Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…

Research on toddlers' mathematical knowledge is sparse. Studies on children's mathematical competencies before school age have mostly focused on older children. Few of the previous studies have included large groups of toddlers, few have been conducted in natural settings, and few have been directed at a broad field of mathematical knowledge. The…

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…

In recent years, there has been increased interest in improving early mathematics curricula and instruction. Subsequently, there has also been a rise in demand for better early mathematics assessments, as most current measures are limited in their content and/or their sensitivity to detect differences in early mathematics development among young…

Teachers have the opportunity to capitalize on a vast array of real-world, two- and three-dimensional objects as they guide students in developing a conceptual understanding of geometric shapes. An important component of the NCTM Standards is to use teaching methodologies that engage children in making real-world connections to the mathematics…

While ice is usually referred to as ice cubes, indeed, most are not really cubes at all. In this 5E learning-cycle lesson, students will investigate different shapes of ice and how shape affects the speed of melting and the rate of cooling a glass of water. Students will compare three different shapes of ice with the same volume but different…

As a secondary mathematics teacher, I used practitioner action research to determine effective ways to intervene with students working in groups, with the goal of improving their communication. Utilising transcripts of group interactions and teacher interventions, field notes, and student feedback, I discovered ten different issues that prevent…

This case study of one class versus a control group focused on the impact of an intervention unit, which is not part of the regular curriculum, on the improvement of spatial ability of high school students (forty-six 12th-graders, aged 17-18, both boys and girls) in general as well as from a gender perspective. The study explored three…

In this article, I (1) argue for approaching processes, events-in-the-making, by means of process categories--to learn, to teach--not by means of categories that denote differences in state and (2) exemplify doing and writing research consistent with process philosophy. To understand process we must not think, research, and write them in terms of…

This paper examines the effects of policies that increase the number of students who take the first course in algebra in 8th grade, rather than waiting until 9th grade. Extending previous research that focused on the Charlotte-Mecklenburg school system, we use data for the 10 largest districts in North Carolina. We identify the effects of…

The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests of…

This study integrates augmented reality (AR) technology into teaching activities to design a learning system that assists junior high-school students in learning solid geometry. The following issues are addressed: (1) the relationship between achievements in mathematics and performance in spatial perception; (2) whether system-assisted learning…

This dataset includes a series of 30 education-related majors' performance measures before and after they completed a 10-hour video game practice in a computer lab. The goal of the experimental study was to examine the effects of action video gaming on students' mathematics performance and mathematics anxiety as mediated by the effect of attention…

The golden mean is often naively seen as a sign of optimal beauty but rarely does it arise as the solution of a true optimization problem. In this article we present such a problem, demonstrating a close relationship between the golden mean and a special case of Newton's aerodynamical problem for the frustum of a cone. Then, we exhibit a parallel…

The paper presents inequalities between four descriptive statistics that can be expressed in the form [P-E(P)]/[1-E(P)], where P is the observed proportion of agreement of a "kappa x kappa" table with identical categories, and E(P) is a function of the marginal probabilities. Scott's "pi" is an upper bound of Goodman and Kruskal's "lambda" and a…