Calculators in society

Summary: Advancements in calculator technology have profoundly changed society and mathematics education.

In the decades since the invention of a truly handheld calculator, these devices have evolved from four-function curiosities costing hundreds of dollars to sophisticated machines capable of performing a wide range of mathematical and statistical functions at the same cost as that “four-banger” from the early 1970s. The effect on society has been considerable, as the laborious arithmetic involved in routine scientific or financial calculations can be done by nearly anyone with minimal effort and accuracy that was unthinkable in the 1950s. A variety of technological advances and a new market for calculating power during the 1970s led to the “calculator wars” among a variety of manufacturers, and frequent major advances in the power of a calculator were marketed to a willing society. These powerful calculators have changed the school mathematics curriculum in a variety of ways and brought a new focus to the Advanced Placement (AP) calculus exams.

Early History of Calculators

In their 1951 textbook Mathematics of Investment, Paul Rider and Carl Fischer made occasional reference to the ability of “computing machines” to facilitate involved calculations in financial mathematics. However, since such machines were by no means common in the 1950s, the book includes 123 pages of numerical tables, roughly one-third of the book’s total length. These references were essential to actuarial calculations for many years, and their analogous tables of values of trigonometric functions, exponentials, and logarithms were a staple of mathematics textbooks for a comparable time period.

The rapid rise of low-cost electronic calculators—a generation beyond the electric computing machines to which Rider and Fischer referred—reduced those tables to a mere historical curiosity within a generation. In 1958, Texas Instruments (TI) engineer Jack Kilby invented the integrated circuit, which became known as the “calculator on a chip,” that revolutionized the world of calculating devices. Large electromechanical desktop calculators soon gave way to more compact electronic machines, which culminated with the development of the Cal-Tech handheld calculator in 1965 at Texas Instruments. The Cal-Tech was a simple four-function calculator that used a paper tape for output. With a new standard for what was possible, the rush to advance calculating machines, both handheld and desktop, was on.

Engineers at Hewlett-Packard (HP) merged the old with the new in 1968 with the development of the HP-9100A, the first fully electronic desktop calculator. The 9100A was considerably larger than the Cal-Tech but was much more versatile. Its function set included all of the functions found on a modern scientific calculator—trigonometric functions, logarithms, reciprocals, and others—and it was fully programmable. On viewing the 9100A, company founder Bill Hewlett included among his words of praise for the developers the challenge that the world needed a similar machine that would fit into a shirt pocket.

In 1972, Texas Instruments introduced the Datamath, a four-function calculator released under the TI name. This was a departure for the company, which until then had confined its calculator work to manufacturing parts for other companies’ machines. Indeed, the Cal-Tech was built primarily to show other manufacturers what the company’s parts could do, not as an eventual consumer product. In that same year, Hewlett-Packard engineers developed the HP-35, a fully scientific calculator that could fit into a shirt-pocket. With these two companies at the forefront of a rapidly advancing technology, and with many other manufacturers in close competition, the “calculator wars” began. The rapid evolution of affordable competing calculators from a variety of manufacturers went on throughout the 1970s and into the early 1980s.

A major innovation was TI’s introduction of the TI-30 scientific calculator, which sold for under $30 beginning in 1976. The full scientific function set of the TI-30 on a low-priced machine was a huge advance over the $395 price tag of the original HP-35, and the TI-30 was regarded for many years as the best-selling calculator of all time.

HP introduced the first handheld programmable calculator, the HP-65, in 1974 (fewer than two years after its first scientific calculator), and followed it up in 1977 with the HP-67. TI countered with the SR-52 in 1975, which was succeeded by the TI-58 and TI-59 in 1977. Each of these milestone calculators allowed the user to specify a sequence of steps into a special memory. These steps could then be repeatedly executed as many times as desired. The HP models and the 52 and 59 provided the option of recording programs onto small magnetic cards for permanent storage, while the 58 and 59 came equipped with a slot for read-only memory (ROM) cartridges with space for dozens of specialized prewritten programs that were stored on the chip and could be run as needed without the need for repeated keying.

Special-Purpose Calculators

Special-purpose calculators are preprogrammed with functions and formulas that are specific to a particular profession or interest. Among the earliest were calculators designed for financial mathematics, with keys and routines for solving the time value of money problems and automating interest calculations—and here was where Rider and Fischer’s prediction was exceeded. These business calculators were considerably more sophisticated than could have been imagined in 1951.

By far the most successful business calculator is Hewlett-Packard’s HP-12C, which was introduced in 1981 and is still in production 30 years later. In most senses, the 12C is the industry standard financial calculator, and it has been the key to HP’s successful focus on the business calculator market. In 2003, the 12C got a facelift—and a faster processor—as the HP 12C Platinum Edition.

Unit conversion calculators inspired by the push in the 1970s to introduce the metric system in the United States live on in a variety of construction calculators, many of which have been produced by a small company, Calculated Industries (CI). CI was founded in the 1978, and its first product was a real estate calculator dubbed “The Loan Arranger.” Future financial calculators from CI would expand in capability to accommodate more sophisticated calculations, and a separate line of CI financial calculators is specific to Canadian interest calculations. Later product lines from CI included the Construction Master and Measure Master lines—which were specialized for the building industry. CI also produces a series of electrical engineering calculators and a pair of professional plumbing calculators.

