Calculators? Why not?

R N A de Silva
rnades@gmail.com

Calculating devices such as the abacus have been used since ancient times. These were hand operated calculating tools. Mechanical devices to perform basic mathematical operations were introduced only in the 17th century. The French mathematician Blaise Pascal is credited as the inventor of calculating machines in 1649. In 1850, the French Entrepreneur Thomas de Colmar manufactured the arithmometer which was the first commercially successful mechanical calculator. The Casio Company of Japan released the world’s first electric compact relay calculator in 1957. The Texas Instruments of USA released the first electronic handheld calculator in 1967. Due to the technical developments of integrated circuits along with LED and LCD, these devices have become progressively better and cheaper.

A standard calculator is designed to perform the four basic arithmetic operations which are addition, subtraction, multiplication and division. A scientific calculator can deal with the calculations of trigonometric, logarithmic and exponential functions in addition to the basic arithmetic functions. Graphic calculators have been available since 1985 and these have additional features such as plotting graphs and solving equations. In Sri Lanka, a standard calculator can be purchased for less than Rs 500 and a Scientific-Calculator costs about Rs 1500 while graphing calculators are not easily available.

The use of a calculator in the classroom has been a controversial issue. Some argue that the use of calculators will dilute the computational abilities of students and they will be too reliant on machines for their calculations thereby slackening the capacity of estimation. Another criticism is that some of the parents will not be able to bear the cost of a calculator. Others argue that the calculator is an essential device in a world of ever advancing technology and also that it can bring enjoyment of learning mathematics which seem to be lacking at present.

In 1975, the National Advisory Committee on Mathematical Education of USA made a recommendation that those in eighth grade and above should have access to calculators for all class work and examinations. Later the National Council of Teachers of Mathematics which is the world’s largest mathematics education organization stated its position as follows:

Calculator use can promote the higher-order thinking and reasoning needed for problem solving in our information- and technology-based society. Their use can also assist teachers and students in increasing student understanding of and fluency with arithmetic operations, algorithms, and numerical relationships and enhancing student motivation. Strategic calculator use can aid students in recognising and extending numeric, algebraic, and geometric patterns and relationships.

It also cited that the calculator use will result in improved student interest, stimulating classroom environments and student self-concept.

My friend Anton Peiris, in his thought-provoking article titled “Mathematics examinations or mathematics curriculum?” published in ‘The Island’ edition of 30th November 2023, suggested that the use of scientific calculators could begin in grade 10 in Sri Lankan schools. Commenting on the criticism that the students will not acquire the ability to carry out mental arithmetic calculation due to the use of calculators, he stated “Mathematics teachers have a total of eight years to inculcate sufficient mental arithmetic skills in their students before the calculators are introduced in grade 10”. With regards to the cost, he stated that an ordinary scientific calculator costs less than 10% of the price of a smartphone. I am in agreement with this proposal.

Teachers play a crucial role in creating an appropriate learning environment with the use of calculators to facilitate understanding and concept development. It needs to be used as a tool to aid in exploring, understanding and learning algorithmic processes. It can be great resource to encourage discovery, exploration and creativity. As an example, consider the estimation of the answer to a given computational problem. Estimates can be obtained first in the classroom without the use of calculators and thereafter have a discussion as to how to distinguish between impracticable answers and responses that fit the general parameters of the problem. In the end comparisons can be made with the solution that the calculator provides.

Test questions also need to be appropriately prepared to maximize the benefit of the use of a calculator. In general, questions can be categorized as follows:

Questions that require the use of a calculator to solve (Calculator active questions)

Questions where the calculator is of no help for solving (calculator inactive questions)

Questions where the calculator use is undeterminable (calculator neutral questions)

An examination question paper can be set to include a combination of these three types of questions to assess the overall ability. Especially in grades 10 and above, the need is to train the students to acquire skills to solve problems that are applicable to real life situations. In this regard the calculator seems to be an essential tool. Finding the Z score of a particular subject given the actual data obtained in a past year, calculating the insurance premium to be charged given the weightings of items of insurance coverage, estimating the trend of population growth of a country given the actual population figures in the past years and finding the magnitude of an earthquake are such examples. What happens now is doctoring figures to make them calculator neutral questions, which in turn make them unnatural. With real life situations being considered, the motivation to learn will also be enhanced.

I taught mathematics for the International Baccalaureate Diploma Program for forty years. Initially scientific calculators were used but it was changed to graphic calculators in the nineties. The final examination consists of three papers one of which is a test to be attempted without the use of calculators. This is also an option for testing as an examination can consist two sections where the calculators are allowed only in one section. Why spend time unnecessarily to multiply 366 X 24 X 60 or divide 299,792,458 by 1.6 or adding a list of salaries of employees in a firm, when a calculator can do it speedily? More classroom time can be used for conceptual understanding rather than computation.

Let me end with this quote of John Van de Walle. “Mathematics is much more than computation with pencil and a paper and getting answers to routine exercises. In fact, it can easily be argued that computation, such as doing long division, is not mathematics at all. Calculators can do the same thing and calculators can only calculate they cannot do mathematics”.

(The author is a senior examiner for mathematics at the International Baccalaureate Organization.)