We study the variation of the apparent weight of an object with height above the surface of a planet with a (buoyant) atmosphere. Interestingly, this variation depends on two competing factors--the reduced gravitational acceleration (which acts to reduce the weight with increasing height) and the reduced buoyancy force in the progressively less…

Based on the article "Participation and Reification: Two Basic Design Principles for Mathematics Professional Development Programs" (Gómez-Blancarte & Miranda, 2021), this commentary aims to discuss how Wenger's concepts of participation and reification may be used in the design of a MPDP. The meanings of participation and…

In this commentary, we explore tensions between engaging students in authentic disciplinary mathematical activity and insights from critical theorists who analyze equity in mathematics education. The tensions arise as engaging students in authentic mathematical activity usually involve having students adopt the language and norms of another…

This paper attempts to deepen our understanding of teachers' selection and modification of mathematical tasks for their classroom instruction. In this paper, we focus on teachers' orientations and resources that subtly influence teachers' choices during their routine undertaking of task selection and modification. Interviews using stimulus…

Even before the pandemic slowed learning for many, only 39 percent of California students demonstrated proficiency on the state math assessment. During the pandemic, the proportion of math-proficient students fell to one-third. At the same time, the STEM workforce faces shortages and a lack of diversity, which call into question the longstanding…

The aim of this paper is to gain a better understanding of the role and scope of historical knowledge in work on using history of mathematics in education. This work can come from three types of actors, namely, teachers, teacher trainers, and educational researchers. The texts written by these actors show that their objectives and practices can be…

Little is known about primary school mathematics middle leaders' aspirations for mathematics learning. We sought to give mathematics middle leaders a voice to articulate their desires for mathematics learning based on what was most salient to them. Statements collected from 149 primary school mathematics middle leaders through an online survey…

Lecture capture (LC), the process of recording face-to-face lectures for future viewing, has become a common technology in Western universities in the twenty-first century, yet research on its effectiveness has lagged behind its implementation. Despite the rapid, widespread implementation, research regarding the impact LC has on pedagogy and…

For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions x [right arrow] -- x, [pi] -- x, and [pi] + x, allow one to decide which of the…

Based on an enactivist perspective on learning mathematics, we articulate three key processes of designing mathematics-grounding activities (MGAs) where students' mathematical thinking can be motivated and shaped with the interactions between their enactments and the evolving tasks in the activities. Then, evaluation criteria and design steps will…

The International Mathematical Olympiad, now 62 years old, has catalyzed the formation of a remarkable international community that meets for 2 weeks each year to celebrate mathematical problem solving. It has influenced and expanded the greater global mathematical culture, and the value of problem-solving in numerous countries. It is time for the…

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we…

Researchers use data from the RAND American Mathematics Educator Study surveys of public school principals and teachers to investigate three school structures--referred to as "school opportunity structures" throughout this report--that may affect kindergarten through 8th grade (K-8) students' mathematics learning. These structures are…

We develop a spreadsheet-based game to illustrate fundamental statistical concepts in the first class of an undergraduate Statistics course to motivate students about the topics that they will learn in upcoming classes. This game has been implemented by Google Forms and Google Sheets and can be played in both online and in-person classes of small…

Storytelling is a valuable form of human expression that allows audience members to connect their own experiences with the narrative. As a pedagogical tool, storytelling has been explored mainly in primary school education but rarely in higher education. However, its potential for assisting students in learning mathematics and the societal…