Optimization is introduced to teaching in secondary school, focussing on functions of one variable with the first derivative criterion for critical points and monotonicity of functions. The second derivative criterion is also used to determine the nature of the critical points. Similarly, in university-level teaching, algebraic work using criteria…

Online learning and teaching, accelerated by the global pandemic and rapid advancement of digital technology, require novel conceptual and analytical tools to understand better the evolving nature of online teaching. Drawing on the classical model of the instructional triangle and previous attempts to extend it, we propose the "Instructional…

Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

With the emergence of COVID-19, public interest in data visualization has surged. Data visualizations also, importantly, raised questions related to the data and the social context in which it occurred. Extending beyond but remaining connected to COVID-19, this context involved the racial and social inequality and economic disparities brought to…

In this work, we consider learning analytics for primary and secondary schools from the perspective of the designer of a learning system. We provide an overview of practically useful analytics techniques with descriptions of their applications and specific illustrations. We highlight data biases and caveats that complicate the analysis and its…

Understanding educators' networks can inform the field of school psychology by offering insight into how the structure of social relationships supports the implementation of school-based programs. However, the difficulties of collecting and modeling network data remain barriers to using network methods in school psychology. To overcome these…

Activities that engage high school students in visualizing chemical phenomena can help them develop representational competence to think about and communicate their understanding of these phenomena. This paper presents a collaborative learning activity that can engage precollege students in designing a poster that describes four different types of…

This technology report presents the main features of a free digital educational tool which aims to introduce middle school level students to the comprehension of the particulate nature of matter in the three states (i.e., solid, liquid, and gas) and during phase transitions. This digital tool is available and is freely accessible online. Its…

Light rays refract when passing through pockets of transparent fluids with different indices of refraction such as ordinary air pockets of varying temperature. This phenomenon makes night stars twinkle, distorts views above hot asphalt roads and hot barbeque grills, and provides an opportunity for visualizing the normally invisible movement of…

With the help of augmented reality apps objects and text can be added virtually to the physical world (e.g. physical experiments) in real time. The augmented reality (AR) app 'PUMA: "Spannungslabor"' enhances simple electric circuits experiments for students with virtual representations based on the electron gas analogy including…

Technological advances, artificial intelligence innovations, and widespread computing have all combined to necessitate a new generation of knowledge workers where data becomes a ubiquitous part of decision making (Sutton, 2006). Teaching today's students through the application of this "new" knowledge to long-established fields…

In this article, the authors offer four specific reading comprehension strategies that mathematics teachers of all levels can employ with their students when working on word problems: (1) visualizing; (2) retelling; (3) making connections; and (4) asking questions. These strategies, which have a substantial research base in literacy, are discussed…

Spatial ability was defined by Lohman (1996) as the ability to create, maintain, retrieve, and change visual pictures. Linn and Peterson (1985) distinguished among spatial perception, mental rotation, and spatial visualization. Spatial perception is the determination of spatial connections with respect to the orientation of the learners' body;…

The author offers practical strategies to introduce and maintain a mindfulness practice with middle-grade students and discusses ethical implications of employing mindfulness in the classroom.

Spatial visualisation is an essential component of geometric thinking and measurement sense. It is a particular type of spatial skill that involves manipulation of spatial images and may not be naturally occurring for students. However, research shows that it is malleable and can be developed through instruction. This article presents an…