Children with low performance in early numeracy are at risk of facing learning difficulties in mathematics, but few trials have examined how this can be ameliorated. A total of 120 first-grade children (M[subscript age] = 6.4 years) were randomly assigned to an intervention or a control condition. The 14-week intervention targeted early numeracy…

Background: Number line accuracy (NL accuracy) shows improvement over the course of a school education. However, there are practically no cross-country longitudinal studies of NL accuracy over the whole course of elementary school. Aims: This study investigated the developmental trajectories of NL accuracy and its types across the elementary…

This paper stems from calls for methodological advancement in two areas of research: primary mathematics education and dialogical education. We respond to these calls from the commognitive standpoint by introducing the "Grove of Realizations" as a tool for capturing and visualizing individual students' learning through collaborative work…

In this study, we investigated prospective secondary mathematics teachers' development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written…

This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools…

Background: The present study delves into the debate surrounding the effectiveness of homework, focusing specifically on the use of online homework in teaching decimal numbers to 5th and 6th grade primary school students. It highlights the challenges students face in representing and identifying decimal numbers, a concept that is often difficult…

LXD Research conducted a study to evaluate the impact of the Zaner-Bloser Kickstart: Number Sense program, a math intervention designed to enhance foundational math skills among first and second-grade students in an Oregon school district over a three-year period from spring 2019 to Spring 2023. The program was implemented in two schools, engaging…

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…

In this article, we present research on eight kindergarten and eight first-grade students' understandings of the arithmetic properties of commutativity, additive identity, and additive inverse during a classroom teaching experiment, selected from a larger study that included 88 students. In this study, we explore the students' types of…

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…

Background: Dot enumeration is the basic mathematics competency in young children and a significant indicator of later mathematics achievement. Aim: The present study focused on (1) how children's dot enumeration ability changed as they progressed from late kindergarten years (K3) to the second year of primary school in Hong Kong (P2), and (2) the…

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…