The main goal of this paper is to show how Vasily Davydov's powerful ideas about the nature of mathematical thinking and learning can transform the teaching and learning of additive word problem solving. The name Vasily Davydov is well known in the field of mathematics education in Russia. However, the transformative value of Davydov's theoretical…

The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operation and examines the deficiencies of existing…

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations.…

This article reviews a particular computational modeling approach to the study of psychological development--that of constructive neural networks. This approach is applied to a variety of developmental domains and issues, including Piagetian tasks, shift learning, language acquisition, number comparison, habituation of visual attention, concept…

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One,…

This paper challenges the emphasis on counting in New Zealand's Numeracy Development Project (NDP), arguing that subitizing provides an alternative pathway to quantification. Longitudinal data is presented showing that children's subitizing skills at the age of five years were a strong predictor of their later success in mathematics at the age of…

This study was designed to investigate preservice elementary school teachers' (PSTs') responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs' conceptions, two correct and two incorrect.…

The aim of the study was to elucidate whether and how reliance on a second language impacts the learning of new information under very basic learning conditions. The paradigm used to investigate this issue required individuals to learn a series of associations between numerals and particular letter strings. Participants were two groups of…

This study examines the reliability and validity of a Chinese-translated version of the Gifted Rating Scales-Preschool/Kindergarten Form (GRS-P) and explores the effect of gender and age on each of the subscales. Data were collected from 250 kindergarten children, with age ranging from 4 years, 0 months to 6 years, 11 months. Results indicated…

The present paper provides a critical overview of how adult neuropsychological models have been applied to the study of the atypical development of numerical cognition. Specifically, the following three assumptions are challenged: 1. Profiles of strength and weaknesses do not change over developmental time. 2. Similar neuronal structures are…

Through the importance of the number three in our culture and the strange preference for a ternary pattern of our nature one can perceive how and why number theory degraded to numerology. The strong preference of our minds for simple patterns can be read as the key to understanding not only the development of numerology, but also why scientists…

A current issue in developmental science is that greater continuity in cognition between children and adults may exist than is usually appreciated in Piaget-like (stages or "staircase") models. This phenomenon has been demonstrated at the behavioural level, but never at the brain level. Here we show with functional magnetic resonance imaging…

Children (n = 122) and adults (n = 200) with dyslexia completed rapid automatic naming (RAN) letters, rapid automatic switching (RAS) letters and numbers, executive function (inhibition, verbal fluency), and phonological working memory tasks. Typically developing 3rd (n = 117) and 5th (n = 103) graders completed the RAS task. Instead of analyzing…

This study examined the hypothesis of superior quantification abilities of persons with high functioning autism (HFA). Fourteen HFA individuals (mean age: 15 years) individually matched with 14 typically developing (TD) participants (gender, chronological age, full-scale IQ) were asked to quantify as accurately and quickly as possible…

This study evaluated the generally recommended concrete-to-abstract hierarchy for presenting a new skill, with three students with learning disabilities in grades 1, 2, and 4. The three subjects enrolled in the Multidisciplinary Diagnostic and Training Program's classroom housed on the University of Florida campus in Gainesville. Following…