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Teaching Mathematical Concepts

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The Personal Perspective of Abraham Nemeth

According to the National Council of Teachers of Math, all students need meaningful math with appropriate tools. It is particularly important for students with visual impairments to be exposed to the use of multiple math strategies and tools, including use of the abacus, braillewriter, mental math, talking calculators, and the calculator function of electronic notetaking devices. These strategies and tools should be introduced early in a child's educational program, and continually reinforced throughout the school years.

Of the three tools (braillewriter, abacus, and talking calculator), use of the braillewriter is the most time-consuming and cumbersome. The braillewriter is extremely slow and awkward to use as a calculation tool. Using it for this purpose is analogous to doing mathematical calculations with a typewriter by a sighted individual. Under these circumstances, the reader may dispute the advisability of expending the time and effort needed to teach the use of the braillewriter as a calculation tool. Nevertheless, blind students benefit from knowing the steps which are required to carry out arithmetic calculations in this manner. In general, while it should not receive heavy emphasis and should be combined with the use of other tools, the braillewriter as a calculation tool should be introduced at the beginning of`mathematics instruction.

Use of the braillewriter emulates how sighted individuals perform arithmetic calculations. Although it is not absolutely necessary for blind persons to perform calculations in the same manner as sighted individuals in order to be successful, it is beneficial to the blind learner to know the processes which are necessary to perform general arithmetic calculations. For true understanding of the procedures for carrying out arithmetic calculations, and thorough comprehension of basic mathematics, the braillewriter is the only device available to blind students. It is the only way for a blind student to write out the steps involved in carrying out an arithmetic operation. In the past, arithmetic slates such as the cubarithm and the Taylor slate were advocated for this purpose. These are no longer used in up-to-date programs for blind students because experience has shown that these tools are very cumbersome and inefficient when compared to the use of the braillewriter.

Instruction with the braillewriter should be combined with instruction on the abacus. There are several advantages which accompany the use of the abacus. First of all, it provides a method which is more efficient than the braillewriter. Secondly, the abacus is much more portable than the braillewriter. Thirdly, the methods employed with the abacus afford the student the additional advantage of having experience with some of the fundamental mathematical principles underpinning arithmetical calculations.

The abacus can be used as a tool to check the accuracy of the calculations performed on the braillewriter. In this way, each method reinforces the other. If both answers are correct, then the calculation was most likely performed successfully. If there is a discrepancy between the two results, then, most likely, one of the results is incorrect, although the reader should note that it is possible for both results to be inaccurate. If a discrepancy exists, the student should be encouraged to perform the calculation again using both methods. This should be done until similar results are achieved.

As the student becomes more proficient in the use of the braillewriter in performing specific procedures, such as two-digit addition, more reliance can be placed on the use of the abacus and less reliance can be placed on the use of the braillewriter. The general principle here is to move from the more cumbersome tool to the more efficient one. This should be done without neglecting instruction on all of the tools. When a new or more complex arithmetic procedure is initially studied, the teacher should emphasize use of the braillewriter to insure that the student gains a full command of the procedures involved. This should be done with simultaneous instruction on the abacus. The principle of moving from the braillewriter (the more cumbersome tool) to the abacus (the more efficient tool) should continue.

Steps should be taken to make calculation procedures with the braillewriter as easily accomplished as possible. Alterations in the symbol forms and format are needed to enhance the effectiveness of the braillewriter as a calculation tool. The recommended changes in methods used to perform arithmetic calculations, as well as relaxation of the strict rules for transcribing Nemeth Code, make it easier for the student to carry out the necessary steps to add, subtract, multiply, and divide with the braillewriter. The following approach should be used in carrying out the four basic operations with whole numbers, decimal fractions, and regular fractions.