Many literature studies point out how the process that moves the student from personal reasoning to the arrangement of fruitful argument could help them in the development of mathematical argumentative thinking. Starting from the above assumptions, in this paper we investigate the interaction among teacher/researcher and students in a Digital…

Exceptional talent includes the ability and willingness to solve varied, complex problems, and having a knowledge structure that facilitates problem solving and creativity. The purpose of this study was to determine changes in students' knowledge structures resulting from fidelity of implementation of Real Engagement in Active Problem Solving…

This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined…

The term speed-accuracy tradeoff is used when an increase in response speed comes at the expense of response accuracy. Although originally a concept from experimental psychology, the speed-accuracy tradeoff has been a topic in psychological assessment, too. In the first part of the manuscript, we discuss motivational factors that may be…

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well…

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

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…

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…

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…

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…

This study aimed to examine the relationship between mathematical modelling and reflective thinking and to examine the effects of employing mathematical modelling processes on perception of mathematical modelling competencies and reflective thinking skills for real-life problem solving of gifted students participating in Project Production and…

This study looks at whether creativity and critical thinking help students solve problems and improve their grades by mediating the link between 21st century skills (learning motivation, cooperativity, and interaction with peers, engagement with peers, and a smart classroom environment). The mediating relationship between creativity and critical…

Recent developments in language models, such as ChatGPT, have sparked debate. These tools can help, for example, dyslexic people, to write formal emails from a prompt and can be used by students to generate assessed work. Proponents argue that language models enhance the student experience and academic achievement. Those concerned argue that…

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…

In this paper it is demonstrated how the free, and easily downloadable, software package called SMath Studio can be used to set up a model of alpha-particle scattering. The basic physics of the motion of an alpha-particle in the nuclear coulomb field is used to produce a simple stepwise computer algorithm which, in conjunction with a novel set of…