We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

The author investigated the effects of the concrete-representational-abstract (CRA) instructional sequence on the computation performance of students with specific learning disabilities and students identified as at risk for failure in mathematics. Researchers have showed the CRA sequence to be effective for teaching basic mathematics facts,…

This article deals with some of the problems that have hindered the application of Samejima's and Thissen and Steinberg's multiple-choice models: (a) parameter estimation difficulties owing to the large number of parameters involved, (b) parameter identifiability problems in the Thissen and Steinberg model, and (c) their treatment of omitted…

Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

Many explanations of the difficulties associated with interpreting object relative clauses appeal to the demands that object relatives make on working memory. MacDonald and Christiansen [MacDonald, M. C., & Christiansen, M. H. (2002). "Reassessing working memory: Comment on Just and Carpenter (1992) and Waters and Caplan (1996)." "Psychological…

Bioinformatics is a relatively new interdisciplinary field that integrates computer science, mathematics, biology, and information technology to manage, analyze, and understand biological, biochemical and biophysical information. We present our experience in teaching an interdisciplinary course, Introduction to Bioinformatics, which was developed…

There are large differences across countries in instructional time in public schooling institutions. For example, among European countries such as Belgium, France and Greece, pupils aged 15 have an average of over a thousand hours per year of total compulsory classroom instruction while in England, Luxembourg and Sweden the average is only 750…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…

Pretest-posttest experimental designs are often used in randomized control trials (RCTs) in the education field to improve the precision of the estimated treatment effects. For logistic reasons, however, pretest data are often collected after random assignment, so that including them in the analysis could bias the posttest impact estimates. Thus,…

This study demonstrates that a popular graphing calculator among students, TI-83 Plus, has a powerful function to draw the NPV profile and find the accurate multiple IRRs for a project with non-conventional cash flows. However, finance textbooks or related supplementary materials do not provide students instructions for this part. The detailed…

This study investigated "individual differences" in different aspects of early number concepts in preschoolers. Eighty 4-year-olds from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; and predicting the results of repeated addition…

Recent empirical literature has seen many multidimensional indices emerge as well-being or poverty measures, in particular indices derived from principal components and various latent variable models. Though such indices are being increasingly and widely employed, few studies motivate their use or report the standard errors or confidence intervals…

This short article describes some useful and quick applications of a cooking electronic balance. Newton's third law, Archimedes buoyancy and an estimate of relative density are accomplished in a very simple way. (Contains 1 figure.)

Recently, R. D. Stoel, F. G. Garre, C. Dolan, and G. van den Wittenboer (2006) reviewed approaches for obtaining reference mixture distributions for difference tests when a parameter is on the boundary. The authors of the present study argue that this methodology is incomplete without a discussion of when the mixtures are needed and show that they…