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 present paper takes its point of departure in risk being a relevant content for science education, and that there are many different approaches to how to incorporate it. By reviewing the academic literature on the use and definitions of risk from fields such as engineering, linguistics and philosophy, we identified key elements of the risk…

The Monte Carlo method and related multiple imputation methods are traditionally used in math, physics and science to estimate and analyze data and are now becoming standard tools in analyzing business and financial problems. However, few sources explain the application of the Monte Carlo method for individuals and business professionals who are…

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…

When wave vortices, that is nodal lines of a complex scalar wavefunction in space, approach transversely, their typical crossing and reconnection is a two-stage process incorporating two well-understood elementary events in which locally coplanar hyperbolas switch branches. The explicit description of this reconnection is a pedagogically useful…

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

Demonstrating probabilistic outcomes using real-time data is especially well-suited to larger lecture classes where one can generate large data sets easily. The difficulty comes in quickly collecting, analyzing, and displaying the information. With the advent of wireless polling technology (clickers), this difficulty is removed. In this paper we…

Distinguishing between good and bad science is not easy. Evaluating whether or not a claim really is supported by good research is like buying a car. There is an optimal solution to the problem, which is to read and digest all of the relevant research, but most people do not have time to execute the optimal solution. What they need is a good…

This compendium organizes information on the math and science projects sponsored by NCER and NCSER into two main sections: Mathematics and Science. Within each section, projects are sorted into chapters based on content area, grade level, and intended outcome. In determining the chapters, we considered the emerging college- and career-readiness…

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

An exercise is presented in which the kinetics of the irreversible "reaction" of pennies in the heads-up state to pennies in the tails-up state is simulated by a hands-on, Monte Carlo approach. In addition, the exercise incorporates a second simulation in which the irreversible "reaction" of dice with a red face uppermost to a blue face uppermost…

Scientists have associated the El Nino/Southern Oscillation (ENSO) phenomenon with extreme climate events such as flooding in California, droughts in Australia, fires in Indonesia, and increased hurricane activity in the Atlantic Ocean. The popular media is constantly attributing individual storms to the ENSO phenomenon. The reality is that a…

Discusses need for introducing material to educate students about the relationship of philosophy to physics and science in general, particularly in light of quantum mechanics. Suggesting the dual nature of electrons as a starting point and citing several supplemental texts, a demonstration is described to be used to introduce the topic. (JM)

Discusses the importance of teaching students when to seek deterministic explanations and when to seek probabilistic ones, pointing out that there are situations in which each is appropriate and inappropriate. Several examples illustrating the appropriateness of these explanations are provided. (JN)

Describes a series of activities without conclusions to introduce scientific reasoning in a ninth grade physical science course. Uses popcorn popping to get students to think about the concepts of graphing, histograms, frequency, probability, and scientific methodology. (CW)