Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

Building activities can be used any time in the school year in mathematics classes to promote problem solving, perseverance, and to develop students' spatial thinking. Spatial visualization skills are the "ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object." The authors were guided by the…

Every teacher aspires to create the ideal lesson! You want to convey the knowledge and skills in the best possible way while also keeping learners motivated. In our design case, we focus on the complex skill of collaborative problem-solving (CPS). In today's complex world, the acquisition of CPS competencies is considered an important learning…

Amid rapid technological advancements, it is increasingly crucial for educational technology research to move beyond a narrow focus on tools and gadgets, addressing instead the broader social and ethical challenges these technologies bring to education and human performance. Translational research, with roots in the biomedical sciences, is…

Students in introductory college physics often have wide ranges of preparation, making it challenging to deliver effective instruction for all. While numerous educational products and strategies have been shown to be broadly effective, there is a need for research-based online materials that support personalized learning and focus specifically on…

This paper reviews algorithmic or artificial intelligence (AI) bias in education technology, especially through the lenses of speculative fiction, speculative and liberatory design. It discusses the causes of the bias and reviews literature on various ways that algorithmic/AI bias manifests in education and in communities that are underrepresented…

ePUZSOLVED is designed to help students understand the general communication models and experience the advantages and disadvantages of each. It will highlight how various modes of communication, when used appropriately, may lead people to solve problems, as exemplified by the online puzzle. Courses: Introduction of Communication Models, Review of…

The duo of artefacts is a simplified model of the complex systems of various manipulatives (either tangible or virtual) that mathematics teachers and their students use in classrooms. It offers a means to study the complexity of the interweaving of the tangible and of the digital worlds in the teaching and learning processes. A duo of artefacts is…

The authors share an online collaborative problem-solving activity that integrates support for students' developing conceptual understanding, focused engagement, and positive feelings of agency and identity.

Nuclear magnetic resonance (NMR) spectroscopy is a very powerful analytical method that has found many applications in physics, chemistry, biology, and medicine. It is an indispensable tool particularly for synthetic chemists because it can be used for a rapid elucidation of the structures of organic compounds. For this reason, NMR spectral…

School consultants often use problem-solving consultation when working with educators and caregivers to support the behavioral and academic outcomes of students. Considering some of the well-known limitations to in-person service delivery, consultants have increasingly relied on telecommunications as a medium through which to deliver…

Partial Latin squares constitute an interesting approach to improve the teaching of different subjects in the mathematics classroom. This paper delves into this topic by introducing the use of a Dynamic Geometry System to deal with these combinatorial structures as a source of loci of points in the Euclidean plane. It is assumed to this end that…

In the preferable educational future imagined here, the year 2030 has seen massive conceptual and structural change throughout systems of education. In the higher educational landscape envisioned only 10 years in the future, institutions of higher education have moved beyond the goals of valuing diversity, equity, and inclusion and beyond…

When thinking about digital equity, often what comes to mind are issues of access to digital technologies. Although that is a divide that must be conquered, once students have access to digital technologies, the next step is to ensure that they wield these technologies in such ways that they help to address the existing inequities in mathematics…

This paper presents an approach to implement learning objects for teaching and learning problem-solving techniques based on computer programming. The demonstrated approach exploits computer-based interactive animations and computer graphics. The main feature of this approach is its simplicity for exploring the concepts and structures of the…