One of my favorite moves is “Apollo 13”. I love this movie for so many reasons but especially for the parts where they show the NASA engineers using their “slide rules” to figure out math problems. Of course if you know what a slide rule is then you might be aging yourself but for those young people out there a slide rule was a hand held mechanical calculator. Yes indeed and it worked great just ask the astronauts that landed on the moon. After slide rules our new math tool became the calculator.
As time went on students did less and less arithmetic by hand because calculators were so easy to use to do the problem. However, the result of this trend was students became less skillful at arithmetic using pencil and paper. As a math teacher I have seen it time and time again, “calculator-ites” a condition where a math student can’t remember basic math skills when holding a calculator in their hand. Let me show you three areas where “calculator-ites” has made a student’s math grade “sick” .
For many students and homeschoolers fractions are their worst nightmare. Many students for whatever reason just hate working with fractions. I understand that tasks like reducing and finding the LCD can be tedious and boring. However students must master these procedures to do well in middle and high school math. Many students will take the path of least resistance and convert fractions into decimals (using that handy $15 calculator) and turn fraction problems into decimal problems. What’s wrong with this? Well if a student turns all fraction problems into decimal problems they will never fully master and comprehend fraction procedures. As a student continues these “short cuts” they make their fraction skills weaker and weaker- not good.
Even worse than fractions! Rational expressions are fractions with variables- yummy! Welcome to the world of algebra. This is where “calculator-ites” really starts to make a student math sick. Remember how our student got into the habit of converting all fractions into decimals using their calculator? Well that trick is not going to work too well with rational expressions. Don’t believe me? Try typing “x / y” into your calculator and see what it reads back to you- trust me it won’t be a number. So unlike regular fractions, rational expressions require a student to have a strong understanding of the step by step procedures we use to do fraction operations. You know that old saying “pay me now or pay me later” a student can cheat the fraction world for while with a calculator but eventually “calculator-ites” will catch up with them and their grades.
Will you accept this “estimation” as my answer? Often when fractions are turned into decimals students will have a tendency to start “rounding off” these decimals. Example, take the fraction 13 / 17. If we use our calculator and turn this into a decimal we get .76470588 a pretty long decimal.
What many students will do is “chop off” the decimal so it’s nice and easy to work with in this example the new decimal maybe .764. Once a student takes this little step and rounds off a decimal they have made their final answer an estimation- not exact as a fraction. Even if they know the steps to solve a problem if they changed the fractions to decimals they very likely will make their solution less accurate. On tests and quizzes most math teachers will want exact solutions so if a student gives an approximation they will likely lose points. Hopefully you see this is another example where a calculator can get in the way if were not careful.
Let’s end our discussion with some praise for the calculator. I agree calculators are important and great tools that students need to use and master. Moreover calculators are wonderful teaching aids and absolutely essential in more complex math involving trigonometry, logarithms and graphing. The point of my article is homeschoolers and students can have a calculator, two, three or as many as they like- they just need to make sure they can handle fractions using that calculator between their ears with a pencil and paper.