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The Evolution of the Graphing CalculatorA Case StudyMichelle RodriguezEDUC 515Prof. GilbreathAzusa Pacific UniversityAbstractTechnology is a huge part in today’s workplace and culture. Thus, it also plays a huge role in today’s 21st century classrooms. This paper explores an important electronic device used in most mathematics classrooms at the high school level: the graphing calculator. It will describe the evolution of the graphing calculator, beginning with the first known hand-made calculator, the abacus, and ending with today’s modern graphing calculator. I will also explore the graphing calculator’s effects on student performance and make predictions for its future uses. Keywords: technology evolution, graphing calculator, and technology in the classroomThe Evolution of the Graphing CalculatorA Case StudyTechnology is always changing and advancing. It is a huge part in today’s workplace and culture, and, hence, it also plays a huge role in today’s 21st century classrooms. One specific piece of technology that is used in most mathematics classrooms at the high school level is the graphing calculator. A graphing calculator is a handheld calculator that has the ability of doing simple calculations, plotting graphs, solving simultaneous equations, and performing other tasks involving variables. They are typically used in advanced math courses, such as trigonometry, pre-calculus, and calculus, as well as, advanced science or engineering classes. This paper examines the evolution of the handheld graphing calculator, its uses in the classroom, and how it might be used in the future. The History of the Graphing CalculatorThe Mechanical AgeThe very first known calculator was the abacus. This was a hand-operated, mechanical calculator that used beads on rods as a means of performing simple calculations. The Sumerians and Egyptians first used this device around 2000 B.C. Then, it wasn’t until the 17th century AD when a notable change in the handheld calculator was seen. Shortly after Napier’s publication of logarithms, Edward Gunter, William Oughtred, and others developed the slide rule, which is also known in the United States as a slipstick. The slide rule is basically a sliding stick or circular disc that uses logarithmic scales to allow rapid multiplication and division and other advanced calculations for trigonometry, logarithms, exponentials, and square roots (Valentine 2015).The slide rule was the very first calculator to enter the classroom and it was the most commonly used calculation tool in science and engineering at that time. Millions of schoolchildren were required to know how to operate a slide rule, which was a basic part of mathematics education even up to the 1980s (Watters 2015). From the 17th century to the mid-20th century, a variety of mechanical calculators were invented, such as, Pascal’s Calculator in 1642, Thomas’ arithmometer in 1820 (which was one of the first successful mechanical calculator to be used commercially), the comptometer in 1887, and the Curta calculator in 1948 (Valentine 2015). Soon after, electronics began to take over.The Electronic AgeThe very first electronic calculators were seen in the late 1930s and were created as a connection for weapon systems. The Sperry-Norden bombsight, the U.S. Navy’s Torpedo Data Computer, and the Kerrison Predictor AA fire control system were all basically mechanical devices using gears and rotating cylinders to produce electrical outputs that could calculate the trigonometry required to drop bombs from 30,000 feet, hit a Japanese warship moving at 30 knots, or bring down a diving Stuka (Valentine 2015). Electronic calculating for the office didn’t appear until 1961, with the invention of ANITA (A New Inspiration To Arithmetic/Accounting). This was the very first all-electronic desktop calculator, which was created in Britain by Control Systems Ltd. Anita used the same push button layout as a mechanical comptometer, but performed calculations electronically, using a mix of vacuum and cold cathode “dekatron” counting tubes. Other early electronic calculators were built with vacuum tubes and later transistors, and were very large, taking up an entire desk (Watters 2015).Jack Kilby, an engineer at Texas Instruments, developed the first working integrated circuit in 1958, which allowed for cheaper, smaller, and better performing computing devices. Then, about a decade later, in 1967, TI engineers invented the very first handheld, electronic calculator. These devices started off costing several hundred dollars, but with a large number of technical developments, especially the invention of the microchip, these calculators improved quickly and decreased in price quickly, and by the end of the 1970s were much more affordable and much more commonplace (Watters 2015). The Virtual Age (Present Day)By the 1980s, calculators had essentially evolved into the familiar forms of today: compact in size, using single chips and LCD displays, powered by solar cells or button batteries, and