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…

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…

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…

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…

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 investigated the role of strategy instruction and working memory capacity (WMC) on word problem solving accuracy in children with (n = 100) and without (n = 92) math difficulties (MD). Within classrooms, children in Grades 2 and 3 were randomly assigned to one of four treatment conditions: verbal-only strategies (e.g., underlining…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

The purpose of this study was to determine whether patterns of strategy use in second, third and fourth grade children's arithmetic supported Steffe's model of numerical development. In addition to student-generated strategies, we looked at commonly taught algorithms not considered in Steffe's model to determine whether these algorithms reflected…

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

The use of problem-solving strategies by 59 deaf and hard of hearing children, grades K-3, was investigated. The children were asked to solve 9 arithmetic story problems presented to them in American Sign Language. The researchers found that while the children used the same general types of strategies that are used by hearing children (i.e.,…

This paper highlights the Indonesian's road transportation contexts, namely, angkot, that used in learning and teaching of addition and subtraction in first grade and second grade MIN-2 Palembang. PMRI approach that adopt from RME [Realistic Mathematics Education] was used in this design research. From teaching experiment was founded that the…

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…