External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to…

This scoping review describes mathematics intervention studies that include initial skill moderation analyses. Sixteen studies were included that focused on students with or at risk for mathematics difficulties (MD). The results revealed that mathematics intervention studies with initial skill moderation analyses focused on students in…

Mathematical word problem-solving skills are crucial for students across their lives, yet solving such tasks poses challenges for many. Therefore, understanding the characteristics of mathematical word problems that are associated with students' performance is important. The objective of this systematic review and meta-analysis was to evaluate the…

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

Whole-number arithmetic is a core content area of primary mathematics, which lays the foundation for children's later conceptual development. This paper focuses on teaching whole-number multiplication (WNM) to build a stepping stone for children's proportional reasoning. Our intention in writing this paper is to obtain a practice-based perspective…

The definitions serve the purpose of communication and preservation of knowledge in scientific inquiry. However, it is quite often to perceive number sense concept without well-accepted definitions in the field of mathematics education research. Despite the mentioned issue, the current literature on children's number sense provides a glean for…

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be…

This study was undertaken to systematically analyze instructional interventions employed to enhance the mathematical performance of elementary school students with math learning difficulties (MLD). Over 20 years (2003-2023), 34 articles that met the inclusion criteria were included in the analysis. The articles in the study were analyzed in terms…

This meta-analysis examines the effects of numerical competency development in mathematics classrooms. An exhaustive search of the quantitative literature yielded 17 studies with 39 effect sizes. The overall mean effect size, d = 0.88 (p < 0.05), indicates that there is a large positive summary effect of numerical competency development on…

In this meta-analysis of 54 longitudinal studies with over 58,000 students in kindergarten through 12th grade, we examined the predictive nature of early numeracy measured at or before the first year of formal schooling in relation to later mathematics. Results showed that early numeracy significantly predicted mathematics measured after 6 months…

Place value is a foundational competency for primary school mathematics and for this reason we have sought to investigate what the recent and current academic conversations are around this important concept. In this paper we present a survey of literature presented in the Australasian, European and Southern African contexts through a review of…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

We review research literature concerning "number sense" from several related fields. Whereas other authors have pointed to difficulty defining "number sense" or to some degree of inconsistency in the literature, we argue instead that this is a case of polysemy: There are 3 different constructs that go by the same name. In this…

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from…

In this synthesis, we analyzed 10 prealgebraic reasoning interventions for students with mathematics difficulty (MD) in Grades 6 through 8. All interventions focused on one or more prealgebraic concepts including integer operations, algebraic expressions and equations, and functions. Of the 10 intervention studies, six employed single-case design…