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From: Loyd <firstname.lastname@example.org> To: Teacher2Teacher Public Discussion Date: 2001111110:31:11 Subject: Re: When to use graphing calculators On 2001111020:15:56, A. Booth wrote: > I am a new teacher although I got my bachelors degree in math about >25 years ago. I would like to know when and when not to allow >students to use graphing calculators. I learned to do all this stuff >without them, but now my students do all kinds of shortcuts with them >and I want to make sure they can perform the tasks they need to >without them. Am I being too picky? > The graphing calculator is very useful for algebra II students and higher. It is not absolutely necessary for a student to get through the course but increases greatly the understanding of functions and graphs. It takes some algebra skill to get the equations in the proper form for graphing. Also, the graphing operation makes clear what a root or zero is; the meaning of minimums, and maximums become much clearer than they did with purely mechanical means. I learned how to graph 46 years ago and then went on to major in mathematics. Still, after I got my TI-83 in 1999 so I could tutor algebra II students, I found that even now, the ability to graph with ease increased my understanding and gave me permanent visuals to store in my memory. I found myself reviewing all my old calculus books and graphing the myriad of functions in the back of the book. I have watched a lot of students use these calculators and some only use them as a scientific calculator replacement. They aren’t always taught how to use them with understanding. In the hands of a good math teacher, they are a great asset. In my opinion, the algebra I teacher should teach the fundamentals of using the graphing calculator and the algebra II teacher should teach it a little more to use as a tool. I have not found a student who is poor at math without a graphing calculator that is good at math with a graphing calculator. Most of these capable students are good with math either way. When I took matrix algebra (linear algebra) in my junior year in college, matrices were taught at a very abstract level so that even simple matrix multiplication was difficult to understand at first. Most of the students didn’t know what the German Professor was even talking about. I finally learned by going to the library where I found a high school textbook that “spilled the beans” with a lot less rigor. Then, I could finally understand the what appeared to be “hen scratches” used by the textbook and professor. Then finally we tried to solve 5x5 systems of equations using the matrix method using elementary row operations. I was able to do maybe one or two problems in my entire college career (5x5 system) because the odds of making an arithmetic mistake were very great. Try it some time. Now with the TI-83 you can punch in coefficients of a 5 by 5 system of equations and find the roots very easily. You can use row operations or you can use the matrix inverse method; the latter is simple with the TI-83. This power gives you the ability to experiment with in a lot of ways that is not possible with only pencil and paper. However, I would not encourage a student to graph linear equations or even quadratic equations until they understand the manual process. Algebra should start with established methods so that the students can get an appreciation for the process. Then they will appreciate the graphing calculator more. There is thinking that goes on with a graphing calculator that would not be available to a student that was educated in say late 40s and early 50s or even 60s and 70s. In the computer age, this thinking is essential.
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