The arithmetical performance of typically achieving 5- to 7-year-olds (N=29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear…

The cognitive processes underlying quantitative estimations vary. Past research has identified task-contingent changes between rule-based and exemplar-based processes (P. Juslin, L. Karlsson, & H. Olsson, 2008). B. von Helversen and J. Rieskamp (2008), however, proposed a simple rule-based model--the mapping model--that outperformed the…

The hierarchical competing systems model (HCSM) provides a framework for understanding the emergence and early development of executive function--the cognitive processes underlying the conscious control of behavior--in the context of search for hidden objects. According to this model, behavior is determined by the joint influence of a…

A problem addressed infrequently in beginning physics courses is that of a moving body with changing mass. Elementary texts often have footnotes referring to jet planes and rockets but rarely do they go further. This omission is understandable because calculations with variable mass generally require the tools of calculus. This paper presents a…

We discuss the identification, estimation, and testing of structural equation models that have causal indicators. We first provide 2 rules of identification that are particularly helpful in models with causal indicators--the 2C emitted paths rule and the exogenous X rule. We demonstrate how these rules can help us distinguish identified from…

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,…

This study compared the accuracies of four differential item functioning (DIF) estimation methods, where each method makes use of only one of the following: raw data, logistic regression, loglinear models, or kernel smoothing. The major focus was on the estimation strategies' potential for estimating score-level, conditional DIF. A secondary focus…

Growth modeling using longitudinal data seems to be a promising direction for improving the methodology associated with the accountability movement. Longitudinal modeling requires that the measurements of ability are comparable over time and on the same scale. One way to create the vertical scale is through concurrent estimation with…

The purpose of this study was to analyze participants' levels of hemoglobin as they performed arithmetic mental calculations using Optical Topography (OT, helmet type brain-scanning system, also known as Functional Near-Infrared Spectroscopy or fNIRS). A central issue in cognitive neuroscience involves the study of how the human brain encodes and…

"Report of a Workshop on the Scope and Nature of Computational Thinking" presents a number of perspectives on the definition and applicability of computational thinking. For example, one idea expressed during the workshop is that computational thinking is a fundamental analytical skill that everyone can use to help solve problems, design…

The concepts of Newtonian mechanics, fluids, and ideal gas law physics are often treated as separate and isolated topics in the typical introductory college-level physics course, especially in the laboratory setting. To bridge these subjects, a simple experiment was developed that utilizes computer-based data acquisition sensors and a digital gram…

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

Through professional development activities involving action research, middle-grades teachers at this author's school learned how to honor students' prior knowledge and experience by finding out about their K-5 computational development. Rather than complaining about what their students did not know, they learned to appreciate results from their…