This paper describes two examples of teaching situations in which the idea of infinity arises, and supports the conclusion that infinity is not a physical reality but a very powerful and useful mathematical device which facilitates modelling and the solution of problems in physics.

An educational lattice model is proposed for the investigation of the influence of the density and indirectly of the pressure on the chemical equilibrium of the ideal gas phase reaction A [equilibrium] 2B. The model can be introduced by a board game simulating a stochastic process. This game can also be used to set up a corresponding computer…

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

The article proposes a new research object for a general physics course--the vapour Cartesian diver, designed to study the properties of saturated water vapour. Physics education puts great importance on the study of the saturated vapour state, as it is related to many fundamental laws and theories. For example, the temperature dependence of the…

Teaching about wave structure and function is a critical element of any physical science curriculum and supported by "Next Generation Science Standards (NGSS)" PS4: Waves and Their Applications in Technologies for Information Transfer. To support students' learning of these ideas, teachers often rely on developing graphic models of a…

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

A classroom exercise is described to introduce enzyme kinetics in an undergraduate biochemistry or chemistry course. The exercise is a simulation in which a student acts as an enzyme that "catalyzes" the unscrewing of a nut from a bolt. With other students assisting, the student enzyme carries out reactions with bolt-nut substrates under different…

An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…

Genetics is a difficult topic as it involves abstract concepts, which are not directly observable. Studies on using simulations to support the learning of genetics have largely been confined to the use of quantitative simulations to replace experimentation. This study describes the use of a new type of simulation built using an iconic modelling…

Presents an activity in which students collect and organize data from a real-world simulation of the scientific concept of half life. Students collect data using a marble sifter, analyze the data using a graphing calculator, and determine an appropriate mathematical model. Includes reproducible worksheets. (MDH)