This study used fraction number line estimation tasks to evaluate students' developmental patterns, and the relationship of such tasks with whole number bias was explored. In total, 189 fourth-grade students in a northern Taiwan elementary school were followed over 2 years. The results demonstrated that the students' fraction learning development…

Theoretical frameworks for mathematics teaching and learning technology-supported provide a systematic structure in examining the contribution of the tool to conceptual development. This study examines the processes for the use of spreadsheets and the mathematical development of the participants in the tasks for performing the conversions between…

Research Findings: This study examined age-based developmental trajectories of four key number sense (NS) skills within an accelerated longitudinal design. Using data from 408 preschoolers, ages 45 to 68 months, linear and latent basis growth curves were evaluated. Results indicated growth across NS skills was best represented as nonlinear for all…

In Spanish, the plural form in plural dominant frequency pairs, like "diente/dientes" [tooth/teeth], occurs more frequently than the corresponding singular form. On the other hand, for the singular dominant frequency pairs such as "cometa/cometas" [kite/kites], the singular form is more common than the plural. The recognition…

Research has shown a link between the acquisition of numerical concepts and language, but exactly how linguistic input matters for numerical development remains unclear. Here, we examine both symbolic (number word knowledge) and non-symbolic (numerical discrimination) numerical abilities in a population in which access to language is limited early…

Given its pedagogical appeal, the number line is a commonly used representation in the teaching and learning of fractions. However, behind its apparent simplicity, this mathematical object may involve layers of complexity when looked at from the perspective of affordances as is the case in this study. In particular, this in situ exploration…

Number and operations form the backbone of the school mathematics curriculum. A high school graduate should comfortably and capably meet an expression like, "Let f(x) be a function of a real variable x," implying that the student has a robust sense of the real number continuum. This understanding is a central objective of the school…

One important concept in the development of number knowledge is the cardinality principle, or knowing that the last word counted refers to the total number of items within the set. One prominent theory suggests that children learn this concept by observing sets being both counted and labeled with the correct set size (e.g., 1-2-3! 3!), thus…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

The study set out to explore different mathematical difficulties among 877 second-grade children and to test the effect of memorization versus conceptual practices with number combinations. It used a latent profile analysis of baseline measurements of digit writing speed, number combination fluency, multidigit calculation, and number sense skills…

Children's participation in cultural, everyday practices and social interactions involving math and money can contribute to the development of their knowledge and skills in these domains. Further work is needed to uncover what features of these activities, such as aspects of the conversations that may occur (e.g., number and money talk),…

Children's early accuracy on place value (PV) tasks longitudinally predicts their later multidigit calculation skills. However, another window into children's emerging base-ten concepts is the pattern of errors -- "smart errors" -- they exhibit on these measures. Past research has speculated that these smart errors -- similar to invented…

This design-based study addresses the issue of how to digitally support students' problem-solving by providing heuristics, in the absence of the teacher. The problem is that, so far, digital tutoring systems lack the ability to diagnose students' needs in open problem situations. Our approach is based on students' ability to self-diagnose and find…

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…