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…

We present mentally efficient algorithms for mentally squaring and cubing 2-digit and 3-digit numbers and for finding cube roots of numbers with 2-digit or 3-digit answers.

This article studies the convergence of the infinite series of the reciprocals of the Catalan numbers. We extract the sum of the series as well as some related ones, illustrating the power of the calculus in the study of the Catalan numbers.

We introduce Lake Wobegon dice, where each die is "better than the set average." Specifically, these dice have the paradoxical property that on every roll, each die is more likely to roll greater than the set average on the roll, than less than this set average. We also show how to construct minimal optimal Lake Wobegon sets for all "n" [greater…

WYTHOFF is played on a pair of nonnegative integers, (M, N). A move either subtracts a positive integer from precisely one of M or N such that the result remains nonnegative, or subtracts the same positive integer from both M and N such that the results remain nonnegative. The first player unable to move loses. RATWYT uses rational numbers…

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

This study aims to identify errors made by primary school students when modelling word problems and to eliminate those errors through scaffolding. A 10-question problem-solving achievement test was used in the research. The qualitative and quantitative designs were utilized together. The study group of the quantitative design comprises 248…

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…

In 1859, on the occasion of being elected as a corresponding member of the Berlin Academy, Bernard Riemann (1826-66), a student of Carl Friedrich Gauss (1777-1855), presenteda lecture in which he presented a mathematics formula, derived from complex integration, which gave a precise count of the primes on the understanding that one of the terms in…

In general, units coordination refers to the relationships that students can maintain between various units when working within a numerical situation. It is critical that middle school students learn to coordinate three levels of units not only because of their importance in understanding fractions but also because of their implications for…

The collection of studies in this special issue make an important contribution to our understanding and measurement of the core cognitive and noncognitive factors that influence children's emerging quantitative competencies. The studies also illustrate how the field has matured, from a time when the quantitative competencies of infants and young…

The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this…

There is substantial evidence that preschooler's performance in early math is highly correlated to math performance throughout school as well as academic skills in general. One way to help children attain early math skills is by using targeted educational software and the paper discusses potential gains of using such software to support early math…

This article presents findings from the first major study to investigate lexical variation and change in British Sign Language (BSL) number signs. As part of the BSL Corpus Project, number sign variants were elicited from 249 deaf signers from eight sites throughout the UK. Age, school location, and language background were found to be significant…

Gestures such as finger counting, pointing, and touching have been found to facilitate mathematical development in preschool and school-aged children. However, little is known about the types of mathematically related gestures used by parent-toddler dyads to facilitate early mathematics learning during the first 3 years of life. A total of 24…