Definitions

acrp

Graphing calculator

A graphing calculator (also known as a graphic calculator or graphical calculator) typically refers to a class of handheld calculators that are capable of plotting graphs, solving simultaneous equations, and performing numerous other tasks with variables. Most popular graphing calculators are also programmable, allowing the user to create customized programs, typically for scientific/engineering and education applications. Due to their large displays intended for graphing, they can also accommodate several lines of text and calculations at a time. Some graphing calculators also have colour displays, and others even include 3D graphing.

Since graphing calculators are readily user-programmable, such calculators are also widely used for gaming purposes, with a sizable body of user-created game software on most popular platforms.

There is also computer software available to emulate or perform the functions of a graphing calculator. One such example is Grapher for Mac OS X and is a basic software graphic calculator.

History

Casio produced the world's first graphic calculator, the fx-7000G in 1985. After Casio, Hewlett Packard followed shortly in the form of the HP-28C. This was followed by the HP-28S (1988), HP-48SX (1990), HP-48S (1991), and many other models. The current top-of-the line model, the HP 50g (2006), features a Computer Algebra System (CAS) capable of manipulating symbolic expressions and analytic solving. The HP-28 and -48 range were primarily meant for the professional science/engineering markets; the HP-38/39/40 were sold in the high school/college educational market; while the HP-49 series cater to both educational and professional customers of all levels. The HP series of graphing calculators is best known for their Reverse Polish Notation interface, although the HP-49 introduced a standard expression entry interface as well.

Texas Instruments has produced models of graphing calculators since 1990, the oldest of which was the TI-81. Some of the newer calculators are just like it, only with larger amounts of memory, such as the TI-82, TI-83 series (including the TI-83, TI-83 Plus, and TI-83 Plus Silver Edition), and the TI-84 Plus series (including the TI-84 Plus and TI-84 Plus Silver Edition). Other models, designed to be appropriate for students 10–14 years of age, are the TI-80 and TI-73 series. Other TI graphing calculators have been designed to be appropriate for calculus, namely the TI-85, TI-86, TI-89 series, and TI-92 series (including the TI-92, TI-92 Plus, and Voyage 200). TI offers a computer algebra system on the TI-89 and TI-92 series models with the TI-92 series having a QWERTY keypad. TI calculators are targeted specifically to the educational market, but are also widely available to the general public.

Graphing calculators are also manufactured by Sharp but they do not have the online communities, user-websites and collections of programs like the other brands.

Graphing calculators in schools

Casio has focused its efforts on the educational sector, and as such the built-in programming language and mathematical features are not as advanced as some of the TI and HP models. Despite this, the TI calculators are more popular than Casio in schools in the United States.

  • In the Canadian and American educational systems, many high school mathematics teachers allow and even encourage their students to use graphing calculators in class. In some cases (especially in calculus courses) they are required. Some of them are banned in certain classes such as chemistry or physics due to their capacity to contain full periodic tables.

Also, some high school courses offered in these countries require a graphing calculators to fulfill.

  • In Finland, Slovenia and certain other countries, it is forbidden to use calculators with symbolic calculation (CAS) or 3D graphics features in the matriculation exam.
  • In Norway, calculators with wireless communication capabilities, such as IR links, have been banned at some technical universities.
  • The College Board of the United States permits the use of most graphing or CAS calculators that do not have a QWERTY-style keyboard for parts of its AP and SAT exams, but IB schools do not permit the use of calculators with computer algebra systems on its exams.
  • In Australia, policies vary from state to state.
    • In Victoria, the VCE specifies approved calculators as applicable for its mathematics exams. For Further Mathematics an approved graphics calculator (for example TI-83/84, CASIO 9860, HP39G) or CAS (for example TI-89, Classpad 300, HP40G) can be used. Mathematical Methods and Mathematical CAS have a common technology free examination consisting of short answer and some extended answer questions. They also each have a technology assumed access examination consisting of extended response and multiple choice questions: a graphics calculator is the assumed technology for Mathematical Methods and a CAS for Mathematical Methods CAS. These two exams have substantial material in common but also some distinctive questions. Specialist Mathematics has a technology free examination and a technology assumed access examination where either an approved graphics calculator or CAS may be used. Calculator memories are not required to be cleared. In subjects like Physics and Chemistry, students are only allowed a standard scientific calculator.
    • In Western Australia, all tertiary entrance examinations in mathematics, Chemistry and Physics assume the student has a graphics calculator. However CAS enabled calculators are forbidden (HP 40g), the HP 39G was also banned due to a hack allowing the user to unlock CAS functions.
    • In New South Wales, graphics calculators are required in the General Mathematics Higher School Certificate exam, but disallowed in the remaining Mathematics exams.
  • In New Zealand, calculators identified as having high-level algebraic manipulation capability are prohibited in NCEA examinations unless specifically allowed by a standard or subject prescription. This includes calculators such as the TI-89 series
  • In Turkey, any type of calculator whatsoever is prohibited in all primary and high schools.
  • In Singapore, graphing calculators are used in junior colleges; it is required in the Mathematics paper of the GCE 'A' Levels, and most schools use the TI-84 Plus or TI-84 Plus Silver Edition.

