The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

This study reports the findings from a year-long randomized evaluation assessing the impact of assigning 62 classrooms in Nigeria to receive either blocked or interleaved math problem sets. Blocked practice sessions focused on a single skill at a time. Interleaved problem sets alternated between different skills within a practice session. On tests…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

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.

Research focusing on the complexities faced by instructional designers have called for pedagogical strategies to equip instructional designers with the ability to problem solve and make decisions. One of the most widely studied strategies for managing cognitive load is the use of worked examples, which provides an alternative to traditional…

We recognise that though teachers may participate in various forms of professional development (PD) programmes, learning that they may have gained in the PD may not always lead to corresponding perceivable changes in their classroom teaching. We offer a theoretical re-orientation towards this issue by introducing a construct we term…

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…

This paper presents a teaching experiment with preschoolers, considering games as means for presenting problem-based situations and focusing on the development of game design in connection to problem posing skills. The study was conducted in a focus group of eighteen 5-6-year-old students who participated in game design sessions, compared to a…

The motivation behind this examination is to present the theoretical structure of Modeling Activities, which is believed to be a vital device for mathematics instruction. Modeling activities are defined as activities to figure out complex problems faced in real life situations that require the creation of a mathematical model as a product. In…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

The study reported on here aimed to examine the effectiveness of the successful intelligence interactive module (SIIM) that employs thinking skills using the successful intelligence theory. This was an empirical study that used mixed method analysis. The rationale for the development of this interactive module was to increase the analytical,…

Climate education is increasingly being taught in schools, and groups are looking to pass climate education into law. This article looks at climate justice, a framing of the overarching climate movement, to advocate for an education that inspires action. Drawing from Freire's 'Pedagogy of the Oppressed', it makes a case for problem-posing…

"When you hear hoofbeats, look for horses, not zebras." This common saying in medicine (often attributed to Theodore Woodward, MD, of the University of Maryland School of Medicine) advises doctors to stick to the expected or likely diagnosis, rather than anticipating an unusual or atypical one. As a result, uncommon medical diagnoses are…