Calculators: The Ugly

Since many current calculators are now CAS (computer algebra systems) with graphing capabilities, the term calculator can be used interchangeably with math technology.

Calculators: The Good

Here are some reasons why calculators and technology should be used in the classroom.  A teacher can focus on these as teaching points in order to make sure the calculator is being used appropriately as a tool instead of a crutch.

  1. Technology can reinforce math skills (order of operations).
  2. Calculators can help you get answers to the problems in your book.
    Not sure about the answer for problem 16? Maybe a calculator can
  3. Technology can save us a lot of time: They allow us to focus on the
    steps for solving a problem without having to worry about a lot of the
    little details.
  4. Graphing calculators can graph most functions quicker and better than
    we can.
  5. Technology is useful in testing conjectures.
  6. Technology forces students to learn a new, practical set of skills and
    concepts which are important issues in jobs relying on math.
  7. Calculators are a necessary part of the sciences. Physics and Chemistry
    have many problems that are too difficult or too time consuming to do
    by hand. Any person studying in a science needs to know how to use
    a calculator properly.
  8. Technology lets us examine more complicated and/or realistic prob-
    lems: For example, most equations and integrals that arise in ”real”
    world applications can’t be solved. Now realistic problems can be stud-
    ied because technology can help simplify the difficult parts.
  9. Using technology can make math more interesting to students which will make them more likely to take more math classes.

Calculators: The Bad

Here are some reasons why calculators and technology can be harmful to a student's mathematical maturity. By being aware of the pitfalls, a  teacher can make sure the calculator is being used appropriately as a tool instead of a crutch.

  1. All technology uses a finite number of numbers to represent an infinite number of
    numbers. This means they are all subject to various problems such as overflow and underflow.
  2. Some calculations/graphs can’t be performed on a calculator.
  3. Some calculations are wrong on purpose.
  4. Graphing calculators have bugs like software.
  5. Calculators are great for checking conjectures but can’t prove many of them.
  6. The repetoire of problem solving approaches declines because students go to the
    calculator first. It becomes a crutch. [Tingyao Zheng]
  7. The efficiency of getting an answer from a calculator may cover a lack of conceptual
    understanding of a subject matter. [Tingyao Zheng]
  8. It’s difficult to debug the mistakes a student makes when a calculator is used.
    [Tingyao Zheng]
  9. Technology may furnish very different meanings and functions to the notations used
    in conventional mathematics. [Tingyao Zheng]


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