Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers' estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the…

Students' construction, coordination, and abstraction of units underlie success across multiple mathematics domains. Structures for coordinating units underscore notions of numbers as composite units (e.g., five is a unit of five and five units of one). In this working group, we seek to facilitate collaboration amongst researchers and educators…

The algebraic group Spin[subscript 3 × 3] arises from spinning collections of the numbers 1-9 on a 3×3 game board. The authors have been using this group, as well as a corresponding online application, to introduce undergraduate students to core concepts in group theory. We discuss the benefits of using this deceptively simple, toy-like puzzle in…

This study examined how colored educational tools improve children's numerosity ("number sense") and/or mathematics. We tested children 6-10 years (n = 3,236) who had been exposed to colored numbers from the educational tools "Numicon" (Oxford University Press, 2018) or "Numberjacks" (Ellis, 2006), which map colors to…

A long-standing debate in the field of numerical cognition concerns the degree to which symbolic and non-symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and…

Researchers, who have studied the understanding of the density property in the set of decimal numbers, have shown that the student uses the property of the discrete of natural numbers to solve tasks related to density. So, a restructuring of concepts is necessary, that is, a conceptual change from "the discrete" to "the dense".…

A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…

This study traces curricular support for concepts related to infinity and division by zero, in both elementary and secondary mathematics curriculum documents in our province. It was motivated by results of our previous and ongoing work related to transition to post-secondary studies in mathematics, in which we identified consistent gaps and…

Ordinality is a fundamental feature of numbers and recent studies have highlighted the role that number ordering abilities play in mathematical development (e.g., Lyons et al. 2014), as well as mature mathematical performance (e.g., Lyons & Beilock, 2011). The current study tested the novel hypothesis that non-numerical ordering ability, as…

In this article, I describe a research/teaching experience I undertook with a class of 5-year-old children in Malta. The topic was subtraction on the number line. I interpret the teaching/learning process through a semiotic perspective. In particular, I highlight the role played by the gesture of forming "frog jumps" on the number line.…

Ever since their serendipitous discovery by Italian mathematicians trying to solve cubic equations in the 16th century, imaginary and complex numbers have been difficult topics to understand. Here the word complex is used to describe something consisting of a number of interconnecting parts. The different parts of a complex number are the…

To assess the strength of conceptual understanding of number sense, a three-tier number sense test (TTNST) for fifth-grade students was developed and validated in this study. The three-tier test includes a content tier that assesses content knowledge of number sense, a reason tier that assesses a reason given for selecting a first-tier response,…

The present study examines the effect of visual scaffolding on promoting number sense skills (including number recognition, counting, ordinality, comparison, and calculation) of Egyptian autistic children mainstreamed in kindergartens. The participants were five autistic children, enrolled in the second level of kindergarten (ages 5-6).…

Children with autism spectrum disorder (ASD) have difficulty generalizing from directly trained responses to untrained responses (i.e., emergent responding). In this study, we used a chain prompt combined with matrix training to teach 2 participants with ASD to tact 192 three-digit numerals. We used a multiple-baseline design across matrices to…

Number talks, a popular mathematics teaching routine in the United States, may offer supports for beginning teachers (BTs) to engage in ambitious instruction. BTs' enactments of number talks, however, are varied, and there are few empirical studies that explore how BTs' enactment of number talks could be more (or less) ambitious. This paper draws…