Graduates in biology or genetics learn Mendel's laws and Hardy-Weinberg equilibrium as students, and they know, use, and sometimes teach these concepts. However, it is unusual to learn about stochastic processes during the graduate studies of these topics, although the applications of Markov chains in the fields of genetics or biology are…

In the era of artificial intelligence (AI), big data (BD), and digital transformation (DT), analytics students should gain the ability to solve business problems by integrating various methods. This teaching brief illustrates how two such methods--Bayesian analysis and Markov chains--can be combined to enhance student learning using the Analytics…

Our original paper tried to characterize the richness of the teaching repertoire of expert human teachers and to give a sense of how far there still was to go in the development of pedagogic expertise in AIED systems. It considered three ways in which more expert teaching strategies and tactics might be developed. These were via (i) the…

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…

The Hint Factory is an implementation of our novel method to automatically generate hints using past student data for a logic tutor. One disadvantage of the Hint Factory is the time needed to gather enough data on new problems in order to provide hints. In this paper we describe the use of expert sample solutions to "seed" the hint generation…

As teachers of first-year college mathematics and science students, the authors are constantly on the lookout for simple classroom exercises that improve their students' analytical and computational skills. In this article, the authors outline a project entitled "Predicting Precipitation in Darwin." In this project, students: (1) analyze…

Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…