This paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities--especially the ones that involve Bayes' rule--with…

Purpose: We investigated whether rhythm discrimination is mainly driven by the native language of the listener or by the fundamental design of the human auditory system and universal cognitive mechanisms shared by all people irrespective of rhythmic patterns in their native language. Method: In multiple experiments, we asked participants to listen…

Background: Verbal short-term memory (STM) capacity has been considered to support vocabulary learning in typical children and adults, but evidence for this link is inconsistent for studies in individuals with Down syndrome (DS). The aim of this study was explore the role of processing demands on the association between verbal STM and vocabulary…

Achieving fluency in important mathematical procedures is fundamental to students' mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasi-experimental studies carried out in a total of 11 secondary schools involving altogether 528…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

In this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention…

In this work we use prior to tutor-session data to generate an individualized student knowledge model. Intelligent learning environments use student models to individualize curriculum sequencing and help messages. Researchers decompose the learning tasks into sets of Knowledge Components (KCs) that represent individual units of knowledge; the…

Purpose: The purpose of this study was to develop and pilot a novel treatment framework called "BEARS" (Balancing Effort, Accuracy, and Response Speed). People with aphasia (PWA) have been shown to maladaptively balance speed and accuracy during language tasks. BEARS is designed to train PWA to balance speed-accuracy trade-offs and…

Working memory (WM) is used for storing information in a highly accessible state so that other mental processes, such as reasoning, can use that information. Some WM tasks require that participants not only store information, but also reason about that information to perform optimally on the task. In this study, we used visual WM tasks that had…

Game-based assessment (GBA) is a specific use of educational games that employs game activities to elicit evidence for educationally valuable skills and knowledge. While this approach can provide individualized and diagnostic information about students, the design and development of assessment mechanics for a GBA is a nontrivial task. In this…

In the machine learning literature, it is commonly accepted as fact that as calibration sample sizes increase, Naïve Bayes classifiers initially outperform Logistic Regression classifiers in terms of classification accuracy. Applied to subtests from an on-line final examination and from a highly regarded certification examination, this study shows…

Given the importance of education and the growing public demand for improving education quality under tight budget constraints, there has been an emerging movement to call for research-informed decisions in educational resource allocation. Despite the abundance of rigorous studies on the effectiveness, cost, and implementation of educational…

Estimating student proficiency is an important task for computer based learning systems. We compare a family of IRT-based proficiency estimation methods to Deep Knowledge Tracing (DKT), a recently proposed recurrent neural network model with promising initial results. We evaluate how well each model predicts a student's future response given…

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…