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…

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…

This article describes an innovative lesson that uses the biography "Barbara McClintock: Alone in her Field" (Heiligman, 1994) to integrate genetics, literature, and mathematics as a context for students to investigate patterns on Indian corn. This two-day lesson requires students to estimate, collect data, identify and describe patterns,…

This article discusses relationships between the development of an understanding of algorithms and algebraic thinking. It also provides some sample activities for middle school teachers of mathematics to help promote students' algebraic thinking. (Contains 11 figures.)

Model-based equating was compared to empirical equating of an Armed Services Vocational Aptitude Battery (ASVAB) test form. The model-based equating was done using item pretest data to derive item response theory (IRT) item parameter estimates for those items that were retained in the final version of the test. The analysis of an ASVAB test form…

As part of No Child Left Behind (NCLB) legislation, many states are using confidence intervals to determine a range of scores for evaluating a school system. More specifically, the states are employing confidence intervals to help minimize measurement error in determining a school system's performance. The methodology and techniques employed in…

The risk of individual citizen's investment in education specifically refers to the benefit changeability of individual investment in education. Risks always go with uncertainty. By adopting the method of quantile regression estimation and taking the Chinese urban citizens as samples, the author makes a positivist study of the risk of Chinese…

Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the…

Teachers often encounter difficulty in teaching estimation of measurement to young children. The intention when teaching the typical "jelly bean jar" classroom activity is to help children develop estimation skills, but most children cannot conceptualise the difference between guessing and estimating. The fact is that many students view…

This article describes an activity that involves the use of simulation for decision-making. It is useful for demonstrating concepts in probability and statistics. (Contains 4 figures and 2 tables.)

The calculation of composite indicators and the derivation of respective rankings is a common method used to benchmark countries or regions. However, although the statistical robustness of these rankings is often criticised, they often still spark off heated political debate. Here, we assess the sensitivity of the province ranking published by the…

This article describes the Mathematics Investigation Center (MIC), a tool to help elementary teachers differentiate the curriculum for their gifted mathematics students. Using the same mathematical theme that the rest of the class is studying, the activities provide depth for the gifted students by shifting from a computation level to a problem…

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…