Is Technology Eroding Our Problem-Solving Skills?

Is technology weakening our problem-solving skills? As a SAT Math teacher, I work with students from different backgrounds, some from boards that permit the use of calculators in Math, and others that prohibit the use of technology. I increasingly feel that excessive use of calculators, even for simple calculations, can make us slower at Math.

For instance, consider the question above - which year shows the highest percentage growth? How would you solve it? I often find students trying to solve such a question by using the following:? ?

Percent Change = ((Final value – Initial Value)/Initial Value)*100

Often, they calculate the value for all data points, as calculations are 'easy'. This is correct, but needlessly complicated, with several extra steps. Every extra step is lost time, and also an opportunity for making a mistake. This is more common with students who use calculators often. Many of the problems in tests such as the SAT are designed to test understanding of concepts and are not particularly heavy on calculations. The dependence on technology also becomes a hindrance in tests such as the MAT (Oxford University), which prohibits the use of calculators. Many questions in the MAT don’t require knowledge of higher mathematics, but quick out-of-the-box thinking can be a huge advantage.

Suppose you had to solve this problem without a calculator – as I have had to do for most of my life.

The first step would be to eliminate options that are clearly incorrect. In this case, a quick visual inspection using an old technology – the Mark I Eyeball – shows that the increase from 2018 to 2019 is too small, and from 2019 to 2020, there has actually been a decline in sales. So we are now down to 2 options instead of four.

Next step – instead of using the detailed formula, I will just calculate (Final Value/Initial Value).

For 2018, I get 130/105 = 26/21

For 2021, I get 155/135 = 31/27.

The fractions show that the growth from 2017 to 2018 is clearly greater. With a calculator, I can calculate these numbers exactly, and would use that to confirm my work.

If you cannot use a calculator, you have to rely on ingenuity and mental math. You develop shortcuts – for instance, the two options that I eliminated, and the simpler formula that I used. The use of technology eliminates this need, and some students are unable to develop these skills. In a test such as the SAT, where time is of the essence, a student who can simplify a problem has an advantage. Students who have not used calculators in the past often have an advantage in such a test.

Boards such as CBSE and ICSE don’t permit calculators. It forces students to know basic calculations and tables. International boards such as A Levels and IB require much greater depth conceptually in Math and Science subjects. However, one disadvantage from a SAT perspective is that students are allowed to use calculators. Being reliant on calculators for small calculations also takes away time from shorter and more efficient ways of solving several questions.

While use of calculators is a policy decided by education boards and schools, students can follow some simple steps to get better at mental math:

1. Memorizing multiplication tables up to 20 is a good first step. This makes it easier to perform some calculations mentally. Try to calculate squares and cubes of numbers mentally.
2. Memorize common formulae – the area of a triangle, the surface area of a sphere, the volume of a cone, etc., as well as common trigonometrical ratios. Give yourself some random problems – if a cube has a volume of 64 cubic centimeters, what is its total surface area? If the diameter of a sphere is the same as the side of a cube, what is the ratio of their volumes? If you have to look up the formulae, you won’t be able to solve such a problem with the clock ticking.
3. Solve puzzles – these often require you to ‘solve' a problem, rather than use brute force aka technology. Books by YI Perelman, George Summers, and Shakuntala Devi are a good way to challenge your mind – at any age.

Quick thinking is a lot about heuristics and reliable shortcuts. The more you practice, the better you get at it.

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