Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the "official" algebraic form of talk. In this paper we take a look at the very beginning of…

The present study aimed to make an error analysis in the problems posed by pre-service elementary mathematics teachers about fractional division operation. It was carried out with 64 pre-service teachers studying in their final year in the Department of Mathematics Teaching in an eastern university during the spring semester of academic year…

Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized…

Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols. We studied the role of syntax in arithmetic thinking, a neglected component of numerical cognition, by examining eye movement sequences during the…

The purpose of this study was to explore strategies used by high-achieving 6th grade students in the United Arab Emirates (UAE) to solve basic arithmetic problems involving number sense. The sample for the study consisted of 15 high-achieving boys and 15 high-achieving girls in grade 6 from 2 schools in the Emirate of Abu Dhabi, UAE. Data for the…

Individuals diagnosed with fragile X syndrome (FXS), the most common known form of inherited intellectual disability, are reported to exhibit considerable deficits in mathematical skills that are often attributed to brain-based abnormalities associated with the syndrome. We examined whether participants with FXS would display emergent…

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach,…

This study aims at examining problematic learning trajectories of students with emotional behavioral disorders (EBD) by means of a longitudinal and time serial (micro genetic) study of individual instruction sessions during arithmetic lessons. Micro genetic analysis techniques were applied on the variable "responsiveness" in the scaffolding…

This intervention study was conducted to document conditions under which a computer based literacy game (GraphoGame™) could enhance literacy skills of first grade students in an African city. The participants were first grade students from Government schools (N = 573). These students were randomly sampled into control (N = 314) and various…

This dissertation is devoted to a history of the New York State elementary school teacher certification requirements, specifically in mathematics, during the nineteenth century. In the last half of nineteenth century, teacher education and uniform certification procedures were beginning to become the norm in the educational systems throughout the…

While both conscious and unconscious reward cues enhance effort to work on a task, previous research also suggests that conscious rewards may additionally affect speed-accuracy tradeoffs. Based on this idea, two experiments explored whether reward cues that are presented above (supraliminal) or below (subliminal) the threshold of conscious…

Solving simple arithmetic word problems is a major ability that children must acquire throughout the primary-grade mathematics curriculum. However, this skill is often challenging for them. For instance, "unknown referent problems" are more difficult to solve than "unknown compare problems." In unknown compare problems, the…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

This study concerns pupils' experience of unit and non-unit fractions of a discrete quantity during specially designed lessons. The aim was to explore pupils' understanding of operations such as "b/c of a" in lessons where the teachers were aware of some pupils' difficulties beforehand and what needed special attention.…

Researchers debate whether one represents the magnitude of a fraction according to its real numerical value or just the discrete numerosity of its numerator or denominator. The present study examined three effects based on the notion that people possess a mental number line to explore how children represent fractions when they compare fractions…