Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…

The statistic of choice to prove that U.S. schools are failing has changed over time. First, it was test scores that meant they could not keep up with Japan. More recently it has become graduation rate. Often accompanying the graduation rate in the failure litany is the drop-out rate. NCLB puts additional pressure on dropout counts because it…

This paper estimates the elasticity of taxable income to the net-of-tax share using a panel of tax returns that follows a random sample of taxpayers from 1999 to 2005, spanning the EGTRRA 2001 and JGTRRA 2003 tax changes. Results suggest that the elasticity of taxable income to the current year's net-of-tax share lies between 0.3 and 0.4 overall,…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the…

In this activity, students will develop an understanding of the economic impact of technology by estimating the cost savings of power management strategies in the classroom. Students will learn how to adjust computer display settings to influence the impact that the computer has on the financial burden to the school. They will use mathematics to…

By providing early, individualized estimates of college costs and financial aid, net price calculators can help prospective college students and their families look past often scary "sticker prices" and start figuring out which colleges they might be able to afford. These online tools, currently available on almost all college websites, can help…

This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures…

For students and their families, deciding whether and where to go to college is one of the most important financial decisions they will ever make. However, unlike buying a computer, house, or car, most prospective students do not know how much it will cost them to attend a particular school until many of their choices about college have already…

Success in early literacy activities is associated with improved educational outcomes, including reduced dropout risk, in-grade retention, and special education referrals. When considering programs that will work for a particular school and context; cost-effectiveness analysis may provide useful information for decision makers. The study…

Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4-8 (aged 9-14). In this paper, we assert that students' development of algebraic…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

Propensity score methods allow investigators to estimate causal treatment effects using observational or nonrandomized data. In this article we provide a practical illustration of the appropriate steps in conducting propensity score analyses. For illustrative purposes, we use a sample of current smokers who were discharged alive after being…

Missing data are a pervasive problem in many psychological applications in the real world. In this article we study the impact of dropout on the operational characteristics of several approaches that can be easily implemented with commercially available software. These approaches include the covariance pattern model based on an unstructured…

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…