WHY CAN'T I USE A CALCULATOR



WHY CAN'T I USE A CALCULATOR?

Modern graphing calculators can perform a lot of basic mathematics. Students often wonder why they are often not allowed on exams and quizzes. There are several reasons.

Mathematical Reasoning One of the goals of any math class is to teach mathematical reasoning. That is the ability to think a problem through and develop a step-by-step solution, with each step justified. Using a calculator to do the hard part circumvents this process. Note that even if you never use the specific skills that you learn in your math classes, the process of logically thinking through and solving problems is valuable in many areas of life.

Basic Knowledge Some mathematical skills are basic enough that you should be able to do them in your head faster than you can do them on a calculator. For multiplication and addition of one-digit numbers, this should be true for everyone. For calculus students, this should be true for taking derivatives of basic functions.

Input mistakes It is easy to hit a wrong key when putting a problem into a calculator. If you do, you will usually get an answer which is clearly absurd--if you understand the underlying mathematics. Unfortunately, students who are dependant on their calculators will often submit such answers without thinking whether they make sense. Thus even when we intend to typically use a calculator to solve a type of problem, we will see how to solve it without one first. That way, we will get a sense of what answers are reasonable. Generally speaking, you should understand what your calculator is doing when you use it.

Interpretation mistakes Even when the problem is input correctly, a calculator can sometimes give misleading or incorrect results. Students who do not understand the mathematics cannot correct for these problems. For example, the calculator will sometimes show an asymptote as part of a function. Also, rounding error will sometimes show an answer that should be zero as a small nonzero number, or vise versa.

There are certainly times when using a calculator is appropriate. These include tedious and unenlightening tasks such as computing the decimal approximation of a number and graphing many types of functions.

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