the effect of developing informal written computation processes through Years 2-4. The "developing computation" project was conducted in Tasmania over the two years 2002-2003 and involved nine schools: five government schools, two Catholic schools, and…

This article describes a statewide project in which weekly progress monitoring of mathematics was implemented with 120 special education students. Curriculum-based measurement probes for computation and concepts/applications skills were administered weekly over seven months. Students were assessed at levels identified as instructional by their…

The paper proposes a simple methodology to estimate an affluence line that depends on the knowledge of the income distribution and the poverty line for a given population. The idea that poverty is morally unacceptable and can be eradicated through redistribution of wealth provides the grounds for the methodology. The line is defined as the value…

This study uses industrial pollution data from the Environmental Protection Agency's Toxics Release Inventory (TRI) and tract-level demographic data from the 2000 U.S. census to determine whether environmental racial inequality existed in the Detroit metropolitan area in the year 2000. This study differs from prior environmental inequality…

The authors conducted design or classroom experiments (R. Gersten, S. Baker, & J. W. Lloyd, 2000) at 2 sites (Pennsylvania and Florida) to test the effectiveness of schema-based instruction (SBI) prior to conducting formal experimental studies. Results of Study 1 conducted in 2 3rd-grade, low-ability classrooms and 1 special education…

This document is a collection of activity-based mathematics lessons for grades 5-8 from the "Ideas" department in "Arithmetic Teacher: Mathematics Education through the Middle Grades." Each lesson includes background information, objectives, directions, extensions, and student worksheets. A matrix is included which correlates…

An international numeracy scale compared how well adults in seven countries--the United Kingdom, France, Netherlands, Sweden, Japan, Australia, and Denmark--handled some basic tasks involving numbers. The questionnaire comprised a set of 12 numeracy tasks that respondents were asked to complete using pen and paper. Within each country, the…

Increasing attention is being paid today to the place of science in general education at the preprimary, primary, and secondary levels. Educational authorities and specialists in many countries throughout the world agree about the important role that science should and can play in the context of education, but specific aims and objectives must be…

Disorder and linearity are essential to science, but empirically derived laws indicate that counts do reflect underlying structure and can support inference. Starting from the premise that a linear structure underlies data, G. Rasch deduced that the necessary and sufficient mechanism to convert from counts to linear measures is the logistic ogive.…

This guide is organized around a list of skills that all students should know and be able to do at each grade level from kindergarten through sixth grade. It provides parents, teachers, and students with knowledge of what is being taught in a logical scope and sequence by grade level. The purpose of this guide is to help build a basis for…

This document offers instructional materials for a 60-hour course on basic math operations involving decimals, fractions, and proportions as applied in the workplace. The course, part of a workplace literacy project developed by Mercer County Community College (New Jersey) and its partners, contains the following: course outline; 17 lesson…

A course is described which was designed to: (1) teach correct use of the calculator; (2) teach appropriate techniques for solving arithmetic problems using the calculator; and (3) develop number sense in students through teaching of appropriate facts, concepts, and techniques to be carried out mentally without the calculator. (Number sense starts…