Mathematics Topics


Calculators

A few parents objected, and continue to object, to the use of scientific and graphic calculators in my mathematics classroom. Their objections generally are based on the notion that students' mathematical abilities are weakened by their dependence on a tool that may not always be accessible to them. I had the same concerns. I was convinced to give it a try when I saw a listing of objections to new tools voiced in educational journals over the past two centuries. (I will try to get that list and share it at this site.) The objectionable tool listed prior to calculators concerned the introduction of ball point pens (I think that was in the 1950's.) At any rate, I gave it a try, and found that my students' abilities were enhanced rather than weakened!

There are at least five reasons why I think this occurred. First, calculators give students confidence. Some of my students don't even use their calculators, but they have them on their desks in case they want to test their answers. Second, calculators are faster. Students are encouraged to try looking at a problem more than one way because they don't have to concern themselves with long and tedious written work. Third, students are encouraged to try more challenging work, the types of problems involving mathematics which are not only more related to real-world problems they will later encounter but are also more fun. It's no wonder that mathematics has gained a terrible reputation over the years when what we required students to do were long and boring and repetitive tasks. Watch a little child sometime, who is first learning to count, or sort, or recognize shapes. They are EXCITED about mathematics! Somewhere down the line, though, many of them lose this enthusiasm Fourth, students NEED the calculators to accomplish the tasks now required of them in a rapidly changing world. They cannot be competitive in a world dominated by technological tools if they are limited to outdated methods! My students are not as smart as I was at their age. They can't afford to be. They are actually SMARTER! Can they do everything as well as I did? No. Some of the things I did, like calculating the square root of a number using pencil, paper, and divisibility, are no longer necessary, and would be a waste of their precious time! Fifth, and finally, computation skills have NOT been eliminated from instruction. My students are constantly encouraged to mentally compute answers, using mental calculation, estimation, and other shortcuts, the type methods we adults have learned to use over the years as the result of our experience.

In regard to the criticism leveled by some that students must be prepared for situations in which calculators are unavailable, I must confess that this appears to be a strong argument on the surface. My response, in regards to mathematics education, is that it's a matter of priorities regarding time allotted and expected results. If I may use an analogy, it is possible that I may find myself sometime stuck out in the wilderness with no matches with which to start a fire. Yet, the school system has not trained me to light a fire using two sticks. Should they have? I doubt it anyone would consider this to be a wise investment of the limited time for instruction. It is an unlikely, though possible, situation. It would be a wiser investment of time, in my opinion, to train me to be a problem solver that is to say, either find myself some matches or find a way to survive without fire. In regard to calculator unavailability, there are all sorts of estimation strategies which can be taught to allow a person to make do until a calculator is available. To me, this is a far wiser use of time at the secondary level. It is not that mathematics educators do not teach computation skills. It is that we no longer spend ninety percent of our time on this limited aspect of mathematics. There are far more important skills to be conveyed.


Key Topics


Introduction
Calculator Use
Cooperative Learning
Student Progression
Assessment Practices
Higher Standards

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