The application of the Reaction Monte Carlo (RxMC) algorithm to standard textbook problems in chemical reaction equilibria is discussed. The RxMC method is a molecular simulation algorithm for studying the equilibrium properties of reactive systems, and therefore provides the opportunity to develop computer-based "experiments" for the…

Computer-based scaffolding plays a pivotal role in improving students' higher-order skills in the context of problem-based learning for Science, Technology, Engineering and Mathematics (STEM) education. The effectiveness of computer-based scaffolding has been demonstrated through traditional meta-analyses. However, traditional meta-analyses suffer…

Computer-based scaffolding provides temporary support that enables students to participate in and become more proficient at complex skills like problem solving, argumentation, and evaluation. While meta-analyses have addressed between-subject differences on cognitive outcomes resulting from scaffolding, none has addressed within-subject gains.…

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software "R for Statistical Computing." The author illustrates the computer simulation approach by focusing on several problems of…

Interactive learning environments can provide learners with opportunities to explore rich, real-world problem spaces, but the nature of these problem spaces can make assessing learner progress difficult. Such assessment can be useful for providing formative and summative feedback to the learners, to educators, and to the designers of the…

Researchers in education are often interested in determining whether independent groups are equivalent on a specific outcome. Equivalence tests for 2 independent populations have been widely discussed, whereas testing for equivalence with more than 2 independent groups has received little attention. The authors discuss alternatives for testing the…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

Monte Carlo methodologies are frequently applied to study the sampling distribution of the estimated proficiency level in adaptive testing. These methods eliminate real situational constraints. However, these Monte Carlo methodologies are not currently supported by the available software programs, and when these programs are available, their…

Discusses computer experiments employing Monte Carlo techniques for describing phase transitions and critical phenomena in theoretical physics. (SL)

Encourages the use of the microcomputer to teach probability theory and concepts. Presents an instructional sequence and provides 10 activities, three of which have short programs listed. (JM)

A description is given in which a computer program can be used to illustrate principles of statistical mechanics. The concepts of ensembles, statistical averages, and responses are classified particularly with respect to the role of statistical fluctuations. (DF)

Representations and changes between them play a major role in education (e.g., Hewson, Beeth, & Thorley, 1998), problem solving (e.g., Bauer & Reiser, 1990), cognitive development (e.g., Vosniadou & Brewer, 1992), and the history of science (e.g., Kuhn, 1970). By definition, change of representations is also indispensable for collaborative work…

Monte Carlo simulation is a computer modeling procedure for mimicking observations on a random variable. A random number generator is used in generating the outcome for the events that are being modeled. The simulation can be used to obtain results that otherwise require extensive testing or complicated computations. This paper describes how Monte…