This study examined the effects of the concrete-representational-abstract integrated sequence (CRA-I) on teaching place value concepts and their application. The research questions addressed the extent to which CRA-I changed student performance in (a) completing equations that required subtraction with regrouping in the tens place, (b) completing…

The purpose of this study was to analyze the performances of students in solving problems presented in different forms including equations, verbal equations, stories, and stories supported by diagrams in problem-solving. A descriptive survey model was employed in the study. The study group consisted of 14 fourth-grade students. Data were collected…

Despite many studies on students' understanding of the equal sign, little attention has been paid to whole-class discourse on their conceptions of equations with two equal signs. This study analyzed the classroom discourse of 30 fourth graders in Korea who participated in a 5-week classroom teaching experiment. A series of discussions on specific…

The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long…

The International Association for the Evaluation of Educational Achievement (IEA) Research for Education series represents a further effort by IEA to capitalize on it's unique datasets, so as to provide powerful information for policymakers and researchers. Each report focuses on a specific topic and is produced by a dedicated team of leading…

An aggregation strategy is proposed to potentially address practical limitation related to computing resources for two-level multidimensional item response theory (MIRT) models with large data sets. The aggregate model is derived by integration of the normal ogive model, and an adaptation of the stochastic approximation expectation maximization…

Research findings have established that students often struggle with mathematical symbols including common misconceptions for literal symbolic representations of variables but provide little evidence of when or how these misconceptions arise. This article reports findings from a study of grade 4-6 students' conception(s) for various…

Algebra is often considered as difficult and mysterious doctrine due to numerous symbols that represent mathematical notions. Results of the research on students' interpretation of literal expressions show that only a small number of students are ready to accept that a letter can represent a variable. The aim of this research with students of the…

This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students' responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

It is often assumed that a vertical scale is necessary when value-added models depend upon the gain scores of students across two or more points in time. This article examines the conditions under which the scale transformations associated with the vertical scaling process would be expected to have a significant impact on normative interpretations…

This article investigates the use of teacher value-added estimates to assess the distribution of effective teaching across students of varying socioeconomic disadvantage in the presence of classroom composition effects. We examine, via simulations, how accurately commonly used teacher value-added estimators recover the rank correlation between…

Although learning mathematics certainly depends upon accurate understanding of the facts of multiplication, it requires much more. This study examines the relationship between a meaningful understanding of arithmetic operations and the mastery of basic facts. The study began with a joke about a mistaken mathematical fact. The children appreciated…

The current study investigated how young learners' experiences with arithmetic equations can lead to learning of an arithmetic principle. The focus was elementary school children's acquisition of the Relation to Operands principle for subtraction (i.e., for natural numbers, the difference must be less than the minuend). In Experiment 1, children…

This article examines the development of social and ethnic disparities in academic achievement in elementary schooling. It investigated whether reading and mathematics development in 136 mixed-ability classes shows path-dependent processes of cumulative advantage (Matthew effects) from Grades 4 to 6 (Grade 4 mean age = 10.62, SD = 0.57) resulting…