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…

As a widely applied theory that has found success across many fields, density functional theory (DFT) is largely taught. Typically, the most effective way to convey DFT concepts is through illustrative examples that are currently lacking in available resources. In this work, we demonstrate total energy calculations for H[subscript 2] using…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

This paper is concerned with the process of selecting between the increasingly popular bi-factor model and the second-order factor model in measurement research. It is indicated that in certain settings widely used in empirical studies, the second-order model is nested in the bi-factor model and obtained from the latter after imposing appropriate…

Massive open online courses (MOOCs) have become one of the most popular ways of learning in recent years due to their flexibility and convenience. However, high dropout rate has become a prominent problem that hinders the further development of MOOCs. Therefore, the prediction of student dropouts is the key to further enhance the MOOCs platform.…

This paper is part 4 in a series of workshops that examine the properties of some simple models of vocabulary networks. This Workshop explores how the overall activity level of a vocabulary network can be altered by changing the connections in the network (i.e., by implementing relinking events). The Workshop is linked to an online practice room…

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

This emerging technology report discusses Google Gemini as a multimodal generative AI tool and presents its revolutionary potential for future educational technology. It introduces Gemini and its features, including versatility in processing data from text, image, audio, and video inputs and generating diverse content types. This study discusses…

The technology of automated short answer grading (ASAG) can efficiently process answers according to human-prepared grading examples. Computer-assisted acquisition of grading examples uses a computer algorithm to sample real student responses for potentially good examples. The process is critical for optimizing the grading accuracy of machine…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

Extracting data from studies is the norm in meta-analyses, enabling researchers to generate effect sizes when raw data are otherwise not available. While there has been a general push for increased reproducibility in meta-analysis, the transparency and reproducibility of the data extraction phase is still lagging behind. Unfortunately, there is…

Computer adaptive testing (CAT) is an increasingly common mode of test administration offering improved test security, better measurement precision, and the potential for shorter testing experiences. This article presents a new item selection algorithm based on a generalized objective function to support multiple types of testing conditions and…

The rapid integration of artificial intelligence (AI) tools into education has introduced both opportunities and challenges for academic institutions. As educators navigate whether and how to allow AI use in their classrooms, syllabus statements have become indispensable for clarifying expectations and promoting digital literacy. This article…

Artificial intelligence is a popular technology that affects many fields today. Its impact is noticeable daily, especially in education, design, and other essential areas. This technology, which stands out with the convenience it creates for users and its help in organizing the workflow, will play a critical role in our lives in the future. This…

This paper details how to effectively share three-dimensional geological models using data conversion between two mainstream mining software, Micromine and Surpac. It also discusses the impact of this conversion method on geological integrated exploration decision-making guidance. The current situation primarily manifests in the fact that both…