As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

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…

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…

Research has highlighted the potential of digital technology to support the development of children's number sense abilities. However, the main focus of such research has been on apps affording directed interactions, where only one solution strategy is available, and it has targeted mostly cardinality. Little is known, in these terms, about task…

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…

This paper provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how…

Number sense has been considered as one of the most important mathematical notions to be addressed in school mathematics in the 21st century. In this paper, we identify how students of a public middle school, located in a rural area in Mexico, showed several aspects of number sense by performing tasks involving arithmetic operations in a shopping…

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…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…

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…

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…