Does modeling matter? We address this question by providing a broad survey of the computational models of cognitive development that have been proposed and studied over the last three decades. We begin by noting the advantages and limitations of computational models. We then describe four key dimensions across which models of development can be…

In this article, the author shares his comments on statistical analysis for multisite trials, and focuses on the contribution of Stephen Raudenbush, Sean Reardon, and Takako Nomi to future research. Raudenbush, Reardon, and Nomi provide a major contribution to future research on variation in program impacts by showing how to use multisite trials…

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

A basketball player attempting a free throw has two parameters under his or her control: the angle of elevation and the force with which the ball is thrown. We compute upper and lower bounds for the initial velocity for suitable values of the angle of elevation, generating a subset of the configuration space of all successful free throws. A…

It has been hypothesized that developmental dyscalculia (DD) is either due to a defect of the approximate number system (ANS) or to an impaired access between that system and symbolic numbers. Several studies have tested these two hypotheses in children with DD but none has dealt with adults who had experienced DD as children. This study aimed to…

Viscous damping is commonly discussed in beginning differential equations and physics texts but dry friction or Coulomb friction is not despite dry friction being encountered in many physical applications. One reason for avoiding this topic is that the equations involve a jump discontinuity in the damping term. In this article, we adopt an energy…

The purpose of this study was to examine the potential for using propensity score-based matching methods to estimate teacher contributions to student learning. Value-added models are increasingly used in teacher accountability systems in the United States in spite of ongoing qualms about the validity of teacher quality estimates resulting from…

C-tests are a specific variant of cloze tests that are considered time-efficient, valid indicators of general language proficiency. They are commonly analyzed with models of item response theory assuming local item independence. In this article we estimated local interdependencies for 12 C-tests and compared the changes in item difficulties,…

The slow flow of a viscous liquid is a thought-provoking experiment that challenges students, academics and the public to think about some fundamental questions in modern science. In the Queensland demonstration--the world's longest-running experiment, which has earned the Ig Nobel prize--one drop of pitch takes about ten years to fall, leading to…

In this computational experiment, students use advanced quantum chemistry tools to simulate the photochromic reaction mechanism in naphthopyran derivatives. The first part aims to make students familiar with excited-state reaction mechanisms and addresses the photoisomerization of the benzopyran molecule by means of semiempirical quantum chemical…

The Remember/Know procedure, developed by Tulving (1985) to capture the distinction between the conscious correlates of episodic and semantic retrieval, has spawned considerable research and debate. However, only a handful of reports have examined the recognition content beyond this dichotomous simplification. To address this, we collected…

Multi-voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel…

One approach for combining single-case data involves use of multilevel modeling. In this article, the authors use a Monte Carlo simulation study to inform applied researchers under which realistic conditions the three-level model is appropriate. The authors vary the value of the immediate treatment effect and the treatment's effect on the time…

As applications of multilevel modelling in educational research increase, researchers realize that multilevel data collected in many educational settings are often not purely nested. The most common multilevel non-nested data structure is one that involves student mobility in longitudinal studies. This article provides a methodological review of…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…