Notes on Embedding – Counting Numbers

I’ve seen calculators that were sold primarily into elementary schools and which had features that allowed them to claim that they were especially suited for use in elementary schools.   What do you think those special features might have been?  (I’m not here addressing whether or not calculators should be used in elementary schools or for what.  I’m asking what you think would be so special about elementary school use that it warrants a special version of a calculator.)

There is a version I’ve seen, and then there is a version I’ve heard of.  The one I’ve seen differs in how division is done.  Instead of 7 / 5 = 1.4, it shows 7 / 5 = 1 R 2.  (more precisely, it has a mode that switches between two different ways of doing division, remainder being the one touted for elementary school use.)  The one that I’ve heard of is one that is specialized for money use, so that answers are always shown in exactly two decimal places, and a “$” is shown in front.  So on these, 5 + 2 = $7.00, and 5 + .5 = $5.50, instead of the more common 7 and 5.5 results.

What does this have to do with the topic of embedding, which I broached in an earlier post?  Well, you might notice that nobody has thought it useful to market a calculator that only handles counting numbers.  I don’t know of any electronic calculators on the market that have no decimal point key.  I don’t know of any electronic calculator on the market that shows an error indication if you subtract a larger number from a smaller number.  It appears that there is a minimal set of functionality that kind of comes for free with the chip when you design a new model calculator, and that nobody thinks is worth stripping out or hiding from those tiny fingers.

The counting numbers exist inside of a wider system of numbers that includes negative numbers and numbers with digits to the right of the decimal point.  The negative numbers and the decimal numbers are essentially harmless when it comes to using the calculator for problems involving counting numbers.  This may seem obvious, and in a way it is.  The counting numbers are embedded inside of the positive and negative “decimal point numbers”.  When I add or multiply counting numbers, I don’t have to know or care about any other kinds of numbers.  Those other kinds of numbers are irrelevant at that moment.  Conversely, my calculator doesn’t need to know that I’m only interested in counting numbers – the calculator does exactly what it always does and spits out a sum or a product, and these (from the calculator’s perspective) happen to be another counting number.

And yet, if you ever get to subtracting a larger number from a smaller number, like 3 – 5, the calculator is ready even if the student is not.

Note 1: “Counting number” is somewhat of an imprecise term.  But sometimes, imprecise terms are convenient.  Counting numbers are the numbers 1, 2, 3, 4, 5, etc but often 0 is included as well.
Note 2: In a prior post, I looked at calculators with a fraction key.  These I’ve seen used in secondary schools, but not in elementary schools.
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