Compare problems are the most difficult type of word problems among primary school students, especially inconsistent problems, when the relational term is not consistent with the arithmetic operation required for the solution. The present study examines whether different methods help students successfully solve them and how these approaches…

This work was developed to present constructive steps of multiple integrals using the open-source software Geogebra. The main focus was directed towards creating three-dimensional graphs of integrals through Riemann sums in two variables. Some practical examples are developed to demonstrate the reliability of the presented results, which are…

A growing body of literature suggests manipulating some graphing conventions can affect visual analysis and adherence to graphing conventions varies widely in single case design publications. Yet use of graphing conventions by the wider population of behavior analysts is largely unexplored. The current study examined relations among types of…

In recent years, online learning methods have gradually been accepted by more and more people. A large number of online teaching courses and other resources (MOOCs) have also followed. To attract students' interest in learning, many scholars have built recommendation systems for MOOCs. However, students need a variety of different learning…

Curriculum-based measurement (CBM) represents a critical strategy for data-based decisionmaking within educational settings. Visual analysis is frequently used to analyze CBM data; thus, CBM vendors often automatically generate graphs based on student data to facilitate analysis. Differences in graph formatting are apparent across CBM vendors, and…

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…