capable of a wide range of functions. Then in 1986 came the arrival of the world’s first graphing calculator developed by Casio of Japan – the fx-7000G. It contained an icon menu for easy access to functions, expandable memory, backlit screen, textbook-like input and output, and allowed graphing in several colors (Demana 2000). This led to other companies producing graphing calculators, such as, Sharp, Hewlett Packard, Casio, and the most popular today, Texas Instruments. In 1990, Texas Instruments produced its own line of graphing calculators, starting with the TI-80. They later added more memory, faster processors, and a connection for a USB, in the series, such as the TI-82, TI-83, and TI-84 series. Other TI graphing calculators have been designed essentially for calculus students, such as, the TI-85, TI-86, TI-89, and TI-92 series. Texas Instruments’ series of graphing calculators have allowed them to specifically target the educational market, making them the number one graphing calculator purchased for school. With the power of the Internet and apps, however, students no longer need to buy expensive graphing calculators. Websites, such as, Desmos and Mathway, and apps, such as, Free Graphing Calculator, have made it possible for students to complete their work and assignments without the use of a handheld graphing calculator. However, these applications are not allowed for use on state tests, AP, or IB tests. The Future of the Graphing CalculatorThe calculator has been one of the most controversial pieces of technology to enter the classroom. Educators fear that students’ computational abilities would weaken and eventually would become too dependent on machines. However, studies have shown that students who used graphing calculators were actively involved in problem solving and would actually discuss and read about the mathematics they were learning (Waits & Demana, 1998). Furthermore, according to Kastberg and Leatham (2005), another study proved that students with the longest access and exposure to calculators incorporated a larger range of problem-solving techniques and tended to attempt more problems and obtain higher test scores in comparison to the students who had not. However, students with only short-term or limited access to graphing calculators ended up becoming confused and were unable to integrate their knowledge of math with their developing understanding of a new tool (Kastberg and Leatham, 2005). According to Waits and Demana (1998), graphing calculators do not replace traditional mathematics content, but are used to give visuals, provide support, confirm results, or conduct mathematical experiments. Moreover, they believe that all three methods of computation – mental, paper-and-pencil, and computation done with technology – are important today and will remain important in the future. Teachers, therefore, must be provided with adequate training and professional development for integration of technology and learning. It is evident that graphing calculators are here to stay in education. The question now is how will they look like in the future? I chose this topic because I teach math at the high school level and I see more and more students turning away from traditional graphing calculators and utilizing their phones or laptops. As more and more technology is being available online and even through simple phone or tablet apps, I believe that the actual physical handheld graphing calculator will become obsolete, since most students can now access it via a laptop or tablet provided by the school or their own cell phones. As technology advances, I think that soon the rules and applications used in state testing, AP, and IB testing will evolve as well. The new SBAC state testing already allows students to access a simple computational calculator for various problems and I’m sure soon the AP and IB tests will follow suit. Of course, the teacher is still the key for student success. Although students will have access to all sorts of graphing calculators, whether they are handheld or online, teachers must ensure that students understand concepts, develop their computational skills, and be able to integrate their understanding of math and science with new technologies developed. Thus, I believe that professional development in technology is a must for all teachers and will soon be a requirement by all school districts. ReferencesKastberg, S. & Leatham, K. (2005). Research on graphing calculators at the secondary level: Implications for mathematics teacher education. Contemporary Issues in Technology and Teacher Education, 5(1), 25-37. Retrieved from , B. K., & Demana, F. (1998). The Role of Graphing Calculators in Mathematics Reform. Retrieved from , F. (2000). Calculators in mathematics teaching and learning. Learning mathematics for a new century, 51. Retrieved from , N. (2015). The history of the calculator. Retrieved from , A. (2015, March 12). A brief history of calculators in the classroom. Retrieved from ................
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