This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the…

Ionization of amino acids (AA) is very important concept in biochemistry. We integrate the mathematical concept of probability with biochemically relevant process of AA ionization. We visualize the ionization process with Mathematica software discussing intramolecular interactions between weakly acidic/basic functional groups and charge--pH…

The transition from the probability mass function for discrete random variables to the probability density function for continuous random variables is not straightforward, especially to students from the health and social sciences. An R Shiny application was created to assist the learning process of probability density function.

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…

Students can struggle to understand and use terms that describe probabilities. Such struggles lead to difficulties comprehending classroom conversations. In this article, we describe some specific misunderstandings a group of students (ages 11-12) held in regard to vocabulary such as "certain", "likely" and…

Mathematics teachers continually look for ways to make the learning of mathematics more active and engaging. Hands-on activities, in particular, have been demonstrated to improve student engagement and understanding in mathematics classes. Likewise, many scholars have emphasized the growing importance of giving students experience with the…

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships,…

There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to "think aloud" so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are…

Data analysis plays a prominent role in various facets of modern life: Schools evaluate and revise programs on the basis of test scores; policymakers make decisions on the basis of information gleaned from polling data; supermarkets stock shelves on the basis of data collected at checkout lanes. Data analysis provides teachers with new tools and…

The benefits of visualizing mathematics by using technology such as TI-92+ and mathematically oriented software (DERIVE 5 and CABRI II) are indisputable. On the basis of some examples we would like to show that visualizing techniques can help students to analyse certain mathematical problems better and give them strong support in finding formal…

This collection of activities is designed to show how graphing calculators can be used to explore statistics. The activities address such topics as data representation, distributions, and statistical tests. Teaching notes and calculator instructions are included as are blackline masters. (MM)

Discusses information retrieval systems and the need to have them adapt to user needs, integrate information in any format, reveal patterns and trends in information, and answer questions. Topics include statistics and probability; natural language processing; intelligent agents; concept mapping; machine-aided indexing; text mining; filtering;…

Revealing or visualizing the thinking involved in making clinical decisions is a challenge. A case study is presented with a visual implement for sharing the diagnostic process. This technique adapts the Bayesian approach to the case presentation. Pretest probabilities and likelihood ratios are gathered to obtain post-test probabilities of every…