Exploring Math with the TI-89

Technology changes possibilities

The TI-89 is a graphing, programmable calculator with symbolic manipulation capabilities. I know that is a mouthful but we can break it down to three main features:

1) This device graphs not only functions of one variable; it also graphs functions of two variables, parametric curves, functions given in polar coordinates, and data from number tables.

2) Programmable means it has commands you can use for writing code that is directly executable on the device. You can save, edit, and execute programs in it. This gives you plenty of flexibility when it comes to calculations for complex problems, because you are not restricted to the built-in operations.

3) Symbolic manipulation means the device displays, and uses standard mathematical symbols like integral, derivative, roots, exponents, and fractions, in a way that is consistent with algebra rules. That means it is not only a number-crunching little machine, but it does many operations of algebra, and calculus, like factoring polynomials, solving equations, multiplying matrices, deriving functions, and finding definite integrals.

All these capabilities present opportunities for teaching math. For example, using this calculator it is very easy to show relationships between formulas of functions, and their graphs. Presenting these relationships in a book usually takes several pages. Students often have some trouble reading, believing, understanding, remembering, and applying the general rules for this level of algebra of functions. On the other hand, typing the examples from the book into the calculator, and seeing the graphs of the functions being displayed in real time in front of their eyes, gives them more confidence to “believe in the evidence.” Therefore they can be puzzled but they do not reject out of hand the result shown. On the contrary, given the easy-to-use editing capabilities of the function editor, they can experiment with the function formulas by changing their parameter values and seeing what happens with the graphic output. In my opinion this may make learning more interactive, fun, and effective.

Math as a Freedom Source

An ongoing dialog

Math gives you freedom because it takes freedom to learn it. Learning math makes you ask questions all the time, like: "What do we have here?" "What could that possibly mean?" "Have we seen something like that before?" "How can I get that?" "How can I figure the answer to that?" "Am I supposed to do something here?" "What would happen if I do this operation?" "Am I off the mark? How far off?" "How can I tell the difference?" "Is there a shortcut for this?" “Does it always work the same way?" and so on and so forth, ad infinitum.

Questions bring answers, and they also bring more questions. Being able to ask questions all the time means the society of ideas that is your mind tends to be pretty open, fluid, flexible, and dynamic. You find ways to free up your mind to ask more questions, and to keep searching for the answers.