# Teaching Problem Solving Using the TI-Nspire

As teachers, we are often caught in the struggle of how much technology is too much? In the early 90’s, Texas Instruments burst onto the scene with the TI-81 plus graphing calculator. As a result, two sides were formed. The purists fought against them, as they simplified many of the sacred tasks like graphing lines by creating a table, and evaluating expressions that require knowledge of the order of operations. Todays calculators have taken things one step further with the use of nSolve, and tools to solve systems of equations. ] I stand in the middle, appreciating the beauty of solving systems of equations by using substitution or elimination, but recognizing that most high school students have a computer in their pocket, with immediate access to google and a world that has youTube videos that can show you how to do anything. I love the fact that the calculator allows us to embrace real world problems, without the worry of having to find data that will factor easily. But the skill I focus on the most is “using the calculator as a hypothesis checker.” A perfect example is simplifying polynomials. For example, my students generally do very well when only one skill is being used, but when I mix up the binomial operations, the results decline quickly. The concept of keeping exponents the same, and multiplying coefficients, or adding the exponents and adding the coefficients can quickly turn into a disaster of epic proportions. But lately, I have had success convincing students that they can use their calculator to test for equivalence. By simply storing a value to x, I can quickly test whether 5x + 3x is 8x or 8x^2. The calculator then becomes a tool for the students, and I spend a few days at the beginning of the year emphasizing that concept. It can be used on any question that requires simplifying, and I like the additional accountability it forces on the students. I think back to my high school days and recall my teachers assigning the odd numbered on a page, despite knowing that the answers to the odd numbers were given in the back of the book! I always thought it was foolish, because everyone could just copy down the answers, but soon realized that having the right answer was meaningless. You had to know HOW to get the right answer, and through a series of guesses and checks, I eventually learned the “rules of math.” I can still hear my teacher telling the class “Having the right answer is meaningless on homework, the answers are being given to you, YOU need to figure out how to get that answer. Knowing the right answer actually made the homework take longer. If my answer was wrong, I had to keep working until I figured out the right way to do it. That’s a lot different than just finishing an assignment and assuming your answers are right, until the assignment is gone over the next day. What is your opinion? Do you embrace the technology as nothing more than a modern day answer key, or are calculators ruining mathematics and the skills that are loved so much?