Technology is a wonderful tool in today's schools. It opens up a whole new world of investigation and exploration. It gives industrious teachers multiple avenues for getting the lesson across. It connects classrooms with the world of international resources. Used properly, technology enhances learning and reinforces knowledge. Used improperly, that same technology becomes a two-edged sword that weakens the cognitive process and fosters push-button addicted students.
Graphing calculators are wonderful for comparing various parameters of graphs. Scientific calculators are super for providing the values of trigonometric functions without having to look the value up in a table. Even basic calculators are acceptable to save the drudgery of routine calculations if the basic math problem-solving skills are in place . However, I would venture that for many students, the trusty old-technology calculator has become a crutch rather than a tool.
In teaching a range of mathematics from algebra and consumer math to pre-calculus and math team, I have noticed a disturbing trend among high school students. For any and all math calculations, they immediately whip out the hand-held wonder of the late twentieth century and allow the microchip do the thinking.
I have seen students so conditioned to the calculator that they have to use it to add simple equations such as 3 + 2 or 6 x 4. Their drawing of the calculator is almost a built-in, automatic reflex. As soon as a math problem appears, their hand drops to the box and the punch it in. And Lord help us if they are asked to add or subtract negative numbers! Even then, they often punch the keys in the wrong order and get a wrong answer. Also, knowledge of fraction operations has been made obsolete with the push of a key. No common denominators. No reducing to lowest terms. Let the box do your thinking! These students have no clue as to why the final number shows up in the display window. They take it at face value and use it without ever questioning its legitimacy. How will they ever know if they are being paid correctly on the job?
To combat this frustrating epidemic, I have tried several approaches. One way, of course, is to simply ban all calculators from the classroom. However, this extreme measure would also prevent us from using the calculators when they would be instructive for exploration activities. A modification of this approach is to keep a classroom set of calculators that are given out only when the activity calls for them, and then lock them away again. That becomes a logistic nightmare of accounting for all of the calculators and checking them in and out, wasting instruction time with material handling chores. Ideally, students would have their own calculator and only use them when allowed.
Other approaches were aimed at reducing students' growing dependence on calculators.
Pulling out the "number line" handouts, I step students through the process of mapping addition and subtraction using arrows on the number line. Addition is a right arrow; subtraction is a left arrow. The resulting positive or negative sign of the answer than becomes obvious.
Believe it or not, I also give these students a multiplication table (the old standard 12 by 12) and make them memorize it a column at a time. It is hard to believe that high school students would need such help, but they do! If they just memorized those answers, it would save having to use the calculator for simple multiplication problems, like those that occur in using the distributive property.
Manipulatives are also useful in helping student visualize basic math operations. There are many creative uses of hands-on objects to help with math, even on the secondary level. The National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html offers many such suggestions, and also be sure to check out http://math.about.com
The problem of student reliance on calculators has been around since calculators became popular in the 1970s. Educators are often divided over the appropriate use of these marvelous devices. In May 1999, The National Council of Teachers of Mathematics issued a Dialogue publication covering this issue. Teacher Kim Makey argued that calculators were being used as a substitute for thinking and were "detrimental to the teaching of mathematics." As far as using calculators in elementary grades, Dr. Frank Wang, president of Saxon Publishers, makes a case for keeping these devices away until the students' basic math thinking skills are developed. These professionals recognized the harm being done to the cognitive power of students by allowing them to take the easy way out. For the entire discourse, pro and con, of the use of calculators, visit www.nctm.org/dialogues/1999-05.pdf
"To calculate or not to calculate" is not the question. The question is to whether to use the brain or a poor man-made substitute.