Putting down the calculator
Students have become, with ever increasing enthusiasm, all too eager to reach for the calculator when faced with even arithmetical challenges. This trend is growing amongst all students, whether they possess a great natural talent for mathematics or if they find it a great struggle. Teachers have become complicit in this corruption and sometimes even encourage it.
So gross has this become that I have witnessed students regularly use this computer crutch for basic multiplication, simplifying fractions, and even two-digit addition and subtraction. In these more extreme cases the self-destructive nature of the overuse of the calculator becomes so obvious it is counterintuitive. The student could clearly perform such basic arithmetic much faster in their head without wasting time typing it into a calculator.
Many students, and indeed teachers, will say that for some this basic arithmetic is too difficult and slow, but it is only so difficult and slow for them because they do not practice it. One wonders if those subscribed to this philosophy will not teach their children how to tie their laces, and just reason that it is easier for them to only wear slip-on shoes.
The increased efficiency gained by a student through practicing their arithmetic will carry through with them to all levels of their learning. Indeed, with practice students can perform arithmetic very quickly, even multi-step interconnected problems. But it is not the simple matter of efficiency that the most serious problems of calculator overuse are to be found, even if it is the most blatantly perverse.
There are much wider implications of outsourcing one’s training to a machine. Consider that the skills one learns in arithmetic are not simply useful things within themselves; they are used across other areas of mathematics, most clearly in algebra. The set of students for whom algebraic manipulation is a great struggle is completely enclosed within the set of students who regularly use calculators for basic arithmetic. If you are too lazy to walk do not be surprised when you cannot run.
It is critical for students to put aside the calculator and toil for a solid foundation on which to build their understanding of mathematics and more. Indeed, upon these foundations they will build more than just their mathematical understanding, for the mind, just as any other component of any living being, can only attain its potential through persistent and vigorous activity. It is well established knowledge and common sense that one’s capacity for concentration, memory, and strategic thinking is improved through mental arithmetic. This, however, is still not the greatest loss one suffers from calculator overuse.
In the act of passing off the heavy lifting to their mechanical slave, students are estranging themselves from a core component of the very mathematics they are supposed to be studying. If one is to truly comprehend any area of mathematics, they must intimately involve themselves with all its elements.
Recent advances in calculator technology have exacerbated this alienation of students with mathematics who now use calculators for basic algebra, calculus, matrices, complex numbers, and the list goes on and on. I have witnessed supposedly high attaining students who do not actually comprehend basic algebraic concepts but still solve related problems by plugging what they see into their calculators. In doing so the student has rendered themselves a machine, just another step in an easily automated process. This leaves the student’s relationship with mathematics void of any virtue.
When we put aside the modern world’s insatiable desire for production and economic growth and recognise that a righteous study of mathematics is the pursuit of beauty,his development takes on a particularly sombre tone.
Nicholas Parkin is a mathematics and physics tutor.
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