Educators are fascinated with technology, particularly calculators. Randall Charles, in the May/June 1999 issue of Math Education Dialogues published by the National Council of Teachers of Mathematics (page 11), is sure that not using calculators in the elementary grades “is almost certain to lead to the development of habits that are counter productive to the development of number sense, problem solving and positive dispositions.” In the same publication, Anthony Ralston suggested abolishing pencil-and-paper arithmetic i,plying that American students will continue to fare poorly in international comparisons until we do.
But technology often looks like magic. For example, a popular software program called Geometer's Sketchpad claims that you can know a square is really a square if you drag a corner with the mouse, and while expanding and contracting it maintains the shape of a square. Then students are presented with two apparent squares. When you drag on a corner of the first square it indeed only expands or contracts. When you drag on a vertex of the second square, it transforms into any number of other quadrilaterals of varying shapes with varying lengths of sides. The second square is obviously not a “real” square. However, the essential difference between the two original apparent squares does not reside in the properties of squares but in software code. The computer code (written by some programmer) makes the first square expand and contract. Different computer code makes the second square wildly transform itself. From the student's point of view it was all magical. Magical and mystical mathematic processes do not promote solid math reasoning ability.
A few years ago I challenged the National Council of Teachers of Mathematics (NCTM) on two occasions six months apart to provide me with a list of the research studies they claimed supported their recommendation on page 78 of the Principles and Standards published in 2000 that even the youngest children should learn to use calculators. Their publications and press releases often asserted that calculators promote mathematics reasoning among the youngest students. NCTM was unable to provide the list on either occasion. I conducted my own diligent search. I found that the most that could be concluded from the research was that calculators could not be positively shown to promote the acquisition of mathematical reasoning skills in our youngest students.
Funny thing—generations of students the world over managed to acquire mathematic reasoning skills in the hundreds of years before calculators and other fascinating technologies were ever invented. Technology is not necessary. It might be nice but any specific technological tool needs to be strictly evaluated and well chosen by elementary teachers skilled in the teaching of mathematics.