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,…

The purpose of this study was to examine the relationship between students' engagement with Legends of Learning's Math Basecamp (MBC) and students' math achievement at the elementary school level in Rialto Unified School District (RUSD) in California. Researchers examined the association between MBC usage and student achievement scores on the…

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…

Math to Mastery (MTM) is a multi-component math intervention that has demonstrated effective results in building math fluency and skill acquisition. Few studies have explored the use of brief experimental analysis (BEA) procedures to create an individualized, abbreviated MTM intervention to address skill deficits in basic math. The purpose of this…

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…

This project seeks to understand the emergence of mathematical meanings mediated by learners' interactions with multiple artifacts. Extending our prior work which took an enactivist approach and revealed the dynamics of embodied interactions fundamental to understanding fraction division, we now employ a semiotic lens to illuminate how learners…

Attention to the disconnection between culture and mathematics has been addressed then and now (Wilder (in: Graves et al., Proceedings of the international congress of mathematicians, American Mathematical Society, 1950; Liu in Taiwan Journal of Mathematics Education, 8:79-88, 2021b). Recently, studies, workshops, and contests about an approach to…

Youth-staff relationships and program activities are important elements in designing high-quality afterschool activities that promote a broad range of outcomes. Using a qualitative approach, Latinx adolescents were interviewed (n = 28, 50% girls) about their experiences in a university-based afterschool math enrichment activity. Findings under the…

Studies have shown that math skills in early childhood are uniquely and strongly predictive of later outcomes across a range of domains and well into adulthood, including the likelihood of graduating from high school and college completion. The Making Pre-K Count and High 5s studies were designed to rigorously test the short- and long-term effects…

Math performance became an increasing concern in the United States after the launch of Sputnik in 1957. This concern began with attempts to prescribe mathematical standards in the United States to improve student mathematics preparation. When the COVID pandemic began in 2020, policies on quarantining and remote learning were implemented, resulting…

This study examines Grade 9 students' mathematics achievement and cognitive engagement under three different instructional approaches: traditional learning, flipped learning with gamification, and online independent study with gamification. The duration of the study lasted an entire school year. The central theories underpinning flipped learning…

Many ways exist to engage students without detracting from the mathematics. Certainly some are high-tech options, such as video games, online trivia sites, and PowerPoint® presentations that follow the same model as Jeopardy; but sometimes low-tech options can be just as powerful. One exciting way to connect with students is by incorporating…

This article reports findings from a one-year evaluation of a kindergarten math enrichment program. A randomized design was used to assess the impact of High 5s on children's math skills, attitudes towards math, language ability, and executive function for a sample of kindergarten students in New York City. High 5s math clubs were designed to…

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…