Single-type, 8-fold-grooved, commercially accessible interlocking disks (ILDs) have been used for modeling of complex polyhedral and reticular topologies with relevance to inorganic and hybrid materials. The assembly of complex topologies relies on the preparation of secondary building units (SBUs), which exhibit different connectivity than that…

The design and initial implementation of a project-based directed study course in mathematical research and communication is described. The intention of the course is to expose students to the foundation of mathematical research through inquiry-based learning. Students are asked to approach an exercise in topology as though it is an open problem.…

In this article, we advocate for and propose a novel concept map driven knowledge tracing (CMKT) model, which utilizes educational concept map for learner modeling. This article particularly addresses the issue of learner data sparseness caused by the unwillingness to practice and irregular learning behaviors on the learner side. CMKT considers…

Many students struggle with proof writing. However, struggle is not universally bad: researchers have distinguished between productive and unproductive forms of struggle and have identified productive struggle as essential for learning mathematics. Yet, in practice, recognizing when learners are engaged in productive struggle or unproductive…

The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…

The introduction of makerspaces in Science, Technology, Engineering, and Math education caused new challenges in research: learning in this innovative environment and the exchange of knowledge. The collaboration is the essence of most parts of activities in these spaces, and the exchange of information is the way to learning. It is usual to…

In this article, a cognitive framework for observing learning activities based on human-computer coupling is proposed. The observation is based on the vectorization of a learning situation along with human-computer interaction factors. An evolutionary high-dimensional topology of learning cognitive flow is introduced for human-computer…

There is a disconnect between the cutting-edge research done in academic laboratories, such as nanotechnology, and what is taught in undergraduate laboratories. In the current undergraduate curriculum, very few students get a chance to do hands-on experiments in nanotechnology-related fields, most of which are through selective undergraduate…

This article presents topological genealogy (TG) as a methodology to research transnational digital governance, and particularly how digital infrastructures are implicated in enacting such forms of governance. Inspired by the field of social topology, TG is centrally interested in investigating the conjoined production of digital infrastructures…

Topology optimization (TO) has been a useful engineering tool over the last decades. The benefits of this optimization method are several, such as the material and cost savings, the design inspiration, and the robustness of the final products. In addition, there are educational benefits. TO is a combination of mathematics, design, statics, and the…

This article analyzes the Common Core State Standards initiative as an innovation network. Using narrative data and quantitative analysis of hypertext linkages on the World Wide Web, we describe a network of about 3200 organizations that arose to scale up the Common Core State Standards and link them to aligned academic resources such as…

This research examined the Olweus Bullying Prevention Program (OBPP) through the perspective of teachers located in a northeast Ohio county who received a grant to implement the program over a period of several years. The current investigation involved a Likert-style questions which were developed using the general implementation requirements of…

Purpose: Despite a tremendous amount of research in this topic, the precise neural mechanisms underlying language recovery remain unclear. Much of the evidence suggests that activation of remaining left-hemisphere tissue, including perilesional areas, is linked to the best treatment outcomes, yet recruitment of the right hemisphere for various…

The goal is to promote the healthy and stable development of music education in China. The time-frequency sequence topology in frequency domain can improve the effect of convolution operation. Therefore, this paper applies the above algorithms to classical music education, including the recognition of classical instruments, the feature extraction…

The equivalent resistance calculation for two circuits in cubic arrangements is solved. Emphasis is placed on the plastic (topological) properties of these circuits. In contrast, the opposite topological behaviour of an analogous arrangement is observed in the calculus of a magnetic field. It is also noted that the solved examples may be used as a…