Mathematically speaking, a "difference" is the result of a subtraction. However, when the number domain is extended from natural numbers to integers, the separation of the magnitude of a number from its value creates "different differences," where the connection to subtraction is no longer straightforward. Based on…

This paper explores the ways preschool teachers orchestrate instructional environments to promote mathematical play related to early number and, how they intervene during play to promote children's engagement with early number. We highlight these practices to identify resources for the growing numbers of early childhood teachers. This is important…

Recent work has demonstrated that how we process the relative order--ordinality--of numbers may be key to understanding how we represent numbers symbolically, and has proven to be a robust predictor of more sophisticated math skills in both children and adults. However, it remains unclear whether numerical ordinality is primarily a by-product of…

Young children spend a much greater amount of time on practicing multiplication facts compared to understanding the concept of multiplication. When students have long-term, foundational concepts rather than a series of fragmented algorithms or facts, they are more likely to understand and generalize the mathematics. Using generalized models that…

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Arabic numerals are diffused and language-free representations of number magnitude. To be effectively processed, the digits composing Arabic numerals must be spatially arranged along a left-to-right axis. We studied one patient (AK) to show that left neglect, after right hemisphere damage, can selectively impair the computation of the spatial…

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with…

Advances in technology have seen a proliferation of touch-screen interfaces available to young children. These screens have changed the way in which young children engage with digital technology; with increased exposure and use, it raises debates about the suitability of integrating digital technology within early childhood settings. There are…

With the aid of longitudinal country-level data from five IEA TIMSS assessments (1995--2011), the current study addresses the issue of the globalisation of curricula and achievement. To explore the hypothesis of global convergence, we study performance in four subdomains of mathematics. Using regression with fixed effects for countries, we…

Conceptualizing numbers as discursive constructs generated in, and for the sake of, communication, we investigated the development of the numerical discourse of Milo, a boy who was 2 years and 8 months old when we first met him and whom we then followed for 18 months. Our analyses of the child's evolving responses to the question "Where is…

Research findings in the field of Mathematics Education emphasize that storytelling is an effective instructional tool in the teaching of mathematics, as it provides a meaningful context that attracts students' interest and makes learning a pleasant process. The use of stories and fairy tales in the teaching of mathematics motivates students to…

"Mathematical Lens" uses photographs as a springboard for mathematical inquiry and appears in every issue of "Mathematics Teacher." Recently while dismantling an old wooden post-and-rail fence, Roger Turton noticed something very interesting when he piled up the posts and rails together in the shape of a prism. The total number…

This study was designed to investigate children's abilities to count and make quantitative comparisons. In addition, this study utilized reasoning questions (i.e., how did you know?). Thirty-four preschoolers, mean age 4.5 years old, participated in the study. According to the results, 89% of the children (n = 30) were able to do rote counting and…

In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…