An agreement table with [n as an element of N is greater than or equal to] 3 ordered categories can be collapsed into n - 1 distinct 2 x 2 tables by combining adjacent categories. Vanbelle and Albert ("Stat. Methodol." 6:157-163, 2009c) showed that the components of Cohen's weighted kappa with linear weights can be obtained from these n - 1…

Cognitive development and learning are characterized by diminished reliance on effortful procedures and increased use of memory-based problem solving. Here we identify the neural correlates of this strategy shift in 7-9-year-old children at an important developmental period for arithmetic skill acquisition. Univariate and multivariate approaches…

The aim of this article is to establish some interesting inequalities involving arithmetic functions.

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

Purpose: Counting and exact arithmetic rely on language-based representations, whereas number comparison and approximate arithmetic involve approximate quantity-based representations that are available early in life, before the first stages of language acquisition. The objective of this study was to examine the impact of language abilities on the…

The purpose of this study is to investigate the mathematical literacy of the 15-year-old students in terms of PISA mathematical literacy questions. The research model of this study is the survey model in the quantitative models. The sample of this study was composed of 1.227 students who received formal education in five different types of schools…

While the value of "schematic representations" in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of "schematic…

This article outlines a discussion had by a group of prospective teachers regarding questions that remained after their previous experiences as students. The discussion was focused on the rules associated with the division of decimals. Prospective teachers' initial discussion showed a strong tendency to handle the rules as taken-for-granted…

This discussion article addresses issues related to expansion of the Wechsler model from four to five factors; multiple broad CHC abilities measured by the Arithmetic subtest; advantages and disadvantages of including complex tasks requiring integration of multiple broad abilities when measuring intelligence; limitations of factor analysis, which…

Preservice elementary teachers often struggle with prime decomposition and other mathematical topics that correlate with number theory. This paper provides a framework for integrating prime factor tiles into their curriculum with a particular emphasis on prime decomposition. Using this framework, preservice teachers explored and evaluated numbers…

Technology has become a major force in developing curricula and educational practice in mathematics education internationally. While many technologies are important in affluent developed countries, the hand-held calculator continues to be the technology most likely to be available to students when and where they need it. Modern calculators have…

This study examined interventions for addition and subtraction that were implemented through single-case design (SCD) research studies. We attempted to extend prior SCD meta-analyses by examining differences in effect sizes across several moderating variables and by including a novel index of effect, improvement rate difference (IRD). We also…

A sophisticated and flexible understanding of the equals sign (=) is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator and the equals sign as signaling the same value on both sides of the equation. We argue…

Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…