The Three-Square Puzzle shows a remarkable relationship between three angles. What happens when the number of squares increases? This article explores that question and brings in Fibonacci and Lucas sequences.

Concerns about the replication crisis and unreliable findings have spread through several fields, including education and psychological research. In some areas of education, researchers have begun to adopt reforms that have proven useful in other fields. These include preregistration, open materials and data, and registered reports. These reforms…

Laboratory experiments that offer interdisciplinary experiences for students are appealing and are increasingly popular additions to undergraduate chemistry curricula. Students can capitalize on their knowledge of multiple areas of chemistry while working through an application, and this fosters the development of progressive problem-solving…

Before students learn Kirchhoff's rules, they are typically taught how to solve "combined series-parallel" circuits. The method presented in many textbooks begins by drawing a series of simplified circuits, replacing series and/or parallel elements with their equivalent resistances, eventually reducing the circuit to a voltage source and…

Employing authentic cases experienced by practitioners in educational contexts is critical to expanding students' experience and engaging students in authentic problems to promote their real-world problem-solving skills. Although in real life, practitioners experience both success and failure and learn from both, little research has been done so…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

How students' rigid perceptions of mathematics persist over years has been a conundrum. Students not only think that only one solution exists for a mathematical task (Schoenfeld 1985) but also rigidly fuse mathematical concepts with specific tasks. Students deserve to learn a variety of mathematical strategies to flexibly deploy at will. Teaching…

Drawing on Kucher's (2021) framework on digital game-based learning (DGBL), this paper introduces the development of game-based scenarios in two culturally distinctive and salient heritage sites in Cyprus and Sweden, the Neolithic village of Choirokoitia and the Iron Age Ringfort of Sandby Borg. The aim was to implement Kucher's (2021) five…

This manuscript proposes the use of the "I notice, I wonder" routine in college mathematics classrooms to address issues of diversity, equity, and inclusion. Examples are given of prompts that incorporate meaningful conversations about real-world issues affecting our students or about issues of inclusion, access, and representation in…

As schools endeavor to provide all students with access to computational thinking and computer science, the hackathon emerges as a competitive and high-energy event that uses authentic problems to motivate learners to engage in the domain of computing. This article presents the design case of a hackathon for teenagers as enacted over five…

This article presents "Be a coach instead of a judge" pedagogy that has resulted in significant improvement in college student learning/performance, highly favorable student comments and better teaching evaluations. This pedagogy inspires students to learn by embracing empathy, enthusiasm, positivity and trust along with other learning…

Industrial drug discovery teams encompass scientists from multiple specialties and require participants to communicate effectively across disciplinary boundaries. In this paper, we present an undergraduate or graduate classroom simulation of this environment. Over a series of five workshops, student teams of mixed scientific backgrounds perform…

Florida State University (FSU) has a long-standing commitment to promoting success for all students. FSU's strategies for student success and equity have resulted in increased and more equitable graduation rates and record fall-to-fall retention rates. This article provides an inventory of student success and equity initiatives at FSU. The…

Learning systems can utilize many practice exercises, ranging from simple multiple-choice questions to complex problem-solving activities. In this article, we propose a classification framework for such exercises. The framework classifies exercises in three main aspects: (1) the primary type of interaction; (2) the presentation mode; and (3) the…