Mathematical Modeling and Programming in Science Education

Abstract

Using mathematical models to represent aspects of physical reality is an essential activity in science and science education. This contribution discusses four approaches of using computer programming and mathematical models in classroom activities:
1) Mathematical models, found in the textbook, are used as a basis for computer programs. Students, when creating useful interactive python programs calculating concentrations or pH-values, experience similar intellectual challenges as in solving traditional text book problems.
2) Scratch-animations simulating physical or chemical systems simulation can be specifically designed to check the validity of given mathematical models.
3) A computer-related challenge is to design a simulation (like gas diffusion in a closed system with two phases) that might be a basis for discovering a mathematical model (like Henry's law) or just an element of a mathematical model.
4) Using sensor technology and a Raspberry Pi, students create a computer program that automatically visualizes the observed system behaviour (like changes in gas concentrations) in order to find a mathematical model.