Calculators in the ClassroomAuthor(s): Gregory Aidala and Peter RosenfeldSource: The Mathematics Teacher, Vol. 71, No. 5, Computers and Calculators (MAY 1978), pp.434-435Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27961292 .

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sharing teaching ideas

Calculators in the Classroom In accordance with the National Council

of Teachers of Mathematics' policy state ment on the use of calculators in the class

room, our program for using calculators with our eighth grade was intended to rein force learning and to motivate the learner in the study of mathematics. Calculators

were used?

1. to provide continued and increased mo tivation toward the subject matter;

2. to furnish faster and more efficient ways of solving problems;

3. to allow problems of greater intricacy to be attempted; and

4. to contribute to further applications and

exploration of related topics.

Fifteen calculators and adapters were

purchased for one class. Initially, ten min utes of free time was set aside for students to explore the capabilities of the calculator.

We had to overcome the fact that many students had access to calculators at home with different logics and keying sequences from the ones we had purchased. To offset this problem, a model calculator made of construction paper (50 cm X 100 cm) was

employed to explain all the capabilities and limitations of the classroom machines.

Although many students claimed to be

proficient in the use of a calculator, we

found that at least two full class periods devoted strictly to problems in addition, subtraction, multiplication, and division were necessary to insure mastery of funda mentals. In particular, division problems

proved to be most difficult for students to

solve. For example, 0.31432, ^|,or

432 +

0.3 all represent identical division prob lems, but on a calculator many students often confused the order of input. As a

result, a great deal of practice in addition, subtraction, multiplication, and especially division was provided before students were asked to solve many applications.

The eighth-grade curriculum at the Beth lehem Central Middle School is composed of many diversified topics representing various branches of mathematics. Units of

study covered during the school year in clude probability, statistics, proportion, percent, coordinate geometry, solid geome try, and algebra. Within each unit there exist several exercises involving the use of calculators that serve to reinforce learning activities from previous class periods.

By way of example, the volume of a rec

tangular prism and the volume of a cylinder were studied from the unit on solid geome try during one week of classes. In class on

Friday, students took a short quiz review

ing the material on volume covered during the previous four days. In the remaining twenty to twenty-five minutes of class, stu dents were required to complete an exercise with the aid of calculators. The exercise involved calculating the volume of two rec

tangular prisms and four cylinders. Stu dents were given the dimensions of each

figure, and formulas were written on the board for reference. The substance of that exercise is summarized in table 1.

Sharing Teaching Ideas offers practical tips on the teaching of topics related to the secondary school curriculum. We hope to include classroom-tested approaches that offer new slants on familiar subjects for the beginning and the experienced teacher. Please send an original and four

copies of your ideas to the managing editor for review.

434 Mathematics Teacher

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TABLE 1

Figure Length of Base Width of Base Height "Volume = 1 X w X h

1. Rectangular Prism 19.85 ft. 11.3 ft. 7.7 ft. 1727.15 cu. ft. 2. Rectangular Prism 42.3 cm 39.6 cm 15.5 cm 25 963.74 cm3

Radius Height Volume =

3. Cylinder** 7.4 in. 16.7 in. 2871.50 in.3 4. Cylinder 29.5 cm 52.8 cm 144 280.48 cm3

5. Cylinder 0.54 m 1.6 m 1.46 m3 6. Cylinder 72ft. 125.8 ft. 2 047 742.2 cu. ft.

* Students were instructed to round off all answers **7t = 3.14.

The use of calculators in the classroom adds a distinctive feature to any mathemat ics program. On the basis of two years of

experience, it is the feeling of the authors that calculators have a definite role in

mathematics classes. We feel that calcu lators should be consistently used as a sup

plemental aid to learning. The following list of guidelines is meant

to assist readers who are in the process of

initiating a program involving the use of calculators.

1. The purchase of all calculators should include a one-year warranty to replace or repair any malfunctioning machine.

2. Distinct and permanent identification is

necessary for all calculators and adapt ers.

3. The authors highly recommend the use

of electrical adapters as opposed to any

type of recharging device. Adapters will

provide uninterrupted and longer-last ing service from the calculators.

4. A locking cabinet must be provided to enhance the easy distribution, collec

tion, and protection of all calculators and adapters.

5. Designated calculators should be as

I the nearest hundredth place.

signed to students so that a particular machine is used by the same pair of stu dents on a continuous basis.

6. Rules and regulations involving the use of calculators must be clearly stated and enforced so that students will exercise care in the operation of each calculator.

7. A trustworthy student should assist the teacher in the distribution and collection of calculators during a class period.

8. At least two full class periods of instruc tion should be provided to all students to learn the methods of operating a cal culator.

9. Although educators should be urged to

explore all avenues of incorporating cal culator use into daily lessons, we highly recommend that the use of calculators not exceed one experience per week. The

novelty of calculators in a classroom en vironment can easily be eroded by over

use; more important, basic computa tional skills might eventually become

weaker.

Gregory Aidala Peter Rosenfeld Bethlehem Central Middle School

Delmar, NY 12054

A Symbiosis between the Computer and the Curriculum

We have added an innovative feature to our mathematics curriculum whereby all mathematics students can now learn to

write computer programs (in BASIC) ap

propriate to the mathematics they are

learning.

May 1978 435

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