Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…

This article describes a mathematics lesson taught by a 5th grade teacher who engages her class in an in-depth examination of one student's incorrect solution to a problem. Because the teacher consistently asks her students to devise alternative calculation strategies and explain how those strategies work, the students have come to expect that…

The aim of this study is to describe and analyze students' levels of understanding of exponents within the context of procedural and conceptual learning via the conceptual change and prototypes' theory. The study was conducted with 202 secondary school students with the use of a questionnaire and semi-structured interviews. The results suggest…

An exercise to compute LLE data is presented to illustrate the problems that can arise when the isoactivity equilibrium condition is used in the LLE calculations. A much more efficient condition is obtained when isoactivity is combined with the common tangent line criterion, avoiding false solutions that correspond with very low values of the…

In the "Sydney Morning Herald" of 23 March 2005, Ross Gittins argued that the funding arrangements for private schools positively encourage parents to move their children from the state system. The then Federal Minister for Education, Dr Brendan Nelson, in a letter to the "Herald" of 25-27 March, responded by saying that 68% of…

In this paper we present new evidence on the impact of school characteristics on secondary student achievement using a rich dataset from rural Bangladesh. We deal with a potentially important selectivity issue in the South Asian context: the non-random sorting of children into madrasas (Islamic faith schools). We do so by employing a combination…

The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain…

Consider test data, a specified set of dichotomous skills measured by the test, and an IRT cognitive diagnosis model (ICDM). Statistical estimation of the data set using the ICDM can provide examinee estimates of mastery for these skills, referred to generally as attributes. With such detailed information about each examinee, future instruction…

The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways…

Multinomial-response models are available that correspond implicitly to tests in which a total score is computed as the sum of polytomous item scores. For these models, joint and conditional estimation may be considered in much the same way as for the Rasch model for right-scored tests. As in the Rasch model, joint estimation is only attractive if…

The past two decades have seen a rising trend in the minimum entrance age for kindergarten in the U.S. A little-noticed, but potentially large, consequence of raising the minimum entrance age is that it imposes additional childcare costs for families whose children are forced to stay out of school for an additional year. This paper develops a…

This article responds to the reply by Cooper and Shallice to Botvinick and Plaut's previous comment . In the authors' view, the reply by Cooper and Shallice left their original responses more or less intact. The present exchange has strongly highlighted the degree to which any account of the habit system will interact with how the goal-directed…

In this article, the author argues that there is a big conceptual difference between number lines and number strips and that number lines should be consistently used as early as Y1. Her interest in the use of the number line as a powerful image of the real numbers, and how this is introduced in the early years, comes from her own experience as a…

Structural equation modeling allows several methods of estimating the disattenuated association between 2 or more latent variables (i.e., the measurement model). In one common approach, measurement models are specified using item parcels as indicators of latent constructs. Item parcels versus original items are often used as indicators in these…

The computation and reporting of effect size estimates is becoming the norm in many journals in psychology and related disciplines. Despite the increased importance of effect sizes, researchers may not report them or may report inaccurate values because of a lack of appropriate computational tools. For instance, Pierce, Block, and Aguinis (2004)…