Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that…

Classroom dialogues have special educational value because they allow students to engage critically but constructively with each other's ideas, solve scientific problems jointly and develop their scientific understanding. The present study focuses on how groups of twelfth-grade high school and university students communicate and co-operate through…

Policymakers, educators, and families throughout the world are concerned about the lingering effects of the COVID-19 pandemic on school-aged youth. Schools are working to help students readjust to school routines and regain lost ground on academic skill development while also addressing the wounds caused by the pandemic. This study describes one…

Systems thinking and abstract thinking are important skills for engineers in general and hardware and software engineers in particular. Systems thinking emphasises the interdependence of system components and their synergy. Abstract thinking permits one to focus on the significant details of the current perspective, while temporarily neglecting…

Purpose: This paper aims to compare two types of prompts, encouraging participants to think about real-world examples or engineering principles to show how these two approaches can result in vastly different design practices. Design/methodology/approach: Two studies (N = 20, N = 40) examine the impact of two different prompts. Non-expert students,…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

This article explains four kinds of inquiry exercises, different in purpose, for teaching advanced-level high school and college students the hypothetico-deductive (H-D) method. The first uses a picture of a river system to convey the H-D method's logic. The second has teams of students use the H-D method: their teacher poses a hypothesis…

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

The 21st-century work environment places strong emphasis on nonroutine transversal skills. In an educational context, complex problem solving (CPS) is generally considered an important transversal skill that includes knowledge acquisition and its application in new and interactive situations. The dynamic and interactive nature of CPS requires a…

Nondeterminism is an essential concept in mathematics and one of the important concepts in computer science. It is also among the most abstract ones. Thus, many students find it difficult to cope with. In this article, we describe some didactic considerations, which guided the development of a "Computational Models" course for high school…

This paper reports on methods of students' justifications of their solution to a problem in the area of combinatorics. From the analysis of the problem solving of 150 students in a variety of settings from high-school to graduate study, four major forms of reasoning evolved: (1) Justification by Cases, (2) Inductive Argument, (3) Elimination…