In preparing to teach speed to a Y10 intermediate class in a multicultural secondary modern, the author was aware of the difficulty in getting students not only to follow a complex logical argument, but also to be able to reproduce it in a variety of different problem situations. Normally one would set out the working out of the problem as a…

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…

This paper presents a strategy for measuring cognitive gains in reading during the early school years. It is argued that accurate estimates of gain scores and their appropriate interpretation requires the use of adaptive tests with multiple criterion referenced points that mark learning milestones. It is further argued that two different measures…

Teachers can use pedometers to facilitate inquiry learning and show students the need for mathematics in scientific investigation. The authors conducted activities with secondary students that investigated intake and expenditure components of the energy balance algorithm, which led to inquiries about pedometers and related data. By investigating…

NCTM Past President Cathy L. Seeley shares her messages on today's most relevant topics and issues in education. Based on Cathy L. Seeley's award-winning NCTM President's Messages, and including dozens of new messages, this must-have K-12 resource offers straight talk and common sense about some of today's most important, thought-provoking issues…

The National Dropout Prevention Center for Students with Disabilities (NDPC-SD) was assigned the task of compiling, analyzing and summarizing the data for Indicator 2--Dropout--from the FY2007 (2007-08 school year) Annual Performance Reports (APRs) and the revised State Performance Plans (SPPs), which were submitted to Office of Special Education…

The National Dropout Prevention Center for Students with Disabilities (NDPC-SD) was assigned the task of compiling, analyzing and summarizing the data for Indicator 1--Graduation--from the 2007- 08 Annual Performance Reports (APRs) and amended State Performance Plans (SPPs), which were submitted by states to the Office of Special Education…

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…