The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.

Human reasoning about and with uncertainty is often at odds with the principles of classical probability. Order effects, conjunction biases, and sure-thing inclinations suggest that an entirely different set of probability axioms could be developed and indeed may be needed to describe such habits. Recent work in diverse fields, including cognitive…

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

Central questions in the study of visual word recognition and developmental dyslexia are whether early lexical activation precedes and supports decoding (a dual-stage view) or not (dual-route view), and the locus of deficits in dysfluent reading. The dual-route view predicts early word frequency and length interaction, whereas the dual-stage view…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

Purpose: Does the rising share of Latino students in US schools help to integrate previously White campuses or exacerbate racial and economic segregation over time? This article details trends in the segregation of Latino children enrolled in elementary schools, 2000-2015, then examines how evolving patterns differ among the nation's school…

Elementary-age students with Individualized Education Programs (IEPs) tend to experience more challenges and demonstrate lower homework completion as compared with peers without IEPs. Parent involvement in homework can significantly improve a child's homework achievement, but little research has examined the factors associated with higher levels…

Examining the sequential patterns of self-regulated learning (SRL) behaviors is gaining popularity to understand students' performance differences. However, few studies have looked at the transition probabilities among different SRL behaviors. Moreover, there is a lack of research investigating the temporal structures of students' SRL behaviors…

Computer science is a dynamic field of study that requires constant review and updating of the curricular designs in academic programs--in general, measuring the impact of plan changes has been little explored in the literature. In most cases, it focuses only on structuring its curricula, leaving aside several factors associated with important…

BASIE is a framework for interpreting impact estimates from evaluations. It is an alternative to null hypothesis significance testing. This guide walks researchers through the key steps of applying BASIE, including selecting prior evidence, reporting impact estimates, interpreting impact estimates, and conducting sensitivity analyses. The guide…

A strong foundation in early number concepts is crucial for students' future success in statistics. Despite its importance in statistics, many first-year students struggle to comprehend the normal distribution due to a lack of basic number sense. Students get confused about the order and magnitude of negative z-scores on a standard normal curve or…

Background: Developmental education (i.e., remedial education) has come under scrutiny given evidence that it is ineffective for learning or hinders students' progress toward degree completion (Scott-Clayton & Rodriguez, 2014; Xu & Dadgar, 2018). However, there is heterogeneity in the effect of developmental education, with positive…

Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

The purpose of this research is to construct a preliminary genetic decomposition delineating the mental constructions underlying probabilistic independence. This delineation is considered within the framework of APOS theory. While the use of the term independence in probability is often conflated with causation, the definition relies instead upon…

Learning introductory quantum physics is challenging, in part due to the different paradigms in classical mechanics and quantum physics. Classical mechanics is deterministic in that the equations of motion and the initial conditions fully determine a particle's trajectory. Quantum physics is an inherently probabilistic theory in that only…