CI also manufactures special-purpose calculators for a variety of niche markets. Do-it-yourselfers can find the calculations they need preprogrammed into the ProjectCalc series. Several of these have been rebranded by Sears under the Craftsman line. The KitchenCalc Pro is preset to convert cooking measurements and includes a built-in timer. The Quilters’ FabriCalc is one of the company’s most successful hobbyist calculators and automates the considerable mathematics involved in quilting. Most recently, the Mr. Gasket Hot Rod Calc was developed to serve performance automotive enthusiasts with a collection of functions for use in assessing an automobile’s performance.

Calculators in the Classroom

In 1976, Texas Instruments released the Abstract Linking Electronically (ABLE) calculator system, which represented the first attempt to manufacture a calculator specifically designed for elementary school classrooms beginning in the earliest grades. The ABLE system consisted of a standard four-function calculator with six interchangeable faceplates. These faceplates blocked access to some of the calculator’s functions and could be switched out to allow a richer selection of options as a child’s mathematical sophistication grew.

There was then, and continues to be, considerable tension over the question of calculator use in school mathematics. The conflict is generated by the ability of inexpensive calculators to automate routine arithmetic problems, which had led one side of the debate to suggest that there is no need to require computational automaticity, such as memorizing multiplication tables, which a calculator can handle. These advocates then assert that calculators free up room in the curriculum for what are called “higher-order” mathematical thinking skills. Those opposed to this view assert that higher-order skills are not useful without a sound foundation based on mastery of routine calculations. Sensible middle ground exists between these two viewpoints, and a variety of combinations of these approaches are advocated in textbooks and available to teachers.

In 2000, TI expanded the Explorer line to include the TI-15 Explorer calculator, which was designed for use in grades 3–6. This calculator contains specialized keys for computations like place value calculations and fraction operations without cluttering the keyboard with higher-level computations, like trigonometric functions, that are not studied in elementary school. Additionally, the TI-15 Explorer includes two keys that can be programmed to repeat simple operations, a randomized arithmetic tutor, and tools for exploring inequalities. A simpler companion calculator, the TI-10, was introduced in 2002 and is aimed at kindergarten through third grade classrooms.

At higher grade levels, one effect was far less controversial. With the advent of inexpensive powerful scientific calculators, there was no longer a need for extensive tables of functions in precalculus textbooks.

Graphing Calculators

In 1985, Casio introduced the first graphing calculator, the fx-7000G. In addition to serving as a fully functional scientific calculator, the fx-7000G had a large (1.4-by-2-inch) LCD screen on which graphs of functions could be displayed. This allowed students to work with functions from both numerical and graphical perspectives, and set the stage for a revolution in mathematics teaching. Graphing calculators soon came to be seen as one of the primary components of this shift in teaching and learning.

Hewlett-Packard advanced handheld capacity further with the HP-28C, introduced in 1987. In addition to numerical and graphical approaches to functions, the 28C was able to perform symbolic algebra and calculus, working with variables directly without the need for numbers. Texas Instruments released its first graphing calculator, the TI-81, in 1990, and the TI-85 soon after. The TI-82, 83, 84+, 86, and 89 have extended this successful product line, while the TI-80 and 73 have reached downward into middle schools.

As graphing calculators and computer algebra systems, such as Derive and Mathematica, competed for space in calculus classrooms around the world, it became clear that standardized testing would have to accommodate these new devices. Beginning in 1995, the Advanced Placement calculus exams have required the use of a graphing calculator on part of the exam, one that can plot graphs of functions, solve equations numerically, compute numerical derivatives, and evaluate definite integrals numerically. The College Board, which administers the AP exams, draws the line at calculators with a typewriter-style QWERTY keyboard, such as the TI-92 (introduced in 1996) and Voyage 200 (introduced in 2002) from Texas Instruments. The concern here is for the security of the tests, as the typewriter keyboard and text-processing capability are thought to make it too easy to collect confidential test questions and remove them from the testing site.

The Future of Calculators

It is unclear what new ground remains to be broken in future calculators. Three-dimensional graphing is available on a variety of TI and HP machines, but the size of the screen and the challenge from computer algebra systems, such as Mathematica, have limited the reach of this feature. Calculating power is finding its way into a variety of other handheld devices. Just as many people no longer wear watches because they can get the time from their cell phones, calculator applications for cell phone platforms may render the cell phone an attractive alternative to a specialized calculator. While there are cost and durability issues to be considered in this comparison, CI has recognized this alternate platform by marketing its Construction Master Pro software for the iPhone.

Bibliography

Ball, Guy, and Bruce Flamm. The Complete Collector’s Guide to Pocket Calculators. Tustin, CA: Wilson/Barnett Publishing, 1997.

Hicks, David G. “The Museum of HP Calculators.” http://www.hpmuseum.org.

Sippl, Charles J., and Roger J. Sippl. Programmable Calculators. Champaign, IL: Matrix Publishers, 1978.

Woerner, Joerg. “Datamath Calculator Museum.” http://www.datamath.org.