Technology Support: Calculators (page 2)
Calculators are devices that assist with simple or lengthy computations. The earliest calculator, the abacus, is still in use in many cultures. Between 1600 and 1960, various mechanical calculators were used—including the logarithmic rule (1620) and slide rule (1622), the Odhner pin-wheel calculator (1874), and the Dalton 10-key add-listing machine (1902) (Tout, 2005). In 1961, the first electronic desktop calculators were sold in England. The first all-transistor calculators appeared in 1964 for about the price of a car at the time. Sharp produced the first battery-powered hand-held calculators in 1969, and the microprocessor-based calculator appeared in 1971. Hewlet-Packard introduced the first scientific pocket calculator in 1972 and by 1975, prices for all handheld calculators had dropped significantly, allowing use by classroom teachers and students. Solar-powered calculators were introduced in 1978. The Little Professor, a dedicated calculator for mathematics practice, appeared in the same year (Texas Instruments) and assumed the opposite function of a calculator—it gave the question and asked for the answer .
Today, calculators are available in many sizes (even on cell phones and in notebooks) with varying functions and applications. The basic types used in school are four-function, scientific, and a range of graphing calculators. Other dedicated calculators (hand held or web-based) are used for specific applications such a loan amortizations, measurement conversions, and currency conversions.
The calculator is considered an “assistive technology device” under IDEA. Calculators can be purchased through special education funding if designated on an IEP and used “to increase, maintain, or improve the functional capabilities of [individuals] with disabilities” (§300.5). However, the IEP team must specify how such an assistive device is to be used to enhance access to the general education curriculum. If calculator use is determined necessary and required per the IEP, it must be allowed to the extent specified.
Requirements for calculator use on district or state-level tests vary considerably, with some tests requiring calculators, some permitting calculator use, and some prohibiting their use. The SAT allows calculator use and recent studies indicated that students using graphing calculators performed better that those using less sophisticated versions, but these results may be due to those students taking more advanced mathematics classes that require graphing calculators (see, for example, Wendler, Zeller, & Allspach, 2003). Other studies of student achievement also indicate that calculator use is more prevalent among white, middle-class students and this difference in technology use contributes to the achievement gaps associated with race and SES (Lubienski & Shelley, 2003).
Teachers cannot simply hand out calculators and expect students to use them effectively and efficiently. The type of calculator needed for the mathematics application should be considered. Elementary students typically are introduced to the four-function calculator in first grade, but many students will have already had calculator experiences at home. This type of calculator is limited to numbers expressed in decimal form and the four arithmetic operations. By middle school, calculators with more advanced functions are needed (e.g., square roots, percent, fractions, and statistics). High school students should learn to use graphing calculators for algebraic, trigometric, statistical, and other pre-calculus applications.
Calculators are more difficult to learn than computers due to the limits of on-screen icons and prompts, so explicit and guided instruction on a common model is recommended, especially for students with learning problems. Teachers should demonstrate calculator use through modeling (overhead projector versions) and think alouds. Students’ initial use should be guided with corrective feedback. Instruction may need to begin with locating each key and learning the effects of each function (e.g., pressing the key followed by a number and the will add to my previous amount).
Teachers should also emphasize questions to prompt accurate use. For example, “the problem states that we should find the average height of five students with heights of and . How can we use the calculator to assist us with this problem? My first question is about the form of the data—can my calculator add feet and inches? My next question is procedural—how do we compute averages on a calculator?” Students with learning problems may need other accommodations, such as larger keys and display screens, paper printouts for monitoring inputs and outputs, or prompting sheets with step-by-step directions for entering specific types of equations or creating graphs. Calculators may actually make advanced mathematics concepts accessible for more students, minimizing the number crunching and tedium of long or multi-step computations.
© ______ 2007, Merrill, an imprint of Pearson Education Inc. Used by permission. All rights reserved. The reproduction, duplication, or distribution of this material by any means including but not limited to email and blogs is strictly prohibited without the explicit permission of the publisher.
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