There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

The aim of this study was to investigate second-grade elementary school students' performance related to their counting skills, place value understanding, and addition operation in natural numbers. A total of 205 second-grade elementary school students from Turkey participated in this study. The data were collected through a 'Personal Information…

This study aims to examine the differences in numerosity estimation on a right-to-left number line between second- to fourth-grade students and undergraduate students, together with whether number-line estimation is related to basic arithmetic tasks (addition and subtraction). Hence, 53 Arabic-speaking children and 63 Arabic-speaking adults…

The present longitudinal study investigated the developmental trajectories of addition, subtraction, and multiplication fluency; their relationships to general cognitive functions; and potential interrelations between reading fluency and growth in arithmetic fluency for different operations. The central prediction was that measures of arithmetic…

According to social dilemma theory, students may be characterized as being indifferent to reciprocal behavior and disengaged from interacting with the board gaming process. Given a common goal, students' prosociality can affect the collective efficacy and goal achievement motivation that reflects their flow experience in a cooperative-competitive…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to…

The purpose of this study was to examine adult developmental mathematics (ADM) students' knowledge of fraction addition and subtraction as it relates to their demonstrated fraction schemes and ability to disembed in multiplicative contexts with whole numbers. The study was conducted using a mixed methods sequential explanatory design. In the first…

Developing high levels of mathematical skills in students is a concern for teachers worldwide, since most of the fastest growing occupations require significant mathematics or science preparation. Teachers need to be prepared to teach mathematics successfully. If teachers are not fluent in simple mathematical calculations, they may not feel…

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…

PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…

Examined patterns of conceptual and procedural knowledge of addition in 5- to 8-year-olds. Found that children were more successful in noticing that addends had been reordered rather than decomposed and in noticing the decomposition of addends presented with objects rather than with symbols. Also found that profiles of procedural competence were…