Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a…

The language that students use with whole numbers can be insufficient when learning integers. This is often the case when children interpret addition as "getting more" or "going higher." In this study, we explore whether instruction on mapping directed magnitudes to operations helps 88 second graders and 70 fourth graders solve…

Research Findings: In this research we explore the relationship between young children's number knowledge and their measurement of length. First, we examined 4- to 5-year-olds' (kindergartners') understanding of and preference for using standard or nonstandard units to measure length. Second, we investigated whether the following tasks were…

The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…

We tested the hypothesis that encoding the numerical-spatial relations in a number board game is a key process in promoting learning from playing such games. Experiment 1 used a microgenetic design to examine the effects on learning of the type of counting procedure that children use. As predicted, having kindergartners count-on from their current…

The current study aimed at exploring the impact of the modality in which numerical trainings proposed in kindergarten school. Participants were recruited from some Sardinian kindergarten schools and were then divided into three groups: a control group, which had to carry out the activities planned by the educational curriculum, and two…

Underperformance in math is a problem with increasing prevalence, complex etiology, and severe repercussions. This study examined the etiological heterogeneity of math performance in a sample of 264 pairs of 12-year-old twins assessed on measures of math achievement, numerosity, and math anxiety. Latent profile analysis indicated 5 groupings of…

The purpose of this study was to examine patterns of mathematical practices evident during children's interactions with touchscreen mathematics virtual manipulatives. Researchers analyzed 33 Kindergarten children's interactions during activities involving apps featuring mathematical content of early number sense or quantity in base ten, recorded…

The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and…

The development of numerical abilities was examined in three groups of 5 year-olds: one including 13 children accomplishing a numerical training in pencil-and-paper format (EG1); another group including 21 children accomplished a homologous training in computerized format; the remaining 24 children were assigned to the control group (CG). The…

Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. Aims: The aim of this study was to test the DD…

This study was conducted to investigate the immediate impacts of preschool attendance on Turkish children's mathematics achievement. The participants were 200 children who attended or did not attend preschool. The number and operation task and the geometric shapes sorting task were used as the data collection tools. The children who attended…

In light of conceptual metaphor theory, historical mathematicians' and students' difficulty with negative numbers reveals that the collecting objects metaphor may be a cognitive obstacle to those first learning about negative numbers. Moreover, consistency of physical motions with targeted ideas is a factor of cognition. Thus, this…

A general program for item-response analysis is described that uses the stabilized Newton-Raphson algorithm. This program is written to be compliant with Fortran 2003 standards and is sufficiently general to handle independent variables, multidimensional ability parameters, and matrix sampling. The ability variables may be either polytomous or…