Since the days that computers emerged as fast and diligent number-crunching devices, mathematicians have searched for ways of getting them to perform increasingly sophisticated tasks. This has led to the latest development in technology, computer algebra systems, a sort of mathematical expert systems which is necessarily changing the way we teach and learn mathematics. We review the development of computer algebra systems over the last 20 years, discuss current trends in which an increasing number of teachers are experimenting with CAS, and offer future visions for teaching with CAS in this new millenium. More and more ministries of education are officially adopting this new technology, and some are even making their use compulsory in examinations. CAS is also entering the International Baccalaureate curriculum and assessment.
First of all, we are teaching students. Second we are teaching subjects such as mathematics. Computer Algebra Systems change the way we teach mathematics and allow us to address the individual needs of students.
Confuzius says: “Give a person a fish – and you feed them for a day. Teach a person to fish – and you feed them for a lifetime.” We demonstrate with examples how to best use CAS to teach students of all abilities to fish for mathematical knowledge. We also provide a general framework around these examples.
Derive is a mathematical computer program, called a computer algebra system (CAS). It processes algebraic variables, expressions, equations, functions, vectors, and matrices like a scientific calculator processes floating point numbers. Derive can perform numeric and symbolic computations, algebra, trigonometry, calculus, and plot graphs in 2 and 3 dimensions. It is a powerful tool for doing and applying mathematics, for documenting mathematical work, and for teaching and learning mathematics.
Through solving typical mathematical high school level problems, you will learn to handle Derive and you will experience how to use it as a pedagogical tool.
Local organizers
Pengyuan Wang (Affiliated High School of Peking University, China)
Meng Zhou (Beihang University, China)