In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules.…

Near the conclusion of their final term in the calculus sequence at The United States Military Academy, cadets are given a week long group project. At the end of the week, the project is briefed to their instructors, classmates, and superior officers. From a teaching perspective, the goal is to encapsulate as much of the course as possible in one…

A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…

The Mobius strip, torus, and Klein bottle are used to graphically and analytically illustrate the differences between orientable and non-orientable surfaces. An exercise/laboratory project using the non-orientable Boy surface is included. (Contains 11 figures.)

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…

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…