We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be…

Across the evidence-based policy and practice (EBPP) community, including education, randomised controlled trials (RCTS) rank as the most "rigorous" evidence for causal conclusions. This paper argues that that is misleading. Only narrow conclusions about study populations can be warranted with the kind of "rigour" that RCTs…

Probabilities tend to become an integral part of early childhood mathematics curricula. Research has shown that at the age of 4, children indicate basics of probabilistic reasoning and can engage with probabilistic tasks and uncertainty. The aim of this study is to examine whether methodological and design alterations influence children's…

In accord with classic schema theory, people are susceptible to forming false memories that align with stored schema representations (Brewer & Treyens, 1981). Furthermore, clinicians schematize mental disorders as causal networks of features (de Kwaadsteniet, Hagmayer, Krol, & Witteman, 2010; Kim & Ahn, 2002). We asked whether one…

Measures of socioeconomic status (SES) are widely used in educational research and policy applications in no small part because of a deeply rooted belief of the importance of SES. This paper argues that the usefulness of common SES measures can be undermined by (a) an atheoretical approach to conceptualizing SES and selecting measures, which…

Identifying mediators in variable chains as part of a causal mediation analysis can shed light on issues of causation, assessment, and intervention. However, coefficients and effect sizes in a causal mediation analysis are nearly always small. This can lead those less familiar with the approach to reject the results of causal mediation analysis.…

According to Wollack and Schoenig (2018), benefitting from item preknowledge is one of the three broad types of test fraud that occur in educational assessments. We use tools from constrained statistical inference to suggest a new statistic that is based on item scores and response times and can be used to detect the examinees who may have…

When children acquire language, they often learn words in the absence of direct instruction (e.g. "This is a ball!") or even social cues to reference (e.g. eye gaze, pointing). However, there are few accounts of how children do this, especially in cases where the referent of a new word is ambiguous. Across two experiments, we test…

Representational competence (RC) is a set of skills to reflectively use a variety of representations to draw inferences, make predictions, and support claims. Despite the important role RC plays in student success in chemistry and the considerable number of investigations into student ability to reason with representations, little is known about…

We examine the effect of an integrity pilot campaign on undergraduates' behavior. As with many costly small-scale experiments and pilot programs, our statistical inference has to rely on small sample size. To tackle this issue, we perform a Bayesian retrospective power analysis. In our setup, a lecturer intentionally makes mistakes that favors…

In many high-stakes testing situations, test-takers are not allowed to draw on external writing resources while writing, a practice observed more frequently in classroom settings. This may pose problems with the representativeness of test tasks and score interpretations. This study investigates the domain definition of one particular test known as…

The current study explores the impact of varying multiple-choice question preview and presentation formats in a test of second language listening proficiency targeting different levels of text comprehension. In a between-participant design, participants completed a 30-item test of listening comprehension featuring implicit and explicit information…

Traditional school laboratory exercises on a system of moving objects connected by strings involve deriving expressions for the system acceleration, a = (?F)/m, and sketching a graph of acceleration vs. force. While being in the form of rational functions, these expressions present great opportunities for broadening the scope of the analysis by…

Informed by reading comprehension and comprehension strategies research, this study explores the Scripture-reading practices of four Methodist youths. Several rounds of inductive thematic analyses of Scripture-reading protocols revealed a set of five strategic reading practices youths used to understand Scripture. They drew inferences about the…

There is a wealth of evidence that people's reasoning is influenced by explanatory considerations. Little is known, however, about the exact form this influence takes, for instance about whether the influence is unsystematic or because of people's following some rule. Three experiments investigate the descriptive adequacy of a precise proposal to…