Calculator Use

Computers, four-function calculators, and graphing calculators have assisted in the development of significant advances in the field of mathematics. For example, the famous 4-color theorem went unsolved for more than 100 years until 1976, when the calculation and visualization powers of computers were utilized to derive a mathematical proof. Advances in production speed, manipulation, and representation of data through the use of calculators and computers have also benefited the field of statistics, including the specific area of educational statistics. Educational psychology has taken advantage of these advancements in product technologies to support research and theory in the field, particularly in regard to these technologies' abilities to support statistical computation and manipulation.

Although the first desktop calculators were available in the 1960s, their commercial availability did not emerge until the early 1970s. These early ‘four-function’ calculators were limited in scope in that they were able to perform only the basic mathematical operations of addition, subtraction, multiplication, and division. In the late 1970s, companies such as Casio, Hewlett-Packard, Sharp, and Texas Instruments began to produce programmable calculators. These models had small memory chips capable of storing a limited number of preprogrammed algorithms, including square root, exponents, and basic statistics. Some of these models also allowed users to input basic computer code and program their own algorithms.

In the early 1990s, graphing calculators greatly expanded the user capabilities of the handheld devices. The ability to compute fixed algorithms, represent functions and data in multiple ways, and support simple computer codes, made the graphing calculator a prime example of a product technology that allows for an enormous amount of mathematical power, speed, and visual representation. Graphing calculators readily support the production and use of educational statistics through the calculation of statistical tools such as mean, standard deviation, and quartiles, allowing researchers an efficient and thorough view of quantitative data. However, educational psychologists have extended the power of calculators beyond the computing of statistics. Graphing calculators can support statistical research through plotting two-variable statistics; looking for patterns in two-variable situations to determine an underlying model to interpolate or extrapolate; and conducting various hypothesis-testing procedures, including t-tests, regressions, and analysis of variance (ANOVA).

To illustrate, let us suppose an instructor believes that attendance is an important factor in student motivation. A survey is given at the beginning of the course to determine beginning motivation levels (0–100 scale). The data are gathered, organized into [Page 126]a list, and entered into the calculator. Various statistics can be quickly produced, including mean, standard deviation, and quartile boundary values. These numbers provide a clear picture of students' self-perception of motivation levels at the beginning of the course. In Figure 1, the middle column shows the mean (55.96) and standard deviation (14.87), whereas the right-hand column shows the five quartile values, including the minimum (20), median (58), and maximum (77).

Figure 1 Students' Self-Perception of Motivation Levels at the Beginning of the Course

Although a four-function calculator could also produce these statistics, users would need to know the algorithms for computing the statistics, and input the quantities and operations in a lengthy, step-by-step process for each one. The built-in algorithms available in graphing calculators (or any calculator with these preprogrammed functions) allow users to produce these statistics quite easily.

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