The notion that mental arithmetic is associated with shifts of spatial attention along a spatially organised mental number representation has received empirical support from three lines of research. First, participants tend to overestimate results of addition and underestimate those of subtraction problems in both exact and approximate formats.…

People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in…

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade…

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…

The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this…

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

"Improving Mathematics in the Early Years and Key Stage 1" reviews the best available evidence to offer five recommendations for developing the maths skills of 3-7-year olds. Recommendations include integrating maths into different activities throughout the day -- for example, at registration and snack time -- to familiarise children…

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard…

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…

In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child's level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children's mathematical reasoning,…

McCrink (McCrink, Dehaene, & Dehaene-Lambertz (2007). "Moving along the number line: Operational momentum in nonsymbolic arithmetic." "Perception and Psychophysics," 69(8), 1324-1333) documented an "Operational Momentum" (OM) effect--overestimation of addition and underestimation of subtraction outcomes in non-symbolic (dot pattern) arithmetic. We…

The underlying neural mechanisms of developmental dyscalculia (DD) are still far from being clearly understood. Even the behavioral processes that generate or influence this heterogeneous disorder are a matter of controversy. To date, the few studies examining functional brain activation in children with DD mainly focus on number and counting…

Number sense has been recognised as central to young children's development of mathematics for a number of decades. A student with a "good" sense of number normally has a thorough understanding of relationships among numbers and operations--being able flexibly to partition and combine numbers in convenient ways to allow appropriate…

Zoo Zillions contains five activities for grades K-2: Annie's Jungle Trail, 3D Gallery, Number Line Express, Gnu Ewe Boutique, and Fish Stories. These activities enable children to review and practice basic mathematics skills; identify three-dimensional shapes, watch them in motion, and create their own three-dimensional designs; locate numbers…

The Assessment Tool for Moderately Retarded Students in Academic Skills (1978) is designed for moderately retarded students (5-21 years) and mildly retarded students (3-14 years) who will be living in sheltered home and work settings. The assessment tool is based on a life centered curricular model concerned with developing--in a sequential…