Hiccups on the Number Line

January 19, 2016

Today, I made another observation about genesis of Robert’s errors while adding integers with the help of a pnumber line.

As long as Robert could mentally add or subtract absolute values of the numbers, he didn’t make any mistakes in his calculations.

He correctly answer problems such as -12+(-15), -20+7, 8+(-10)

However, he hesitated and/or kept guessing the answer to such operations as: -19+31, -17+ (-38). The level of difficulties required to mentally subtract 31-19 or add 17+38 compounded with the need to decide on the sign, resulted in confusion.

I believe that such puzzlement cannot be addressed through more practice with the number line alone.  I think, it is time for Robert to grasp the fact  that when the numbers have opposite signs he is subtracting them (well, their absolute values) and when they have the same signs he is adding them (yes, yes, their absolute values).

Still, I am reluctant for practical purpose of teaching Robert mechanics of adding integers to involve the term “absolute value” in this context. This is a phrase which sacrifices simplicity for the sake of mathematical correctness. That creates additional difficulties for someone whose language is still in the early stages of development and every additional word baffles instead of elucidating.

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