Non-mathematical uses of graphing calculators

The programming features of nearly every major graphing calculator on the market have been exploited to produce games of various sorts. Imitations of Tetris and Pac-Man are among the most popular. A variety of other non-technical applications have been written for graphing calculators as well. Among these include organizers, phonebooks, text editors and even password protection and encryption programs. A software solution also exists for using the infrared port on the HP-48 series of calculators as a remote control for televisions (another method for this has been discovered using home-built infared units for use with the Texas Instruments series of graphing calculators), and those calculators with built-in speakers have been transformed into monophonic music sequencers. As a result of such programs, their use in schools has also received a great degree of criticism as it is extremely common to find that students have downloaded non-educational programs onto their calculators, presenting a potential distraction in the classroom.

Another major criticism of graphing calculators by school teachers is their ability to store large amounts of text in the same memory that is used to store programs. Such a feature presents a potential for students to cheat on examinations by storing notes and solutions on their calculators. While some enforce a rule by which students must perform a supervised memory clear of their calculator before an exam, this has become an increasingly difficult problem as the variety of available brands and models increases and false memory clear programs are released over the internet to deceive the proctor. In addition, many students use the calculator's memory to store useful programs, particularly those which improve the mathematical functionality of their calculators to be on par with other newer models, and requiring such students to clear their calculator memories would put them at a disadvantage. On the other hand, many courses have disallowed calculators on examinations altogether, and designing the assignment appropriately to purely test conceptual knowledge. Others argue that graphing calculators are too expensive. For example, if one compares a one hundred dollar graphing calculator (or any graphing calculator of arbitrary price) to a cell phone, GPS device, or PDA of equal price, one finds that the cell phone or other device outperforms the graphing calculator in terms of hardware (faster CPU and more memory). A new TI83+ typically costs $100 and has a 6 MHz processor. For $100 one can get a PDA with about 200 MHz and far more memory (and a colour screen). Opponents of this view argue that graphing calculators are more reliable because they last longer and that they also use less energy allowing them to use alkaline batteries which are far cheaper than the lithium ion - batteries that PDA and other devices typically use. The next generation of graphing calculators (ie: the TI-Nspire) may also help alleviate this criticism.

References

Dick, Thomas P. (1996). Much More than a Toy. Graphing Calculators in Secondary school Calculus. In P. Gómez and B. Waits (Eds.), Roles of Calculators in the Classroom pp 31-46). Una Empresa Docente.

Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education. 34(5), 433-463.

Heller, J. L., Curtis, D. A., Jaffe, R., & Verboncoeur, C. J. (2005). Impact of handheld graphing calculator use on student achievement in algebra 1: Heller Research Associates.

Khoju, M., Jaciw, A., & Miller, G. I. (2005). Effectiveness of graphing calculators in K-12 mathematics achievement: A systematic review. Palo Alto, CA: Empirical Education, Inc.

National Center for Education Statistics. (2001). The nation’s report card: Mathematics 2000. (No. NCES 2001-571). Washington DC: U.S. Department of Education.

See also

External links

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