In this paper the authors demonstrate how play can serve as a space for assessing and promoting children's mathematical thinking. Analyzing data from a larger study of professional development to support culturally and developmentally responsive mathematics teaching in preschool, we found that through Learning Stories, a holistic narrative…

Among the wide range of factors related to the acquisition of statistical knowledge, competence in basic mathematics, including basic probability, has received much attention. In this study, a mediation model was estimated to derive the total, direct, and indirect effects of mathematical competence on statistics achievement taking into account…

The European Union defines lifelong learning as all activities aimed at improving an individual's knowledge, skills and competences individually, socially or vocationally throughout his/her life. In 2007, eight key competences necessary for lifelong learning were identified by the European Union Education and Culture Commission. These competences…

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively…

We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…

Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13-8 think "what + 8 = 13?"): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common…

In this theoretical paper, I consider reversibility as a defining characteristic of mathematics. Inverse pairs of formalized operations, such as multiplication and division, provide obvious examples of this reversibility. However, there are exceptions, such as multiplying by 0. If we are to follow Piaget's lead in defining mathematics as the…

In the domain of "Operations & Algebraic Thinking," Common Core State Standards indicate that in kindergarten, first grade, and second grade, children should demonstrate and expand their ability to understand, represent, and solve problems using the operations of addition and subtraction, laying the foundation for operations using…

In the domain of "Counting & Cardinality," Common Core State Standards indicate that by the time students leave kindergarten, they should know the names and sequence of number words up to 100, be able to count to determine the number of objects in a small set (up to 20), and make comparisons between small sets of objects (National…

The Louisiana mathematics standards were created by over one hundred Louisiana educators with input by thousands of parents and teachers from across the state. Educators envisioned what mathematically proficient students should know and be able to do to compete in society and focused their efforts on creating standards that would allow them to do…

Formative Assessment Collaborative Team (FACT) meetings provide educators with a structured time each week to engage in peer collaboration focused on students' mathematical thinking. In these meetings, educators work together to analyze their students' mathematical thinking and make purposeful adaptations to instructional plans based on the…

The majority of students in Maryland spent at least a portion of the last school year learning virtually, from public prekindergarten through college. Throughout the year, jurisdictions made individual decisions to allow for a gradual return to in-person school in a variety of ways. Lessons learned from the earliest stages of the pandemic made it…

In Afghanistan, 93% of children cannot read a simple text by the age of 10. Education is not available to everyone, especially for girls and children in remote areas. A form of community-based education, called Accelerated Learning Centers (ALCs), can help close the distance barrier and meet the needs of out-of-school children and girls. In May…

The purpose of the inquiry was to understand how children in primary grades (i.e., preschool, kindergarten, and second grade) engaged with affordances and constraints of features in a Base-10 Blocks virtual manipulative mathematics app designed to promote learning opportunities. Researchers conducted one-to-one interviews with 100 primary grade…

HEAT, an instructional program emphasizing a nontraditional hands-on approach to algebraic instruction for urban, predominantly African American middle schoolers, provides a space to explore teachers' beliefs about urban students' mathematical abilities and motivation and addresses how teacher perceptions can intersect with instruction, learning,…