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…

This study examines the effect of small-group game play before and after a Number Sense Test (NST). Fifty-seven 7-year old children were assigned into two conditions: (a) NST-Game Play, in which students sat for the NST before game play; or (b) Game Play-NST, in which students experienced game play before sitting for the NST. Findings suggested…

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…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts.…

Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small…

Whether human infants spontaneously represent number remains contentious. Clearfield & Mix (1999) and Feigenson, Carey & Spelke (2002) put forth evidence that when presented with small sets of 1-3 items infants may preferentially attend to continuous properties of stimuli rather than to number, and these results have been interpreted as evidence…

Some people automatically and involuntarily "see" mental images of numbers in spatial arrays when they think of numbers. This phenomenon, called number forms, shares three key characteristics with the other types of synaesthesia, within-individual consistency, between-individual variety, and mixture of regularity and randomness. A theoretical…

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition…

How can it be explained that early literacy and numeracy share variance? We specifically tested whether the correlation between four early literacy skills (rhyming, letter knowledge, emergent writing, and orthographic knowledge) and simple sums (non-symbolic and story condition) reduced after taking into account preschool attention control,…

The purpose of this study was to determine the efficacy of specific, individualized training for students with different levels of mathematical difficulties. Fifty-four students, with either severe or mild math difficulties, were assigned to individualized training or to a control condition. Ten students with severe math difficulties…

Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…

A number triangle, discovered using a recurrence formula similar to that of Pascal's triangle, yields sequence A077028 from the Online Encyclopedia of Integer Sequences.

Newborn chicks were tested for their sensitivity to number vs. continuous physical extent of artificial objects they had been reared with soon after hatching. Because of the imprinting process, such objects were treated by chicks as social companions. We found that when the objects were similar, chicks faced with choices between 1 vs. 2 or 2 vs. 3…

The main purpose of this research is to determine whether the attainment of the number concept by children aged between 4-7 differs depending on age variant as well as receiving preschool education or not. Attainment of the number concept has been examined by means of One-to-One Matching Test consisting of Piaget's experiments. The test was…