The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic…

MOOCs might be an important organization way to realize the online learning process. Online technology and sharing technology enable MOOCs to realize the adaptive scheduling of learning resources, as well as the independent construction of learning sequences. At the same time, it also generates a large number of complex learning behaviors. How to…

Directed acyclic graphs (DAGs) are now a popular tool to inform causal inferences. We discuss how DAGs can also be used to encode theoretical assumptions about nonprobability samples and survey nonresponse and to determine whether population quantities including conditional distributions and regressions can be identified. We describe sources of…

In recent years, knowledge tracing (KT) within intelligent tutoring systems (ITSs) has seen rapid development. KT aims to assess a student's knowledge state based on past performance and predict the correctness of the next question. Traditional KT often treats questions with different difficulty levels of the same concept as identical…

This case study investigated the development of prospective mathematics teachers' technological pedagogical content knowledge (TPACK) in graphical data displays with (VM) within the context of a microteaching lesson study (MLS). This research investigated how five participants integrated technology and implemented a lesson plan aimed to teach…

When informants from a given culture are asked to list items from a specified semantic domain, their lists provide two indicators of each term's prominence or salience: its frequency of appearance across lists and its mean position within the lists that include it. Smith et al. (1995), Sutrop (2001), and most recently Robbins et al. (2017) have…

Inverse and injective functions are topics in most college algebra courses. Yet, current materials and course structures may not afford students' conceptual understanding of these important ideas. We describe how students' work with digital activities, "techtivities," linking two different looking graphs that represent relationships…

This paper proposes a three-step approach to develop knowledge graphs that integrate textbook-based target knowledge graph with student dialogue-based knowledge graphs. The study was conducted in seventh-grade STEM classes, following a collaborative problem solving process. First, the proposed approach generates a comprehensive target knowledge…

The visual analysis of data presented in time-series graphs are common in single-case design (SCD) research and applied practice in school psychology. A growing body of research suggests that visual analysts' ratings are often influenced by construct-irrelevant features including Y-axis truncation and compression of the number of data points per…

In single-case research designs (SCDs) to determine a functional relation a time-series graph is constructed. Preliminary evidence suggest the approach used to scale the vertical axis and the data points per x- to y-axis ratio (DPPXYR) impact visual analysts' decisions. We conducted a systematic review to evaluate time-series graphs published in…

Currently, the search history in search engines is presented in a list view of some combination of enumerated results by title, URL, or search query. However, this classical list view is not ideal in collaborative search environments as it does not always assist users in understanding collaborators' search history results and the project's status.…

This study aims to determine the graphical literacy levels of middle school mathematics teachers. The participants of the study consisted of 33 middle school mathematics teachers working in different provinces. The data of the study were collected with the help of the graphical literacy test created by the researchers. The data were analyzed by…

The study reported in this paper is motivated by an article published on a financial portal that presented loan repayments with a continuous approach, as opposed to the discrete approach of addressing loan repayments applied in mathematics courses for economists. Using the Anthropological Theory of the Didactic, we analyse the current didactic…

Given the extensive use of online learning in educational settings, Knowledge Tracing (KT) is becoming increasingly essential. KT primarily aims to predict a student's future knowledge acquisition based on their past learning activities, thus enhancing the efficiency of student learning. However, the effective acquisition of dynamic and evolving…

One of the promises of edu-metaverse is its ability to provide a virtual environment that enables us to engage in learning activities that are similar to or on par with reality. The digital enhancements introduced in a virtual environment contribute to our increased expectations of novel learning experiences. However, despite its promising…