Some current models of mathematical cognition (Dehaene, 1992; Campbell & Clark, 1992) make strong claims about the code in which arithmetical operations are solved, basing themselves on how these operations were originally acquired or are most frequently employed. However, data on acquisition and use are often derived from anecdotic reports…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…

We compared the learning from playing a linear number board game of preschoolers from middle-income backgrounds to the learning of preschoolers from low-income backgrounds. Playing this game produced greater learning by both groups than engaging in other numerical activities for the same amount of time. The benefits were present on number line…

This longitudinal study assessed (a) whether performance changes in working memory (WM) as a function of dynamic testing were related to growth in reading comprehension and (b) whether WM performance among subgroups of children with reading disabilities (RD; children with RD only, children with both reading and arithmetic deficits, and low verbal…

In the elementary grades, students learn procedures to compute the four arithmetic operations on multidigit whole numbers, often by being shown a series of steps and rules. In the middle grades, students are then expected to perform these same procedures, with further twists. The Reasoning and Proof Process Standard suggests that students need to…

Kinesthetic learning, one of the VAK learning styles, is now also being adapted by different gaming consoles and platforms. This paper presents Salapiggy, a two-part kinesthetic educational Sifteo game that has both a tutorial on money and sorting game. It is localized in the Philippines and uses Filipino as the User Interface Language and the…

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…

The main purpose of this study was to investigate the level of student's achievement in mathematics in Yemen. This study use a sample of 200 male students and 200 female students, chosen from eight government schools on the basis of diversified sampling techniques. A mathematics test which composed of seventy five items that covered geometrical…

The primary purpose of the study was to determine if computer-based training programs promoted fluent and flexible use of reasoning strategies to solve addition problems using different tasks. Specifically, does participation in strategy training result in the fluent application of the target strategy on a traditional mental arithmetic task? Does…

Subtraction combinations are particularly challenging for children to learn (Kraner, 1980; Smith, 1921; see Cowan, 2003, for a review). This study examines whether the group of children receiving the "experimental subtraction-as-addition" training outperform the "control" group, which received training on a different reasoning…

Prospective elementary teachers must understand fraction division deeply in order to meaningfully teach this topic to their future students. This paper explores the nature of the subject content knowledge of fraction division possessed by a group of Taiwanese prospective elementary teachers at the beginning of their mathematics methods course. The…

The main aim of this paper is to report on an investigation into primary pre-service and inservice teachers' content knowledge of decimals. The participants were asked to complete four decimal tasks including the ordering of decimals, operating with decimals and converting a fraction to a decimal. The results from both sets of participants are…

In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning…

Using 4 years of mathematics achievement scores, groups of typically achieving children (n = 101) and low achieving children with mild (LA-mild fact retrieval; n = 97) and severe (LA-severe fact retrieval; n = 18) fact retrieval deficits and mathematically learning disabled children (MLD; n = 15) were identified. Multilevel models contrasted…