A typical graphing calculator.
A
graphing 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. Recent models like the HP 50g
(2006), feature 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 its 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, TI- Nspire CAS 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
- 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 requires
a graphing calculator to fulfill.
- In the
UK
, a graphic calculator is required for most A-level maths courses, the use of such
devices is both taught and tested. However, for GCSE maths exams, a limited number of calculator models
are allowed, none of which are capable of graphic operations
(although they are capable of scientific and statistical
operations).
- 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
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 [42672].
- In
Turkey
, any type of calculator whatsoever is prohibited in
all primary and high schools except the IB and American
schools.
Criticisms and 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
[42673] 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 color screen. Opponents of
this view argue that graphing calculators are more reliable because
they last longer. They also argue that graphing calculators also
use less energy, allowing them to be powered by 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
, Slovenia
and certain
other countries, it is forbidden to use calculators with symbolic
calculation (CAS) or 3D
graphics features in the matriculation exam.
, calculators with wireless communication capabilities,
such as IR links, have been banned at some
technical universities.
, 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.
, graphics calculators are required in the General
Mathematics Higher School
Certificate exam, but disallowed in the remaining Mathematics
exams.
, 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.
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