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.…

Play is one of the most widely used teaching strategies in Foundation Phase. Grade 3 is the exit grade off the Foundation Phase in the South African context. This paper is an output of a Masters' dissertation that explored the use of play when teaching number sense to Grade 3 learners. The dissertation findings encouraged the researchers to…

Number line estimation (NLE) tasks are widely used to investigate numerical cognition, learning, and development, and as an instructional tool. Interpretation of these tasks generally involves an implicit expectation that responses are driven by the overall magnitudes of target numerals, in the sense that the particular digits conveying those…

This study aims to explore the notion of the density of the set of rational numbers in the set of real numbers, as interpreted by undergraduate mathematics students. The data comprise 95 responses to a scripting task, in which participants were asked to extend a hypothetical dialog between two student characters, who argue about the existence of…

It is widely assumed within developmental psychology that spontaneously-arising conceptualizations of natural number--those that develop without explicit mathematics instruction--match the formal characterization of natural number given in the Dedekind-Peano Axioms (e.g., Carey, 2004; Leslie et al., 2008; Rips et al., 2008). Specifically,…

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…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

This study explores the identification of discourse communities within mathematics education using factor analysis. Given the exponential growth in mathematics education research, understanding the evolving dialogues within the field has become increasingly challenging. This study employs a systematic literature review, examining the landscape of…

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…