A good deal of primary data in mathematics consists of tables and graphs. These data make the abstract formulas and equations concrete and down to earth. They also exhibit phenomena which stimulate investigation. Much of the theory can be motivated by the desire to explain what is observed, or to answer natural questions arising out of the data. Most mathematical theories have originated in the search for answers to specific questions. To present the theory divorced from the data is to give the students answers to questions they have never asked.

The data usually require computation. The main purpose of the calculation is to find which phenomena the data exhibit. The drudgery of the computation and concern over computational error are distractions from this purpose. Therefore the students should be encouraged to use computational aids such as hand or desk calculators. Many schools and colleges also have computer facilities available. The most common language used in educational computers is BASIC.

We shall give here an introduction to the use of calculators and to BASIC programming, to be used in conjunction with the later chapters. There are minor variations in the versions of BASIC used in different installations, so that our explanations may have to be modified slightly in some institutions.

The calculator: learning how to use it

We use the term calculator for any hand-held calculator. Obviously, in any case, one should first make sure that all students know how to use it. This entails some care on the part of the instructor, since he should check that, although different makes or models may be used concurrently, all students can perform the same operations.