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Graphing Calculator - Curse and Blessing

Over the past couple of years, I have found myself more and more often recommending graphing calculators for Algebra 1 students. This wizard instrument, capable of far more than I myself know how to tap into, works well with my tutoring style. However, I have seen firsthand what the consequences can be when students learn to use them without guidance. So many times, I have worked with high school upperclassmen and college students who cannot perform basic operations with fractions, graph by hand, evaluate an expression by hand, or perform addition and subtract with positive and negative integers because they became reliant on their calculators before ever properly learning the skills. These students usually lack the time or motivation to go back and learn how to do the skills by hand. Their courses move along rapidly and they need to spend their tutoring time keeping pace with the more advanced ideas. This is particularly unfortunate because these are the same skills they are most likely to need in day-to-day life. This is probably also the reason that some teachers seem to delay introduction of the calculator until Algebra 2 or Pre-calculus, and some teachers avoid them completely. Yet, I find this to be to the student's disadvantage. The visual aspect of the graphing calculator, and the fact that you can see the results of small changes in numbers quickly, makes it a valuable learning tool when it comes to fostering those "lightbulb" moments. Furthermore, an electronic device covered with buttons can hold the interest of students from the computer and video game generation. In addition, I have found that the tactile interaction can help students with mild ADD focus better and that early introduction of students to an "advanced level" device gives them a feeling of mastery and confidence. If a student becomes (gasp!) curious about the material at hand, I can take advantage of the moment and quickly show him or her a few little extensions of the idea on the calculator. Graphing calculators also help students become more independent learners because they can be used to check homework problems and answers on tests. Most teachers require that work be shown, so I like to guide students through the process of doing the problem and checking their work with the calculator at the end. Because the calculator method and the hand method often differ, this also helps the student see the concept from multiple angles. For instance, if the student is learning the quadratic formula, I might show him or her that the answers for X correspond to the X-intercepts of the parabola graph and have him or her calculate these on graphing calculator to check the answer. In time, this increases the student's understanding of the material. Moreover, it helps him or her prepare for the SAT and ACT where graphing calculators are allowed. Not only do students learn how to use them more quickly arrive at certain answers, they develop a feel for which situations the calculator is faster and for which situations the hand method is faster. This feel is difficult to teach a student preparing for the SAT or ACT in a few weeks or months leading up to the test. In addition, the calculator give them "back-up" methods that they can use to solve problems where they do not recognize the particular skill or idea. Lower level classes move a little more slowly than their more advanced counter parts. Consequently, I can work with students on remedial skills while also teaching them how to use the calculator. For example, we can work on common denominators and adding fractions by hand while also working on entering and adding fractions on the calculator. As the tutor, I make sure that the student develops the basic skills and does not come to depend on the calculator as a crutch. Often, at this level, there are two goals in tutoring – 1. develop a better and deeper understanding of the material, and 2. help the student improve his or grades. The calculator can help the student get a better grade on an imminent test while buying time that I can use to build the skills and understanding that are lacking. Over the years, I have seen these advantages of the graphing calculator in person and have come to firmly believe it its use as a tutoring tool.