In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into…

Chess is a game of minds, bodies, and emotions. Most players recognize each of these as essential to playful competition, and all three are embedded in social relations. Thus chess, despite its reputation as a game of the mind, is not only a deeply thoughtful exercise, but also a test of physical endurance and strong emotions in its joys and…

The development of numerical concepts is described from infancy to preschool age. Infants a few days old exhibit an early sensitivity for numerosities. In the course of development, nonverbal mental models allow for the exact representation of small quantities as well as changes in these quantities. Subitising, as the accurate recognition of small…

Many developmental mathematics programs emphasize computational fluency with the assumption that this is a necessary contributor to student success in general studies mathematics. In an effort to determine which skills are most essential, scores on a computational fluency test were correlated with student success in general studies mathematics at…

Governments and other stakeholders have become increasingly interested in assessing the skills of their adult populations in order to monitor how well prepared they are to meet the challenges of the new information world. The current paper provides an overview of the conceptual framework for the assessment of numeracy developed for the OECD's…

In regression analysis, the notion of population validity is of theoretical interest for describing the usefulness of the underlying regression model, whereas the presumably more important concept of population cross-validity represents the predictive effectiveness for the regression equation in future research. It appears that the inference…

Discusses the importance of mental mathematics beyond the middle school. Presents sample objectives for different courses or strands, and teaching ideas to make mental mathematics an important, ongoing goal in secondary mathematics instruction and beyond. (KHR)

Describes the basic and exceptional calculation abilities of a calculating prodigy whose performances were investigated in single- and multi-digit number multiplication, numerical comparison, raising of powers, and short-term memory tasks. Shows how his highly efficient long-term memory storage and retrieval processes, knowledge of calculation…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

Reported is a teacher's efforts to introduce mental methods in arithmetic to seven-year-olds over a four-week period. (PK)

Reviews research concerning problems in children's understanding of place value in multidigit numbers. Discusses four elements essential to programs focusing on place value: counting, partitioning, grouping, and understanding number relationships. Proposes a framework and an educational program for nurturing and assessing children's understanding…