A calculator is the sort of thing that creates a massive change in the way that people study and approach a certain topic. In fact, the calculator has changed the way we teach, learn, and approach mathematics so much so that, after the fact, it is easy to forget how radically different things used to be. If we want to really understand the enormous impact that the calculator has had on math as a subject in school, we have to think about the way that faculty members had to train their students way before the advent of the affordable pocket calculator. Before we do that, though, let us think about the way we teach math today, in general terms.
Early on, we learn the basics of numbers. We do this often through pictorial representations of different amounts of objects, and also simple word problems. For example: If I have one peanut butter and jelly sandwich, and you have two peanut butter and jelly sandwiches, how many peanut butter and jelly sandwiches do we have together? In this was we become comfortable with the ideas of concrete object being associated with, and represented by, numbers, and we also at the same time are able to take the first steps away from the more discrete and tangible world around us to the frequently abstract world of math and numbers.
Afterwards, we spend more time on simple operations which are the cornerstones of this subject. We learn how to add and subtract, then how to multiple and divide. A lot of the initial work in these areas is done with small values and it involves a lot of memorization until the larger concepts become more familiar and automatic. Not long after that, we head to the advanced concepts like trigonometry and calculus, and we basically can t go very far in anything like that without the help of a calculator to do the heavy lifting. This creates a situation where the student stops learning and practicing the fundamental skills of math, instead choosing to rely on a tool to take care of those details for him.
Before calculators, however, students had to know those fundamental skills perfectly, and be able to perform them on demand. The effect was that, although it may have been a little more challenging to enter into the advanced higher levels of math, most people were a lot more comfortable with manipulating numbers by hand, or even in their heads. This creates a much greater level of comfort with the subject, and avoids the classic situation seen so often today where people working at stores are unable to calculate sales tax, or other relatively simple operations, without a functioning computer or calculator.
The calculator is certainly a useful tool, but any tool has its place. It is vitally important that we not forget how to do math on our own, without any electronic assistance, or else we will have too many people who, once they graduate from high school or college, are unable to perform even basic operations in everyday life. This is one situation where advancements in technology can actually make some of us less able to perform tasks because we fail to force ourselves to maintain the necessary skills.
Diana Washington writes about teaching, preparing for standardized tests, and LSAT Prep, a significant concern for thousands of students hoping to go to law school. She is a staff writer for the Test Prep Blog Testing Is Easy. http://www.acethelsat.com/