In several important senses, our children’s informed use of calculators has increased their intelligence. First, the calculators have removed virtually all of the computational errors they once would have been likely to have made in their work. Just in terms of the answers they can produce, therefore, what was once a common source of error has been removed. Second, the use of calculators changes the way they think about mathematics—and for the better. In the past, they would have had to devote substantial mental resources to the adequate implementation of computational formulas. Much of the time they would have spent doing mathematics would therefore have been spent in fairly mindless computations. Today those computations—done by calculator—take only a fraction of a second. The mental resources they once would have placed into computation can now be spent more productively on important mathematical operations—figuring out what the problem is, visualizing how to represent the problem, formulating a strategy for solving the problem, and programming or performing the operations that will enable the calculator to compute answers. Third, the very act of using the calculator forces them to learning programming skills, which are important for developing computer-based skills as well as for developing the kind of logical thinking one needs to succeed in disciplines including but not limited to mathematics.
With computers, typing mistakes can be corrected with the push of a button. Whole passages can be deleted, transformed, or moved from one place in a document to another in a fraction of the time it once took. My own productivity has increased many times over as a result of my being able to use a computer-based word-processing program to do my writing, including the writing of this article. With word processors, students and other people can devote more time to thinking about the quality of their writing and less to the low-level mechanics of getting the writing...
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