This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher…

This article reports on a study in which third-grade students (8-9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained…

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of…

In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

How accurately can final-year students majoring in statistics, physics, and finance label the vertical axis of a normal distribution, explain their label, identify units, and answer a question about the impact of horizontal-axis rescaling? Our survey finds that only 27 out of 148 students surveyed (i.e., 18.2%) could label the vertical axis of the…

This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…

Item response theory (IRT) is a statistical paradigm for developing educational tests and assessing students. IRT, however, currently lacks an established graphical method for examining model fit for the three-parameter logistic model, the most flexible and popular IRT model in educational testing. A method is presented here to do this. The graph,…

Explanations of phenomena in chemistry are grounded in discussions of particulate-level behavior, but there are limitations to focusing on single particles, or as an extension, viewing a group of particles as displaying uniform behavior. More sophisticated models of physical processes evoke considerations related to the dynamic nature of bulk…

Everyday encounters with graphical representations include a variety of graphs that superficially appear similar due to their use of bars. This article examines students' conceptions and misconceptions regarding the interpretation of variability in histograms, bar graphs, and value bar charts. A multiple choice assessment with brief written…

The current study evaluated the degree to which novice visual analysts could discern trends in simulated time-series data across differing levels of variability and extreme values. Forty-five novice visual analysts were trained in general principles of visual analysis. One group received brief training on how to identify and omit extreme values.…

Randomized controlled trials (RCTs) and quasi-experimental designs like regression discontinuity (RD) designs, instrumental variable (IV) designs, and matching and propensity score (PS) designs are frequently used for inferring causal effects. It is well known that the features of these designs facilitate the identification of a causal estimand…

The influence of classroom context on the probability of being caught cheating is compared between face-to-face classes and online classes. A decision tree model assigned in the context of a management science class presents alternatives, including unethical choices, risks and rewards, and a decision facing a potential ethical dilemma. Part of the…

Curriculum-Based Measurement of Reading (CBM-R) is frequently used to monitor instructional effects and evaluate response to instruction. Educators often view the data graphically on a time-series graph that might include a variety of statistical and visual aids, which are intended to facilitate the interpretation. This study evaluated the effects…

Experimental and quasi-experimental designs play a central role in estimating cause-effect relationships in education, psychology, and many other fields of the social and behavioral sciences. This paper presents and discusses the causal graphs of experimental and quasi-experimental designs. For quasi-experimental designs the authors demonstrate…

The volume of data that can be captured and stored from students' everyday interactions with digital environments allows for the creation of models of student knowledge, skills, and attributes unobtrusively. However, models and techniques for transforming these data into information that is useful for educators have not been established. This…