The nature of the area of mathematical competitions as a design science is considered, historical roots of mathematical problem-solving competitions are traced, the complementary aspects of mathematics as theory building and as problem solving are touched upon in relation to the practice of competitions. Two historical figures, Euler and Erdos,…

This article investigates the potential mathematical learning opportunities arising from a digital activity designed to enhance students' comprehension of equations. Employing a commognitive-oriented lens, the analysis explores the potential mathematical discourses that could emerge from students' interactions with a digital scale inspired by the…

Mathematics Challenge for Young Australians is a unique enrichment program that has been produced annually by the Australian Mathematics Trust since 1991. In its present form, it is divided into four levels and caters for talented students from years 3 to 10. In a typical year, it attracts over 15,000 entries. Individual schools arrange a period…

In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

The old canard that Indigenous and First Nations peoples had, or have, only rudimentary mathematical skills has been curiously persistent, against widespread published evidence over the past century and a half. In Australia, attempts to include Indigenous mathematical knowledge in curriculums have encountered strong resistance. After more than…

Scholars have increasingly argued that we need to attend to adolescents' race, ethnicity, and culture in after-school activities to ensure positive effects. Still, little is known about adolescents' perceptions of culturally responsive practices in after-school activities (i. e., the use of diverse teaching practices, cultural engagement, and…

When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…

Whereas equity issues are mainly discussed with respect to students at risk, this article focuses on mathematical potentials of under-privileged students and therefore elaborates a wide, dynamic and participatory conceptualization of (sometimes still hidden) mathematical potentials. An extended research review theoretically and empirically grounds…

Imagine two classfuls of American high school students, separated by 1,500 miles and profound differences in local cultures (East Coast urban and Midwestern rural) as they correspond and collaborate in writing between their geometry classes. Reading the students' observations, one sees authentic voice, specific detail, precise language, what…

This intervention study compared the efficacy of small-group tutoring on the mathematics learning of third-grade students at risk for mathematics difficulty using either a school-provided standards-based curriculum (SBC) or a schema-based instruction (SBI) curriculum. The SBI curriculum placed particular emphasis on the underlying mathematical…

The present study investigated the effectiveness of a cognitive enrichment programme as a tool for enhancing the chances of immigrant and minority students to be admitted to a technological college. Students received two weekly sessions (four hours) of "Instrumental Enrichment" (IE) during the second semester of the college preparatory…

A deep conceptual understanding of elementary mathematics as appropriate for teaching is increasingly thought to be an important aspect of elementary teacher capacity. This study explores preservice teachers' initial mathematical understandings and how these understandings developed during a mathematics methods course for upper elementary…

Middle grades are a critical time for capturing the interest and imagination and developing the potential of mathematically promising students. This is a time for students to make sense of mathematics, build a solid foundation and enthusiasm, and set the course for the highest levels of mathematics in the future. This is a time to explore their…

The author of this paper submits that a mathematics student needs to learn to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method (MMM) across the…