Problem-based learning (PBL) has been widely applied as an alternative to improve learning outcomes, but it is still little studied in the context of the probability theory course. This study described how implementing the PBL model improves students' problem-solving and critical thinking skills in probability theory course and evaluates its…

Knowledge tracing algorithms are embedded in Intelligent Tutoring Systems (ITS) to keep track of students' learning process. While knowledge tracing models have been extensively studied in offline settings, very little work has explored their use in online settings. This is primarily because conducting experiments to evaluate and select knowledge…

Here, we present a strong test of the hypothesis that sacrificial moral dilemmas are solved using the same value-based decision mechanism that operates on decisions concerning economic goods. To test this hypothesis, we developed Psychological Value Theory. Psychological Value Theory is an expansion and generalization of Cohen and Ahn's (2016)…

One of the central goals of modern science and chemistry education is to develop students' abilities to understand complex phenomena, and productively engage in explanation, justification, and argumentation. To accomplish this goal, we should better characterise the types of reasoning that we expect students to master in the different scientific…

This report is based on an activity completed by 89 Grade 6 students carrying out a statistical investigation with a focus on posing an initial question given a context and then refining it for a chosen data set. Having reached a conclusion based on evidence from their data analysis, students were given additional information on the context and…

This paper attempts to quantify the accuracy limit of "nextitem-correct" prediction by using numerical optimization to estimate the student's probability of getting each question correct given a complete sequence of item responses. This optimization is performed without an explicit parameterized model of student behavior, but with the…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

In 1881, Donald MacAlister posed a problem in the "Educational Times" that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a…

Arthur Cropley (2006) emphasized the critical place that convergent thinking has in creativity. Although he briefly refers to the blind variation and selective retention (BVSR) theory of creativity, his discussion could not reflect the most recent theoretical and empirical developments in BVSR, especially the resulting combinatorial models.…

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem…

This study aims to develop a semiotic declarative knowledge model, which is a positive constructive behavior model that systematically facilitates understanding in order to ensure that learners think accurately and ask the right questions about a topic. The data used to develop the experimental model were obtained using four measurement tools…

Being able to characterize the size of raindrops is useful in a number of fields including meteorology, hydrology, agriculture and telecommunications. Associated with this article are data sets containing surface (i.e. ground-level) measurements of raindrop size from two different instruments and two different geographical locations. Students may…

Bayesian techniques have become increasingly present in the social sciences, fueled by advances in computer speed and the development of user-friendly software. In this paper, we forward the use of Bayesian Asymmetric Regression (BAR) to monitor intervention responsiveness when using Curriculum-Based Measurement (CBM) to assess oral reading…

The Gain-Loss model is a probabilistic skill multimap model for assessing learning processes. In practical applications, more than one skill multimap could be plausible, while none corresponds to the true one. The article investigates whether constraining the error probabilities is a way of uncovering the best skill assignment among a number of…

We present a new method for analyzing a student's learning over time for a specific skill: analysis of the graph of the student's moment-by-moment learning over time. Moment-by-moment learning is calculated using a data-mined model that assesses the probability that a student learned a skill or concept at a specific time during learning (Baker,…