LearningArithmeticinthe21stCenturyNickAberle
Given the choice, I would recommend option number two: after students have mastered arithmetic skills, allow the use of hand-held calculators. I feel as though it is unwise to entirely disallow calculators in the classroom, as they are an extremely powerful tool utilized in higher education and beyond the academics. Calculators prove to be invaluable for complex operations where computing results manually would require a prohibitive amount of time to complete.
This being said, dependence on calculators can easily lead to a lack of fundamental understanding of mathematics. If they are treated as black boxes that solve problems, then little cognition is required on the part of the user. This is demonstrated by an example given in the paper "Impacts of Using Calculators in Learning Mathematics" [1]. A group of students were asked if they could graph the function y = sin
. All of the students answered yes, but when asked to discuss the properties function in detail, none could. While the graphing task could be completed, the students lacked conceptual understanding and comprehension of the underlying concepts behind the function.
It is excellent that a graphing calculator can give us instant visual feedback of a function; it is terribly inefficient to have to manually plot out a function every time we want to see it visually represented. This is why when calculators are used wisely, they are great tools for education. These tools lose some of their appeal when they allow students to take shortcuts that circumvent understanding. This is why in my personal experience, I have felt that a solid foundation in arithmetic should precede the use of computational devices. I have always been a fairly good mathematics student and I don't remember using calculator assistance to do my math homework until at least the fifth grade, long after learning things like multiplication tables and long division.
This debate also brings up the topic of artificial intelligence (AI) versus intelligence augmentation (IA). Having the calculator perform all the work without the user comprehending the underlying principles of the operation being performed places the calculator in the position of an artificial intelligence entity. Without a knowledgeable operator, the power of a calculator is extremely hindered. Likewise, without a calculator, an intelligent student is limited in the efficiency of his or her calculations. This is why in the proper hands, calculators can lead to beneficial intelligence augmentation. The power of both the calculator and the cognition of the student are increased by using both together. Victor Guskov, a teacher of mathematics and a Ph.D. in the study of Pedagogical Sciences makes the analogy of a calculator being like a mode of transportation [2]. "For advanced students a calculator is a comfortable vehicle, which helps him to reach their aim more rapidly and more easily, but in case of need they can go out of it and move themselves ... Whereas for bad achieving pupils a calculator is a motored wheel chair for cripples, without which they cannot move."
Author: Nick Aberle
References:
1. Impacts of Using Calculators in Learning Mathematics by Tingyao Zheng
http://www.atcminc.com/mPublications/EP/EPATCM98/ATCMP015/paper.pdf
2. The Hazard of Using Calculators at School by Victor Guskov
http://ezinearticles.com/?The-Hazard-of-Using-Calculators-at-School&id=195066
3. Making Calculator Use Add Up by Lee V. Stiff
