As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

In this paper we report on findings from a study of 5-to-6-year-old children's ways of structuring part-part-whole relations using finger patterns. We focused our analysis on data from interviews with 28 children who during their last year of preschool learned to enact a structural approach. We used this data set to analyze their different ways of…

Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed…

In Asia, some children are taught a calculation technique known as the 'mental abacus'. Previous research indicated that mental abacus experts can perform extraordinary feats of mental arithmetic, but it disagrees as to whether the technique improves working memory. The present study extended and clarified these findings by contrasting performance…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students' difficulty in mental calculations with rational numbers as has also the switching to…

Although an increasing number of studies have suggested that students with low mathematics achievement (LMA) tend to perform worse in arithmetic strategy use than children with typical development, the potential reasons remain unclear. Accordingly, the current study investigated the potential impact of task switching on strategy use for children…

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high…

It is aimed to determine the strategies used by the fourth-grade elementary students during the operational estimations in this research which is designed by using basic qualitative analysis. The study group consists of 26 fourth-grade students selected through convenience sampling method and attending at a state school which was located in the…

This paper provides insight about the development of addition and subtraction strategies for nearly 22,000 Australian primary school children in 2016. The children were each assessed by their teacher using a task-based assessment interview that identified the strategies they used to mentally perform addition and subtraction, and matched these to a…

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. "Solving for x" in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems…

This study was conducted on year 4 students enrolled in the Bachelor of Education program for Cycle one teacher candidates. The effect of practicing mental calculation strategies in improving students' numeracy proficiency was put under some tests to measure its effect in a scientific way. A Pre-quiz was conducted before with no prior practice…

Three studies explore arithmetic tasks that support both substitutive and basic relational meanings for the equals sign. The duality of meanings enabled children to engage meaningfully and purposefully with the structural properties of arithmetic statements in novel ways. Some, but not all, children were successful at the adapted task and were…