The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article, we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of [tau], the between-study standard deviation, and the shrunken estimates of the study effects as a…

Causal inference is a central topic in education research, although oftentimes it relies on observational studies, which makes causal identification methodologically challenging. This manuscript introduces causal graphs as a powerful language for elucidating causal theories and an effective tool for causal identification analysis. It discusses…

We use a tensile testing machine to create stress-strain plots and determine Young's modulus for some ductile and plastic materials. Supplementary videos are also provided.

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…

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…

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…

Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function…

Automatic short answer grading (ASAG) is a challenging task that aims to predict a score for a given student response. Previous works on ASAG mainly use nonneural or neural methods. However, the former depends on handcrafted features and is limited by its inflexibility and high cost, and the latter ignores global word cooccurrence in a corpus and…

The decomposition of the overall effect of a treatment into direct and indirect effects is here investigated with reference to a recursive system of binary random variables. We show how, for the single mediator context, the marginal effect measured on the log odds scale can be written as the sum of the indirect and direct effects plus a residual…

Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

Using the educational knowledge graph to express the logical characteristics of knowledge, this paper takes project-driven learning in the teaching of "Information Technology in Secondary Schools" as an example and studies the group cooperative teaching mode based on the educational knowledge graph. The relationship between knowledge…

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) limits students' expression of their affective states. As a complement to existing methods that rely on verbal reports, we explore how graphing can be used to study affect during…

This Concise Review is an appraisal of contemporary research on teaching single-case experimental design (SCED) graphical creation published between 2017-2021. Recent work on SCED graphical creation is summarized and areas for future research are highlighted.

Exploratory graph analysis (EGA) is a commonly applied technique intended to help social scientists discover latent variables. Yet, the results can be influenced by the methodological decisions the researcher makes along the way. In this article, we focus on the choice regarding the number of factors to retain: We compare the performance of the…

Researchers tasked with understanding the effects of educational technology innovations face the challenge of providing evidence of causality. Given the complexities of studying learning in authentic contexts interwoven with technological affordances, conducting tightly-controlled randomized experiments is not always feasible nor desirable. Today,…